WRSWorld Research StateContribute
WORLD RESEARCH STATE

Significance in context

Published grades for specific contributions, within their fields.

C · B · A · S support optional − / + placements. SS · SSS are available for evidence-bound nomination and assessment; none is assigned in this edition. Z · U are horizon nominations only. A grade is separate from scientific correctness.

A · Mathematical methods for reliable digital communication

Hamming: systematic error-correcting codes

Redundant check bits could locate and correct specified transmission errors through an explicit code construction.

S · Theoretical physics

Einstein: special relativity

Developed a relativistic account of time, simultaneity and electrodynamics from the relativity principle and invariant light propagation, deriving transformations between inertial frames.

S · Logic

Gödel: incompleteness

Establishes limits to formal provability in sufficiently strong, effectively axiomatized systems of arithmetic.

S · Vaccination

Jenner: evidence for protection against smallpox

Collected cases and inoculation observations suggesting that cowpox exposure could protect against smallpox, helping establish vaccination as a reproducible research approach.

A · Molecular biology

Modified RNA and innate immune recognition

Reported that incorporating selected modified nucleosides reduced RNA-triggered Toll-like-receptor activity and dendritic-cell activation in the tested cellular systems.

A · Anesthesia

Ether anesthesia: surgery without the same experience of pain

Bigelow’s report described surgical operations performed after inhalation of ether. It supplied published clinical evidence that anesthesia could make major procedures possible without the usual conscious experience of surgical pain.

A · Medical microbiology

Koch: identifying the bacterial cause of tuberculosis

Koch identified and investigated the bacillus responsible for tuberculosis, connecting a major disease to a specific microbial cause. The work supplied a basis for subsequent diagnosis, prevention and treatment research.

A · Public-health treatment research

Oral maintenance therapy in cholera

A controlled clinical study used an oral glucose–electrolyte solution for cholera maintenance therapy and reported a reduced need for intravenous replacement fluids.

S · Computer science

Codd: the relational model of data

Organized data through n-ary relations, separated users and programs from internal storage representation, and discussed relational operations, normal form, redundancy and consistency.

A · Operating systems

UNIX: a reusable operating-system design

Ritchie and Thompson described a multi-user system combining a hierarchical file system, common input/output conventions, processes and a programmable shell.

A · Web infrastructure

The World Wide Web proposal

Berners-Lee proposed a linked information system to make distributed research information easier to connect and navigate.

S · Numerical computation

Cooley and Tukey: fast discrete Fourier computation

Reorganized discrete Fourier computation through factorization of the transform length, reducing operation counts for the factorizable lengths treated and describing machine implementation.

A · Cosmology

Penzias and Wilson: an isotropic microwave excess

Measured an unexplained, nearly isotropic microwave antenna-temperature excess after estimating atmospheric, instrumental and ground contributions; the letter connected it to a possible cosmological explanation in a companion paper.

S · Number theory

Gauss: Disquisitiones Arithmeticae

Organized higher arithmetic around congruences, residues and quadratic forms, with new investigations connecting arithmetic and the division of the circle.

S · Differential geometry

Riemann: manifolds, measurement and curvature

Developed a way to discuss spaces of arbitrary dimension, local measurement and curvature, separating geometrical hypotheses from the question of which geometry describes physical space.

A · Analytic number theory

Hardy and Ramanujan: the growth of integer partitions

Used complex analysis and modular transformations to derive precise asymptotic estimates for the number of partitions of an integer, developing a route that became part of the circle method.

A · Cosmology

Hubble: the distance–radial velocity relation

Using 24 extragalactic objects with distance estimates, analyzed individually and in nine groups, reports an approximately linear distance–radial velocity relation in the historical sample.

S · Analysis

Newton: the 1666 tract on fluxions

Uses relations between quantities and their rates of change to address tangents and quadrature, including a method for deriving rate relations from variable relations.

A · Thermodynamics

Joule: the mechanical equivalent of heat

Compared mechanical work with heat produced by friction in water, mercury and cast iron, establishing an experimental conversion relationship.

A · Genomics

T2T Consortium: the CHM13 genome assembly

Published the 3.055-billion-base T2T-CHM13 human genome assembly, resolving previously unfinished regions with gapless assemblies for every chromosome except Y.

A · Algorithms and graph theory

Dijkstra: the shortest-path algorithm

Gave a method for finding a shortest path in a graph with positive edge lengths; the original note also treats construction of a minimum-total-length tree.

S · Game theory

Nash: equilibrium in finite games

Established existence of a mixed-strategy equilibrium for every finite game by applying a fixed-point theorem to the correspondence of best replies.

S · Mathematical logic

Hilbert’s tenth problem: the negative solution

Matiyasevich supplied a Diophantine representation of exponential growth, completing the prior Davis–Putnam–Robinson route from enumerable predicates to polynomial equations and the impossibility of a general integer-solvability algorithm.

A · Complexity theory

Levin: universal search problems

Defined efficiently checkable witness-search problems and reductions between them, identified universal examples and stated an optimal-search construction in the specified computation model.

A · Social choice

Arrow: the social-choice impossibility theorem

Showed an incompatibility between unrestricted preference orderings over at least three alternatives and the stated social-ordering, positive-association, independence, non-imposition and non-dictatorship requirements.

A · Monte Carlo methods

Hastings: general proposal-based Markov-chain sampling

Generalized the Metropolis construction through proposal probabilities and acceptance ratios chosen to preserve a target distribution, while treating dependence and estimation error in Markov-chain samples.

A · Automated reasoning

McCune and EQP: Robbins algebras are Boolean

EQP found a proof in 1996 that every Robbins algebra is Boolean, completing a longstanding algebraic problem after earlier human and automated work on sufficient conditions.

A · Machine learning

Generative adversarial networks

Proposed learning a generator through a minimax game against a discriminator, with an idealized distribution-matching optimum and an alternating gradient-based implementation.

A · Machine learning

Residual networks for deep image recognition

Reformulated stacked layers to learn residual functions around shortcut connections, making much deeper image-recognition networks easier to optimize in the reported experiments.

A · Machine learning

Long short-term memory

Introduced recurrent memory cells with controlled access to constant error flow, addressing learning over long temporal gaps and demonstrating the method on constructed sequence tasks.

A · Machine learning

Support-vector networks for nonseparable data

Extended the support-vector approach beyond perfectly separable training data, using linear decision surfaces in transformed feature spaces and evaluating classification on character-recognition tasks.

S · Set theory

Cohen: forcing and the independence of the continuum hypothesis

Developed forcing to construct models in which the continuum hypothesis fails while choice holds. Together with Gödel’s consistency direction, this establishes independence from the usual set-theoretic axioms, conditional on their consistency.

S · Nuclear astrophysics

B²FH: stellar nucleosynthesis and the origin of the elements

Connected stellar evolution, nuclear reaction mechanisms and observed element abundances in a detailed synthesis. Its account distinguishes fusion and slow and rapid neutron-capture processes, with capture rates compared against beta decay.

A · Nuclear physics

Chadwick: evidence for the neutron

Interpreted recoil measurements from penetrating beryllium radiation as evidence for a neutral particle with mass close to the proton, testing that account against the high-energy photon alternative.

A · Microbiology and biochemistry

Pasteur: microbial fermentation and oxygen

Connected fermentation and spoilage to specific microbial activity, investigating how oxygen availability changes the relationship between growth and fermentation.

A · Optics and photonics

Maiman: the ruby laser

Demonstrated stimulated optical emission from optically pumped ruby, establishing a working solid-state laser.

B · Antibiotic discovery

Halicin: AI helps find an antibacterial lead

Combined neural-network screening with laboratory experiments to identify antibacterial activity of halicin, including activity in the reported mouse infection models.

B · Functional genomics

Adam: a robot closes a small research loop

Integrated hypothesis generation, experiment selection and automated yeast experiments to investigate gene functions in a defined biological system.

B · Mathematics

AI guides new mathematical intuition

Used learned patterns and attribution to guide human research in knot theory and representation theory, leading to new mathematical relationships and conjectures.

A · Earth science

Wegener: continents can move

Proposed large-scale movement of continents as an explanation for linked geological and geographical observations.

A · Experimental physics

Röntgen: discovering X-rays

Observed penetrating radiation produced around a discharge tube, opening a way to investigate structures hidden from visible light.

A · Radiochemistry

The Curies & Bémont: evidence for radium

Separated a strongly radioactive barium-associated fraction from pitchblende and proposed a new element, radium, using chemical and spectroscopic evidence.

B · Chemistry & materials

FermiNet: learning quantum wavefunctions

Optimized antisymmetric neural-network wavefunctions with variational Monte Carlo to calculate electronic energies for tested atoms and molecules.

A · Program verification

Hoare logic for reasoning about programs

An axiomatic framework made program properties expressible through assertions and rules of inference, supporting systematic reasoning about code.

A · Distributed systems

Byzantine agreement and its fault thresholds

Lamport, Shostak and Pease analyzed agreement when some participants send inconsistent or malicious messages, with different results for oral and authenticated messages.

A · Distributed systems

The FLP limit on asynchronous consensus

Fischer, Lynch and Paterson showed that deterministic consensus can have a nonterminating execution in an asynchronous system even with one possible process failure.

A · Machine-learning datasets

ImageNet: a large visual learning resource

ImageNet organized a large collection of labeled images around a semantic hierarchy, providing a reusable resource for visual recognition research.

A · Computer vision

AlexNet and deep convolutional image recognition

A large convolutional network trained with GPUs demonstrated strong large-scale image classification, using architectural and training choices that made deep learning practical at this scale.

A · Machine learning

The perceptron learning model

Rosenblatt proposed a trainable pattern-recognition model connecting weighted responses, experience and classification.

A · Language modeling

GPT-3 and in-context few-shot language tasks

The GPT-3 paper studied a large autoregressive language model performing many tasks from instructions and examples in its prompt, without task-specific gradient updates.

A · Generative modeling

Denoising diffusion probabilistic models

Ho, Jain and Abbeel developed an effective image-generation approach by learning to reverse a noise-adding process, connecting variational learning with denoising score matching.

B · Autonomous materials synthesis

A-Lab autonomous synthesis, with corrected outcomes

A-Lab combined source-derived recipes, machine learning, active learning and robotics for inorganic synthesis. The corrected article reports 36 compounds realized from 57 targets during a 17-day campaign.

S · Chemical bonding

Lewis electron-pair bonding

Lewis framed chemical bonding using valence electrons and shared electron pairs, providing a practical way to reason about molecular structure.

A · Photosynthetic biochemistry

Tracing the photosynthetic carbon cycle

Bassham, Benson and colleagues traced radioactive carbon through photosynthetic intermediates to explain regeneration of the carbon-dioxide acceptor in a cyclic pathway.

A · Plant physiology

The C4 carbon-fixation pathway in sugarcane

Hatch and Slack traced carbon through four-carbon acids and into sugar precursors, supporting a distinct photosynthetic carbon-fixation pathway in sugarcane.

A · Photovoltaics

A practical silicon junction solar cell

Chapin, Fuller and Pearson developed a silicon junction device that converted sunlight into usable electrical power, helping establish practical photovoltaics.

S · Statistical inference

Neyman–Pearson hypothesis testing

Neyman and Pearson organized statistical tests around error rates and power, deriving most-powerful tests for specified hypothesis comparisons.

S · Statistical inference

Bayes’s essay on inverse probability

Bayes’s posthumous essay developed an inverse-probability calculation, connecting observed outcomes to uncertainty about an unknown chance.

B · Porous materials

MOF-5 and permanently porous framework design

Li, Eddaoudi, O’Keeffe and Yaghi reported a metal–organic framework that remained crystalline after solvent removal, supporting a reusable approach to porous-material design.

A · Inertial-confinement fusion

Fusion target gain above unity at NIF

The NIF collaboration measured fusion output exceeding laser energy delivered to the target in its December 2022 experiment. LLNL reports that machine-learning-assisted simulation supported pre-shot predictions alongside expert design.

S · Metabolism

The citric acid cycle

Krebs and Johnson connected metabolic reactions into a cycle explaining how carbon compounds are oxidized in animal tissues.

S · Algebraic logic

Boole: expressing logical reasoning with algebra

Boole developed an algebraic treatment of logical classes and propositions. It made symbolic calculation a systematic tool for reasoning and belongs among the mathematical foundations on which later digital logic was built.

A · Computer architecture

The EDVAC report: describing a stored-program computer

The circulated EDVAC draft described a computer organized around memory, arithmetic, control and input/output, with instructions represented in memory. It provided an influential account of the stored-program approach.

A · Coding theory

Hamming: correcting errors in digital information

Hamming showed how redundant check bits can make specified transmission or storage errors detectable and correctable. The work supplied constructive tools for reliable digital information, beyond simply stopping when an error is noticed.

A · Programming languages and compilers

FORTRAN: translating scientific formulas into efficient programs

The FORTRAN team built a language and compiler that let scientific programmers express formulas at a higher level while producing efficient machine code. The 1957 system helped make compiled scientific programming practical.

A · Programming languages

Lisp: computing with symbolic expressions and recursive functions

McCarthy described symbolic expressions, recursively defined functions and their realization in the Lisp programming system. Programs could manipulate structured symbols, providing a foundation for symbolic computing and AI research tools.

A · Computer networking

Baran: resilient networks using distributed message blocks

Baran studied networks that route standard message blocks through multiple possible paths using local decisions. The report investigated how distributed connectivity and adaptive routing could preserve communication after damage.

A · Microprocessors

The Intel 4004: a programmable processor on one chip

The Intel and Busicom project realized a programmable four-bit CPU within the MCS-4 chip set. Integrating processor functions on one chip helped make general programmable electronics accessible to smaller systems.

B · Database recovery

ACID: a framework for reliable database transactions

Härder and Reuter organized transaction-oriented recovery around atomicity, consistency, isolation and durability. Their framework made assumptions about failures and recovery explicit and comparable across database implementations.

A · Infection prevention

Semmelweis: hand disinfection and fewer maternal deaths

Semmelweis introduced chlorinated hand disinfection in a maternity clinic and linked the change with a major fall in maternal mortality. The historical intervention helped establish the importance of preventing infection during care.

A · Antiseptic surgery

Lister: preventing infection during surgical treatment

Lister set out an antiseptic approach to surgical practice, connecting the control of contamination with better wound outcomes. It changed the research and practice of preventing postoperative infection.

A · Clinical trial methodology

The MRC trial: testing streptomycin with controlled allocation

The Medical Research Council compared streptomycin plus bed rest with bed rest alone for pulmonary tuberculosis using randomized allocation and concealed assignments. The report made both the treatment comparison and its evaluation method inspectable.

B · Transplantation medicine

A functioning kidney transplant between identical twins

The clinical team reported a successful kidney transplant between identical twins. It demonstrated that a transplanted human kidney could sustain function in a setting that greatly reduced the immunological barrier.

A · Vaccination

The Salk vaccine: a major step in preventing polio

Development, large-scale evaluation and licensing of an inactivated poliovirus vaccine made widespread preventive vaccination possible. The 1955 milestone was followed by other vaccine designs and extensive public-health programmes.

A · Targeted cancer therapy

Imatinib: testing a cancer drug against a defined molecular target

A phase 1 trial of the BCR-ABL inhibitor STI571, later known as imatinib, reported substantial antileukemic activity in chronic-phase CML after interferon treatment had failed. It provided clinical evidence for targeting a specific molecular abnormality.

A · Vaccine clinical research

BNT162b2: a clinical trial of an mRNA vaccine against COVID-19

The randomized BNT162b2 trial provided clinical evidence that an mRNA vaccine could prevent symptomatic COVID-19 under the trial’s conditions. It connected a molecular vaccine platform with a measured disease-prevention outcome.

A · Soil fertility and long-term experiments

Broadbalk: measuring soil fertility and crop yields across generations

Broadbalk established long-running comparisons of manure, mineral fertilizers and untreated plots in wheat. Its continuing measurements and retained samples made long-term questions about soil nutrients and crop production researchable.

A · Crop breeding

Double-cross maize: making hybrid seed production practical

The double-cross approach used crosses between hybrids derived from inbred lines to make hybrid maize seed production more practical. Jones’s work helped translate hybrid-vigour research into a usable seed-production method.

A · Quantitative genetics and breeding methods

QTL mapping: locating genetic factors behind complex traits

Lander and Botstein developed methods for locating factors underlying quantitative traits using genetic linkage maps, including interval mapping and selective genotyping. The framework helped connect measured traits to regions of a genome.

B · Crop protection biotechnology

Bt maize: testing insect-resistant plants in the field

Koziel and colleagues reported field performance of maize engineered to express an insecticidal protein derived from Bacillus thuringiensis. The study linked a molecular construct with protection against a target insect in field trials.

B · Crop stress tolerance

SUB1A: a genetic basis for rice survival during submergence

Xu and colleagues identified a SUB1A allele that improves rice survival during complete submergence and tested its function. The paper also reported transferring the SUB1 region into a widely grown variety using marker-assisted selection.

A · Epidemiology

Snow: investigating cholera through water supply

Compared cholera occurrence with water exposure and water suppliers, using observations across households and outbreaks to investigate a route of transmission and possible prevention.

B · Soil microbiology

Beijerinck: a free-living aerobic nitrogen fixer

Isolated the aerobic nitrogen-fixing microorganism named Azotobacter, adding a distinct route for investigating biological nitrogen acquisition outside a plant-root symbiosis.

S · Atomic theory

Dalton: a chemical atomic theory

Chemical combining proportions acquired a reusable particulate explanatory framework and quantitative programme.

S- · Particle physics

Weinberg: A Model of Leptons

Electroweak unification gained a concrete broken-symmetry lepton model with testable structure.

S- · Mathematical analysis

Cauchy: Cours d’analyse

Core analysis concepts were given a more systematic definition-and-proof framework.

A+ · Statistical learning

Breiman: Random Forests

A robust, reusable tree-ensemble method with internal error analysis became available.

A+ · Distributed computing

Dean and Ghemawat: MapReduce

Developers could express many large data jobs in a compact model while runtime handled distribution and failures.

A · Multimodal machine learning

Radford and colleagues: CLIP

Natural-language prompts could specify many visual categories without task-specific training in the tested benchmarks.

A · Instruction-following language models

Ouyang and colleagues: InstructGPT

A human-feedback pipeline improved evaluated instruction-following preferences over a larger base model.

A · Network security

Dierks and Allen: TLS 1.0

An Internet standards-track secure-transport protocol was concretely specified for independent implementations.

A · Cryptography

Merkle: tree authentication

Large sets of messages or keys could be authenticated with compact root commitment and logarithmic proof data.

A · Computer engineering

Patterson and Séquin: RISC I

A reduced instruction set became a concrete VLSI processor design and performance strategy.

A- · Computer science

Torvalds: Linux kernel 0.01

A publicly available 386 Unix-like kernel seed became available for collaborative development.

A+ · Mathematics and AI

Zadeh: fuzzy sets

Membership could be treated as a degree rather than only present or absent.

A- · Artificial intelligence and medical imaging

Ronneberger, Fischer and Brox: U-Net

A trainable encoder-decoder design produced strong reported biomedical segmentation with scarce annotations.

A- · Statistical learning

Chen and Guestrin: XGBoost

Tree boosting could be trained at larger scale with explicit algorithmic and systems techniques.

S- · Complexity theory

Shamir: IP equals PSPACE

Interactive verification gained an exact complexity-class characterization.

A · Symbolic reasoning and automated deduction

Wang: toward mechanical mathematics

Reported computer procedures for proving large collections of propositional and elementary predicate-calculus theorems and framed a broader programme of machine-assisted formal mathematics.

A+ · Algorithms and data structures

Hoare: Quicksort

Presented the partition-based recursive sorting method now known as Quicksort and analyzed its storage and running-time behavior.

A+ · Astrophysics and cosmology

Saha: ionization in the solar chromosphere

Related thermal ionization to temperature, pressure and ionization potential and used the relation to explain stellar and solar spectral behavior.

A+ · Infectious disease and microbiology

Yersin: bubonic plague in Hong Kong

Described bacilli recovered from plague buboes in Hong Kong, their cultivation and animal-inoculation observations supporting a causal role in bubonic plague.

A · Maternal, reproductive and child health

Chang: fertilization of rabbit ova in vitro

Reported a repeatable procedure for fertilizing rabbit ova in vitro and evidence for normal in-vivo development after transfer of the fertilized ova.

B+ · Programming languages and compilers

Stroustrup: The C++ Programming Language, first edition

Provided the first-edition reference and tutorial for C++, documenting its C-compatible design together with type checking, data abstraction, operator overloading and object-oriented programming facilities.

A · Probabilistic artificial intelligence

Blei, Ng and Jordan: latent Dirichlet allocation

Introduced latent Dirichlet allocation as a generative probabilistic model for collections of discrete data, with documents represented through mixtures of latent topics.

B+ · Human-computer interaction and graphics

Bush: As We May Think and the memex

Described the conceptual memex and associative trails as a way for an individual to store, consult and connect records beyond conventional indexing.

A- · Algorithms and data structures

Pagh and Rodler: cuckoo hashing

Introduced cuckoo hashing, using two hash tables and displacement of existing keys to obtain constant worst-case lookup time with expected constant amortized update time under the paper’s model.

A · Fluids and plasma

Parker: hydromagnetic dynamo models

Developed hydromagnetic models for the regeneration and amplification of magnetic fields in rotating conducting fluids, including wave-like behavior connected to solar magnetic activity.

B+ · Knowledge representation

Berners-Lee, Hendler and Lassila: The Semantic Web

Articulated a Web architecture in which machine-processable meaning, shared ontologies and reasoning rules enable software agents and people to cooperate over linked information.

A+ · Networking and internet

Mockapetris: Domain Names—Concepts and Facilities

Introduced the domain-style namespace, distributed name servers, resolvers, resource records, delegation and caching framework for Internet host, mail and other resource naming.

A · Optics and photonics

Hentschel and colleagues: attosecond metrology

Measured a 650 ± 150 attosecond soft-X-ray pulse and its synchronization with the driving light field, demonstrating access to sub-femtosecond electronic dynamics.

A · Programming languages and compilers

Liskov and Zilles: programming with abstract data types

Presented a language-oriented approach in which user-defined abstractions are specified through their operations and behavior while hiding representation details, enabling extensible high-level programming.

B+ · Software engineering

Dijkstra: Go To Statement Considered Harmful

Argued that unrestricted go-to statements obstruct useful coordinates for reasoning about program progress and advocated structured control constructs that preserve intelligible program structure.

A- · Security and cryptography

Kerckhoffs: La Cryptographie militaire

Systematized requirements for military cryptography, including the principle that a cryptosystem should remain secure even when everything about the system except the key is public knowledge.

S · Relativity and gravitation

Hawking: particle creation by black holes

Showed that quantum effects cause black holes to emit an approximately thermal particle spectrum with a temperature set by surface gravity, linking quantum field theory, gravitation and thermodynamics.

A+ · Multi-agent systems

Shapley: stochastic games

Defined a class of two-player zero-sum stochastic games with state transitions and proved the existence and characterization of values for the discounted finite-state setting treated in the paper.

A · Statistical learning

Quinlan: induction of decision trees

Described the ID3 approach to synthesizing decision trees from examples and examined extensions for noisy or incomplete information and a stated shortcoming of the basic procedure.

A · Statistical learning

Rissanen: modeling by shortest data description

Formulated model selection by minimizing the description length of observed data under a model, jointly addressing discrete model structure and real-valued parameter estimation.

S- · Security and cryptography

Shannon: communication theory of secrecy systems

Developed an information-theoretic framework for secrecy systems, including formal treatment of equivocation and perfect secrecy under the paper’s stated assumptions.

A- · Security and cryptography

Thompson: reflections on trusting trust

Demonstrated how a compiler can be modified to insert a Trojan horse into target programs and reproduce the attack when compiling a clean compiler source, exposing a source-level verification limit.

A+ · Combinatorics and discrete mathematics

Ramsey: on a problem of formal logic

Established finite and infinite homogeneous-set results now known as Ramsey’s theorem while addressing a restricted decision problem in formal logic.

A- · Knowledge representation

Minsky: a framework for representing knowledge

Proposed frames as structured data representations for stereotyped situations, carrying expectations, defaults and procedures for adapting stored knowledge to a current situation.

A- · Networking and internet

Maymounkov and Mazières: Kademlia peer-to-peer lookup

Described a peer-to-peer key-value lookup system organized by an XOR distance metric, with symmetric routing information, parallel asynchronous queries and stated consistency and performance properties.

B · Scientific and high-performance computing

Dongarra: the LINPACK benchmark

Explained the LINPACK benchmark based on solving dense systems of linear equations and set out how the computation and reported performance were organized for comparing high-performance systems.

A+ · Thermodynamics and statistical mechanics

Fermi, Pasta and Ulam: studies of nonlinear problems

Used numerical experiments on a nonlinear oscillator chain to test energy sharing among modes and observed unexpected recurrence rather than the anticipated rapid approach to equipartition.

S · Topology

Poincaré: Analysis Situs

Developed invariants and constructions for manifolds, including homology, Betti numbers and the fundamental group, helping establish algebraic topology as a systematic field.

S- · Geometric group theory

Gromov: hyperbolic groups

Developed hyperbolic groups through Cayley-graph geometry, boundaries and algorithmic consequences.

S · Mathematical logic

Frege: Begriffsschrift

Introduced systematic quantified formal inference in an arithmetic-like concept script.

A- · Knowledge representation

McCarthy: programs with common sense

Proposed the Advice Taker architecture: formal common knowledge and deduction of action-relevant consequences.

S- · Statistical learning

Valiant: a theory of the learnable

Defined resource-bounded learnability protocols and proved learnability for nontrivial propositional classes.

S- · Combinatorics and discrete mathematics

Erdős and Rényi: on random graphs I

Studied fixed-edge labelled random graphs and derived connectivity/isolated-vertex threshold behavior.

S- · Arithmetic and number theory

Maynard: small gaps between primes

Developed a multidimensional sieve proving bounded intervals with arbitrarily many primes for fixed multiplicity.

A- · Epidemiology and public health

Omran: the epidemiologic transition

Proposed staged epidemiologic-transition framework linking disease and mortality changes to social development.

A+ · Databases and information retrieval

Corbett and colleagues: Spanner

Documented a global replicated database whose TrueTime uncertainty bounds support externally consistent transactions and timestamped reads.

A · Evaluation, safety and interpretability

Minsky and Papert: Perceptrons

Provided rigorous analysis of representational limits and capabilities for specified perceptron classes.

B+ · Multi-agent systems

Shoham: agent-oriented programming

Specified a mental-state-based agent programming framework with communication primitives and an implemented interpreter.

A · Programming languages and compilers

Liskov: data abstraction and hierarchy

Distinguished hierarchy roles and articulated that subtype behavior must support use wherever its supertype is expected.

S- · Astrophysics and cosmology

Bethe: energy production in stars

Worked out nuclear reaction cycles, especially the catalytic carbon-nitrogen route, under stellar conditions.

S- · Logic, foundations and set theory

Girard: linear logic

Introduced linear logic with resource-sensitive connectives, modalities and proof rules.

S · Algebra

Scholze: perfectoid spaces

Built perfectoid rings and spaces and a tilting correspondence, yielding almost-purity and stated weight-monodromy cases.

A- · Natural language processing and speech

Elman: finding structure in time

Demonstrated an Elman-style recurrent context network on structured temporal and simple linguistic sequences.

S · Quantum field and particle physics

Fermi: a theory of beta decay

Formulated a contact-interaction beta-decay theory with electron and neutrino creation in nuclear transitions.

S- · Quantum field and particle physics

Witten: topological quantum field theory

Constructed a four-dimensional topological quantum field model relating observables to Donaldson and Floer structures.

S · Arithmetic and number theory

Langlands: letter to André Weil

Formulated conjectural links between automorphic representations and Galois or Weil-group data in the 1967 letter.

S- · Combinatorics and discrete mathematics

Hall: representatives of subsets

Proved the condition for choosing distinct representatives from each set in a finite family.

A+ · Optimization and operations research

Nash: non-cooperative games

The 1951 paper made the finite-game proof more direct and added symmetry and equilibrium-set structure beyond the 1950 existence note.

B+ · Natural language processing and speech

Weaver: Translation memorandum

Proposed computer translation as a research programme using cryptography, statistics, information theory and context.

A+ · Computer vision

Marr: Vision

Synthesized computational, algorithmic and implementation levels in a staged theory of visual representation.

A · Distributed systems

Burrows: the Chubby lock service

Described deployed Chubby locking, leader election, metadata and caching under operational constraints.

A+ · Combinatorics and discrete mathematics

Cayley: a theorem on trees

Extended labelled-tree enumeration with degree-sensitive formulas in the 1889 note.

B · Robotics and autonomy

Walter: An Imitation of Life

Described sensor-circuit tortoises exhibiting exploratory, phototactic and recharging behavior.

A · Combinatorics and discrete mathematics

Alon: Combinatorial Nullstellensatz

Proved a coefficient-based polynomial nonvanishing criterion and applied it to discrete problems.

A+ · Neural and deep learning

Werbos: backpropagation through time

Set out backpropagation through time for dynamic systems, propagating sensitivities over an unfolded temporal computation.

S- · Programming languages and compilers

Floyd: assigning meanings to programs

Associated assertions with flowchart points and gave rules for checking program partial correctness and termination.

A+ · Statistical learning

Breiman: bagging predictors

Introduced bootstrap aggregating of predictors by averaging or voting over bootstrap-trained models.

S- · Probability

Wiener: Differential-Space

Constructed an integration framework on continuous paths underpinning Wiener measure.

S · Probability

Itô: stochastic integral

Defined integration against Brownian motion for random integrands and proved fundamental properties.

A+ · Epidemiology and public health

Hart: the inverse care law

Formulated the inverse care law and linked service availability to need and market exposure.

A+ · Epidemiology and public health

Nightingale: Notes on Hospitals

Synthesized hospital construction and administration recommendations from observational evidence.

A+ · Human-computer interaction and graphics

Sutherland: The Ultimate Display

Outlined head-coupled visual output and force-feedback goals for an ultimate display.

S- · Logic, foundations and set theory

Lurie: Higher Topos Theory

Developed higher-topos and infinity-category machinery with systematic limits, adjunctions, and presentability.

A+ · Evaluation, safety and interpretability

Buolamwini and Gebru: Gender Shades

Built a balanced evaluation set and quantified large subgroup error disparities in three commercial gender classifiers.

A+ · Neural and deep learning

Zaheer and colleagues: Deep Sets

Characterized invariant set-function form under stated conditions and designed pooling-based Deep Sets models.

S- · Networking and Internet

Hartley: transmission of information

Defined information from selectable symbol sequences by a logarithmic count and related its transmission to frequency range and time.

A+ · Topology and geometry

Listing: Vorstudien zur Topologie

Developed an early organized topology vocabulary and spatial examples including complexes and orientation.

B · Foundation language models

Touvron and colleagues: the LLaMA foundation-model family

Developed a family of 7B–65B-parameter foundation language models trained on publicly available datasets and reported competitive language-task performance relative to much larger contemporary models.

B · Small language models and data curation

Gunasekar and colleagues: textbook-quality data and phi-1

Trained the 1.3B-parameter phi-1 code model using selected web data and synthetic textbook-style material, reporting strong Python coding benchmark results for its size and training budget.

B · Mechanistic interpretability

Elhage and colleagues: toy models of feature superposition

Used sparse-feature synthetic data and small ReLU networks to demonstrate regimes in which models encode more features than available dimensions, with interpretable geometric changes as feature sparsity and importance vary.

B · Vision-language models

Bai and colleagues: Qwen-VL vision-language model

Reported the Qwen-VL vision-language model family for image understanding, object localization and text reading, including conversational and higher-resolution variants.

A · Object detection

Girshick: Fast R-CNN object detection

Proposed Fast R-CNN to train and evaluate region-based convolutional object detectors more efficiently through joint multi-task training.

A · Genomics

AlphaGenome: predicting regulatory effects of DNA variants

AlphaGenome predicts multiple types of genomic activity from long DNA sequences, combining broad sequence context with high-resolution outputs. The study reports strong held-out variant-effect prediction and analysis of known regulatory mechanisms.

A · Coding theory and reliable communication

Arıkan: polar codes approach a channel’s symmetric capacity

Arıkan introduced channel polarization and polar codes that achieve the symmetric capacity of binary-input discrete memoryless channels, with encoding and successive cancellation decoding costs of O(N log N) under the stated operation model.

A · Normalization for neural-network training

LayerNorm: normalize each example without batch statistics

Ba, Kiros and Hinton introduced layer normalization, computing activation mean and variance within each example instead of across a mini-batch, with learnable gains and biases and a recurrent-network formulation.

A · Finite positive-time routing

Bellman: improve a route by updating what remains

Bellman applies dynamic-programming cost-to-go equations to positive-time finite routing and gives policy-initialized monotone successive approximations that reach the optimal travel cost after a bounded number of iterations.

A · Randomized asynchronous agreement

Ben-Or: randomized agreement without a common clock

Ben-Or presents randomized binary-agreement protocols for fully asynchronous message-passing systems: crash tolerance with N>2t and a Byzantine construction with N>5t, with probability-one termination under the stated admissible scheduling model.

A · Optimization and operations research

Benders: separating a hard decision from a linear subproblem

Benders partitions a mixed-variable optimization problem into a master problem and a linear subproblem, generating only the dual constraints needed to identify an optimum or detect infeasibility or unboundedness, under explicit solution and compactness assumptions.

B · Quantum search and query complexity

BBHT: how to stop quantum search without knowing the solution count

Boyer, Brassard, Hoyer and Tapp analyze quantum-search success after a specified number of iterations and give a randomized procedure with order sqrt(N/t) expected query cost when the positive number t of marked items is unknown.

A · Computing

Bresenham: drawing straight lines with integer decisions

Bresenham described a compact integer-update algorithm that selects adjacent plotter-grid points to follow a straight line between integer-coordinate endpoints, handling all eight octants without per-step multiplication or division.

A · Failure detection and asynchronous agreement

Chandra and Toueg: unreliable failure detectors for reliable systems

Chandra and Toueg define unreliable failure detectors through completeness and accuracy, construct crash-tolerant consensus algorithms using them, and reduce consensus and atomic broadcast to one another under the stated asynchronous model.

S · Solid-state physics and quantum statistical mechanics

Debye: a vibration spectrum explains the heat capacity of solids

An acoustic elastic-mode spectrum with finite3N cutoff replaces a single frequency and predicts a cubic lowT lattice law, highT classical limit and elastic-property characteristic temperature within one model.

S · Foundations of real analysis

Dedekind: real numbers constructed through rational cuts

Proper rational cuts define real numbers, equivalent rational-endpoint partitions are identified, and the completed order supports a cut-completeness principle linked to bounded monotone convergence.

A · Distributed consensus under timing assumptions

Dwork, Lynch and Stockmeyer: consensus with partial synchrony

Dwork, Lynch and Stockmeyer define partial synchrony and give deterministic consensus constructions and fault-tolerance bounds when timing bounds are unknown or start holding after an unknown stabilization time.

S · Fluid dynamics

Euler: general equations for inviscid fluid motion

Mass continuity and pressure/body-force momentum balance organize three-dimensional fluid motion in spatial velocity/density fields; nonpotential examples establish the broader admissible flow class.

S · Quantum statistical mechanics

Fermi: exclusion-based statistics of an ideal gas

An at-most-one occupation hypothesis is extended to ideal-gas state counting and thermodynamics, yielding a degeneracy distribution and low-temperature pressure/heat-capacity consequences.

A · Physics

Finkelstein: the Schwarzschild surface as a one-way causal boundary

Finkelstein constructs a regular analytic continuation across the Schwarzschild surface and explains its one-way causal character in time-reversed branches, while the paper itself records that this continuation is not the complete Schwarzschild spacetime.

A · Approximate distinct counting

HyperLogLog: counting distinct items with a small sketch

HyperLogLog estimates the number of distinct stream items by combining per-bucket bit-pattern registers through a normalized harmonic mean, reducing variance while keeping a small mergeable state.

S · Time-dependent cosmological solutions

Friedmann: a changing radius in positively curved cosmology

Friedmann shows that the Einstein equations under a positively curved pressureless cosmological ansatz allow a time-dependent curvature radius, and classifies monotone and expanding-contracting possibilities depending on constants.

S · Stable two-sided matching

Gale and Shapley: a match that no pair wants to break

Gale and Shapley construct stable two-sided matchings by deferred acceptance and show applicant-optimality among stable college assignments under strict preferences, acceptable applications and stated quotas.

A · Mathematics

Godunov: use local wave problems to calculate shocks conservatively

Godunov constructs conservative gas-dynamics updates from local discontinuity-resolution problems and proves a linear monotonicity/order barrier, while the paper’s nonlinear limit and stability claims retain explicit convergence and time-step conditions.

A+ · Computer science

Goemans–Williamson: rounding geometry into a graph cut

Goemans and Williamson combine a semidefinite vector relaxation with random hyperplane rounding to obtain an expected approximately 0.87856 approximation for nonnegative weighted MAXCUT, with an epsilon loss for finite-precision optimization.

A · Quantum search and query complexity

Grover: square-root quantum search

Grover gives a quantum algorithm for finding a unique marked item in an unstructured search space using order sqrt(N) oracle iterations, by combining a conditional phase flip with inversion about the average amplitude.

A · Parallel computing and performance models

Gustafson: larger machines can tackle larger workloads

Gustafson argued that parallel computing should also be evaluated with workloads that expand as processor counts grow, deriving scaled speedup and reporting near-linear results for three Sandia applications on a 1,024-processor system.

A · Earthquake frequency statistics

Earthquake frequency: a historical magnitude-scale regularity

Gutenberg and Richter compare earthquake frequencies in California with worldwide counts and fit a log-linear relationship between magnitude bins and event frequency, with explicit regional and extrapolation limits.

A · Unnormalized statistical estimation

NCE: learning a statistical model by contrasting data with noise

Noise-contrastive estimation learns an unnormalized statistical model by distinguishing observed data from samples drawn from a known noise distribution, treating the normalization constant as a learnable parameter.

A · Quantum algorithms and numerical linear algebra

HHL: a quantum state of a linear-system solution

Introduces inverse-eigenvalue quantum-state preparation and selectedobservable estimation for suitable linear systems, connecting numerical tasks to quantum algorithmic complexity.

A · Model theory and higher-order logic

Henkin: complete proof rules for general models of type theory

Henkin proved completeness of a simple type calculus for general models whose function domains satisfy the interpretation closure conditions, and constructed countable models of consistent theories in the stated language.

A · Mathematics

Jiang–Shu WENO: accurate smooth waves and sharp changes

Jiang and Shu develop derivative-based smoothness indicators and efficient finite-difference WENO implementations that recover fifth-order spatial accuracy in regular smooth regions while reducing the contribution of stencils crossing discontinuities.

A · Graph methods for electrical networks

Kirchhoff: solving a network through its cycles and trees

Kirchhoff gives a combinatorial solution of steady linear wire-network currents using independent cycles, resistance products and sums of electromotive forces around the remaining cycles.

S · Electrical network theory

Kirchhoff: currents balance at junctions and around loops

Kirchhoff states and derives steady-circuit junction and loop relations: current balances at a junction, and signed resistance drops around a closed path equal the electromotive forces on that path.

A · Physics

Kitaev: unpaired Majorana modes in quantum wires

Kitaev constructed a one-dimensional superconducting chain with unpaired boundary Majorana modes and related their presence to a bulk parity invariant for gapped quadratic fermion systems.

S · Algorithmic information

Kolmogorov: description length through algorithms

Description length under optimal methods supplies a non-probabilistic account of the information in an individual object, invariant up to an additive constant and generally noncomputable.

A · Weighted bipartite assignment

Kuhn: solve the whole assignment, with a certificate

Kuhn combines bipartite matching and an adequate-budget dual certificate into a finite method for maximum-score one-to-one assignment with positive integer ratings, supplying explicit transfer and budget-improvement routines.

S · Analytical mechanics

Lagrange: an analytical framework for mechanics

A common analytical organization formulates constrained mechanical problems with independent variables and kinetic-energy variations instead of bespoke geometric constructions.

S · Numerical linear algebra

Lanczos: minimized iterations for matrix eigenvalues and operator problems

Lanczos develops progressive polynomial and minimized-iteration procedures for spectral and resolvent problems, including the symmetric three-term orthogonal recurrence and a two-sided nonsymmetric construction, with numerical vibration examples and proposed integral/differential operator extensions.

S · Quantum magnetism

Landau: quantum orbital motion gives free electrons a magnetic response

Landau counts the partly discrete quantum energies of nonrelativistic electrons in a uniform magnetic field and derives a nonzero orbital diamagnetic response, distinct from spin paramagnetism, with an explicit smooth-field approximation and separate conjectures about real materials and transport.

A · Generative modeling and probability transport

Flow Matching: learn a transport field from simple conditional paths

Conditional vector-field regression yields the marginal FM parameter gradient under exchange/integrability assumptions; Gaussian path design includes conditional straight displacement paths and simulation-free CNF training.

S · Algorithmic randomness

Martin-Löf: universal effective tests for random sequences

Martin-Löf constructs universal effective tests and defines infinite random binary sequences by avoidance of effectively specified null tests, connecting finite-string randomness to conditional description complexity.

A · Atmospheric dynamics

Matsuno: a wave framework for the equator

A coherent modal framework retaining latitude-varying rotation resolves the mixed lowest westward branch, the separate Kelvin-like solution and a controlled forced-response example.

A · Computer science

Mattern: vector time that preserves distributed causal order

Mattern formulated vector-valued logical time that captures potential causal order and concurrency, connected possible time vectors with the lattice of consistent cuts, and described distributed debugging applications.

A · Computer science

Merkle’s puzzles: agreeing on a key in public

Merkle describes selecting a shared key over a publicly readable but integrity-protected channel using many deliberately solvable encrypted puzzles, producing a quadratic passive-search work gap in the stated classical model.

A · Computational number theory

Miller: conditional efficient deterministic primality testing

Miller gives deterministic compositeness-witness algorithms and establishes polynomial-bit-length primality testing conditional on the stated Extended Riemann Hypothesis, alongside number-theoretic functional reductions under declared assumptions.

A · Programming languages and type systems

Milner: polymorphic typing with a sound inference algorithm

Let-local polymorphism and constrained non-generic parameter variables are organized into a usable type discipline, a recursive inference algorithm and separate semantic/syntactic soundness theorems for Exp.

A · Computing

PATRICIA: indexing genuine branches instead of every prefix

Morrison described a compact binary-text index that records only genuine branching positions, finds a candidate from selected key bits, verifies it in the text, and enumerates marked occurrences without scanning the entire library.

S · Atomic spectra and element ordering

Moseley: making atomic number experimentally accessible

Moseley measured characteristic X-ray spectra and showed that their frequencies follow an approximately regular relation to element number, providing physical evidence for ordering elements by atomic number rather than atomic weight.

A · Assignment and transportation optimization

Munkres: make optimal assignment a bounded procedure

Munkres gives a constructive starred/primed-zero variant of Kuhn's assignment algorithm, proves finite termination without requiring integer costs and provides an explicit polynomial bound in the paper's line-operation model, then states a transportation generalization.

B · Computer science

Nagle: grouping small TCP writes behind acknowledgments

Nagle proposes letting acknowledgments trigger the sending of buffered TCP data instead of creating a new packet for every small application write, reducing small-packet overhead without a fixed inter-packet timer.

A · Parallel programming

CUDA: cooperating locally, scaling across processors

The 2008 CUDA article explains a GPU programming model in which independently schedulable thread blocks combine local cooperation, shared memory and barriers, allowing a fixed problem decomposition to run across different processor counts.

A · Galactic differential rotation

Oort: how nearby stars reveal a rotating Galaxy

Oort compares nearby stellar radial velocities and proper motions with a first-order differential-rotation model, finding a longitude-dependent velocity pattern supporting Lindblad's rotating Galactic system.

A · Numerical linear algebra

LSQR: stable sparse linear equations and least squares by bidiagonalization

Paige and Saunders present LSQR, using Golub-Kahan bidiagonalization and orthogonal transformations to solve sparse rectangular linear equations and least-squares problems using matrix and transpose actions, with inexpensive norm estimates and data-aware stopping criteria.

A · Numerical linear algebra

MINRES and SYMMLQ: solving sparse symmetric indefinite systems

Paige and Saunders derive the Lanczos-based MINRES residual-minimizing and SYMMLQ LQ-factorization methods for large sparse real symmetric linear systems, avoiding the intermediate factorization failures that can defeat ordinary conjugate gradients on indefinite matrices.

A · Computer science

Paillier: add messages while keeping them encrypted

Composite-residuosity classes provide a factorization trapdoor for probabilistic public-key encryption whose ciphertext multiplication implements plaintext addition modulo n, with explicit computational and decisional security assumptions.

S · Atomic quantum theory

Pauli: an occupation rule explains atomic electron groups

Pauli proposes that no two equivalent atomic electrons can occupy the same complete four-quantum-number state, using strong-field spectral bookkeeping to account for closed electron groups and restricted atomic terms, without deriving a general spin-statistics theorem.

A · Stellar-atmosphere spectroscopy and elemental-abundance inference

Payne: stellar spectra, ionization and the abundance anomaly

The 1925 monograph joined comparable stellar spectra with ionization analysis to estimate atmospheric temperatures and relative abundances, exposing extreme hydrogen/helium estimates while explicitly questioning those values.

A · Topology and real analysis

Peano: a continuous curve that fills an entire square

Peano explicitly constructs a continuous mapping from the closed unit interval onto the whole unit square through ternary digits and parity-controlled complements, showing that continuity alone does not restrict a parametrized curve to an arbitrarily small enclosing area.

A · Computer science

Pedersen: verify shared secret pieces without exposing the secret

Two-generator perfectly hiding commitments combine with polynomial shares so recipients verify consistency non-interactively; secret privacy is information-theoretic while share consistency relies on the dealer not knowing the generator discrete-log relation.

A · Computer science

Perlman: a spanning tree for a bridged network

Perlman gives a distributed protocol that selects a root and forwarding subset of a bridged extended LAN, preserving connectivity while removing forwarding loops after convergence, with explicit aging and reconfiguration delays.

S · Communication nets and concurrent computation

Petri: communication nets, concurrency and conflict

Petri develops communication nets built from discrete locations and local actions, with explicit causality, parallelism and conflict, and presents constructions for asynchronous, extensible computation instead of assuming one global sequence of machine states.

A · Computational number theory

Pollard: finding integer factors with a short collision search

Pollard introduced a low-storage iterative method for finding integer factors through collisions modulo an unknown factor, with a heuristic square-root operation estimate in the factor size under a random-mapping model.

S · Viscous boundary layers and separation

Prandtl: the thin layer that changes the whole flow

Prandtl introduces a thin viscous boundary region coupled to the outer flow, derives reduced equations for small-viscosity incompressible motion, and relates boundary-layer separation to observed wakes and a suction experiment.

A · Relativistic quantum magnetism

Rabi: solving the relativistic electron in a uniform magnetic field

Rabi solves the four-component Dirac electron equations in a homogeneous magnetic field, obtains discrete transverse energy branches with continuous longitudinal momentum, and explains a special lowest-state current condition, without deriving thermodynamic diamagnetism.

A · Computational number theory

Rabin: randomized primality testing with one-sided witness error

Rabin analyzes randomized compositeness-witness sampling: for each fixed composite, independent uniform trials give exponentially decreasing false acceptance, while a witness certifies compositeness; the journal paper includes implementation and reported experiments.

A · Computer science

Rabin: relating trapdoor-function inversion to factorization

Rabin gives a public-key function based on modular quadratic equations and a randomized reduction showing that inversion on a substantial fraction of its invertible unit-domain outputs enables factorization of the modulus.

A · Direct preference learning

DPO: learn response preferences without a separate reward-training loop

Rafailov and colleagues reparameterize a KL-regularized preference-learning objective as a direct policy classification loss, removing the separate learned-reward/PPO optimization stage and reporting results on sentiment, summarization and single-turn dialogue.

A · Instrumental earthquake magnitude

Richter: a local instrumental earthquake magnitude scale

Richter constructs an empirical local earthquake magnitude scale from the logarithm of standardized instrumental amplitudes corrected for epicentral distance, separating event size from intensity at a particular site.

S · Abelian integrals and complex curves

Riemann: periods and theta functions on algebraic surfaces

Cut-system period increments obey bilinear constraints; normalized periods have symmetry and a definite quadratic form compatible with convergent multivariable theta series and their transformations.

S · Complex analysis

Riemann: complex functions on branched surfaces

Complex functions are organized through local conformal behavior, branched multisheeted domains and connectivity, supporting study by domains and boundary/singularity data rather than only expressions.

S · Electroweak gauge theory

Salam: broken-gauge unification of leptonic interactions

A1968 published construction joins weak/electromagnetic leptonic fields with neutral mixing and spontaneous breaking that produces massive modes while preserving a massless electromagnetic mode.

A · Radiative corrections in quantum electrodynamics

Schwinger: a radiative correction to the electron magnetic moment

Schwinger reports a finite radiative correction to the electron spin magnetic moment after expressing electrodynamic interactions in terms of measured mass and charge, and compares it with contemporary atomic measurements.

A · Mathematical semantics of programming languages

Scott: lattice models for computation and self-application

PRG-2 combines information approximation, complete-lattice types, continuity, effective bases and a recursive self-function-space outline to model higher-order computation mathematically.

S · Quantum field theory

Tomonaga: quantum states on spacelike surfaces

A spacelike-surface state functional and local-deformation formalism exposes Lorentz-compatible free/interaction separation under explicit commutation/density conditions.

A · Random-matrix probability and integrable systems

Tracy and Widom: Airy-kernel distributions at a random-matrix spectral edge

Tracy and Widom derive differential equations for Airy-kernel Fredholm determinants and characterize the soft-edge gap distribution on a half-line through a specified Painleve II solution, giving computable distributions for the largest ordered eigenvalues in the declared unitary random-matrix limit.

A · Astronomy

Tully and Fisher: using galaxy line widths to estimate distances

Tully and Fisher developed and calibrated an extragalactic distance method connecting corrected global neutral-hydrogen profile width with intrinsic photographic luminosity or galaxy diameter, and applied it to nearby calibrators and two galaxy clusters.

A · Thermal engineering and power systems

Watt: separating the steam cylinder from the condenser

The inspected specification isolates a hot working vessel from a cold condensation vessel and provides non-condensable-air removal, changing the inherited thermal arrangement.

A · Lossless data compression

LZW: rebuilding a compression dictionary as data arrives

Welch presents a practical adaptive dictionary compressor that sends codes for previously encountered strings while its decoder reconstructs the dictionary, with simple mechanisms suited to high-throughput storage systems.

S · Quantum gauge structure

Weyl: local quantum phase and electromagnetic potential

Local unit-modulus phase freedom is compensated by a potential transformation in covariant differentiation; the specified action connects gauge invariance with electromagnetic current conservation.

A · Electrical measurement and instrumentation

Wheatstone: measuring resistance by restoring a balance

Wheatstone develops practical adjustable-resistance and balance methods for comparing electrical circuit constants, including a differential resistance measurer whose original principle he credits to Christie.

A · Thermal radiation and spectral scaling

Wien: how blackbody spectra shift with temperature

Constrains full temperature-dependent equilibrium spectra through reversible compression/Doppler reasoning, preserving a constant wavelength-temperature coordinate and appropriate spectral-density rescaling.

A · Thermal radiation and historical spectral models

Wien: an exponential thermal spectrum and its limits

Supplies a concrete equilibrium thermal spectral model with explicit uncertain microscopic hypotheses, temperature/peak properties and experimentally testable limits.

B · Normalization for neural-network training

GroupNorm: train visual models with small batches

Wu and He introduced group normalization, computing mean and variance across spatial positions and groups of channels within each example, enabling visual-network normalization without batch statistics.

A · Cosmology

Zeldovich: a Lagrangian approximation for growing cosmic density perturbations

Zeldovich extrapolates a growing-mode Lagrangian displacement from linear pressureless Newtonian cosmology and obtains density through its deformation Jacobian, predicting generic first compression into sheet-like structures while explicitly retaining uncertain nonlinear accuracy and post-compression limits.

A · Engineering

Ziegler and Nichols: practical rules for tuning a controller

Ziegler and Nichols give practical proportional, integral-reset and derivative-pre-act tuning rules based on measured ultimate sensitivity and period or on a process reaction curve, with a declared decay-versus-offset compromise.

A · Information theory and lossless data compression

Ziv and Lempel: individual-sequence variable-rate lossless coding

The exact 1978 joint paper broadens the encoder class to generalized variable-rate lossless coding and supplies a constructive incremental-parsing family with converse/attainment results for the finite-state compressibility of every individual infinite sequence.

A · Efficient neural-network computation

Dao: FlashAttention-2 GPU work partitioning

Reorganized exact-attention work across GPU blocks and warps and reduced non-matrix-multiplication operations to improve accelerator utilization.

A · Sequence-model architectures

Dao and Gu: state-space duality and Mamba-2

Connected structured state-space models and attention variants through semiseparable matrix representations, using this duality to design Mamba-2 computation.

A+ · Reasoning-model post-training

DeepSeek-AI: R1 reasoning post-training and distillation

Studied reasoning reinforcement learning without a supervised cold start in R1-Zero, then combined cold-start examples and staged training in R1 and distilled reasoning outputs to smaller models.

A · Foundation-model training systems and resources

Gemini Team: controllable-thinking multimodal model systems

Developed a multimodal model family combining reasoning-oriented post-training, adjustable thinking computation, long-context inputs and native tool use, with sparse-teacher distillation and resilient distributed training.

B+ · Foundation-model training systems and resources

Google: PaLM 2 multilingual mixed-objective training system

Combined diverse multilingual data and mixed pretraining objectives with compute-aware model/data allocation, reporting a more inference-efficient language-model family and a larger-scale scaling study.

B+ · Foundation-model training systems and resources

Bai et al.: Qwen multilingual and tool-using language-model system

Built and documented the original Qwen pretraining and human-alignment pipeline, including multilingual tokenization, context extension and chat models evaluated on tool use, code interpretation and specialized reasoning.

A · Reasoning supervision and alignment experiments

Lightman et al.: process-supervised reward models and PRM800K

Compared step-level and outcome-only supervision for mathematical reward models, reporting stronger solution selection with process feedback and active-learning gains, and releasing the PRM800K human-label resource.

A · Reasoning supervision and alignment experiments

Guan et al.: policy-reasoning deliberative alignment

Trained reasoning models to internalize explicit safety specifications through specification-referencing synthetic supervision followed by reinforcement learning, reporting better jailbreak resistance and less overrefusal on the evaluated tasks.

A · Optimization and large-model systems

Shazeer and Stern: Adafactor factored optimizer state

Approximated matrix-valued second-moment accumulators from row and column statistics and combined update clipping, decay scheduling and relative-step scaling for low-memory adaptive optimization.

A- · Optimization and large-model systems

Gupta, Koren and Singer: Shampoo tensor preconditioning

Maintained separate matrix preconditioners for tensor dimensions to exploit parameter structure, with an online/convex analysis and empirical neural-network optimization comparisons.

B+ · Optimization and large-model systems

Chen et al.: symbolic optimizer search and Lion

Used evolutionary program search, selection and simplification to discover Lion, a momentum-based sign-update optimizer, and evaluated its transfer from proxy tasks to larger vision and language training.

A · Optimization and large-model systems

Ren et al.: ZeRO-Offload heterogeneous training

Partitioned model training between GPU execution and CPU optimizer state/computation, combining communication-aware placement, a CPU optimizer and delayed updates with ZeRO data parallelism.

A · Audio modeling, latent dynamics and learning feedback

Zeghidour et al.: SoundStream scalable neural audio coding

Jointly trained convolutional audio encoding/decoding with residual vector quantization, reconstruction/adversarial losses and quantizer dropout to support several bitrates within one streamable model.

A · Audio modeling, latent dynamics and learning feedback

Borsos et al.: AudioLM semantic and acoustic token generation

Combined coarse self-supervised semantic tokens with fine neural-codec tokens in hierarchical language modeling, generating prompted speech and piano continuations without transcript-based supervision.

A+ · Audio modeling, latent dynamics and learning feedback

Hafner et al.: robust cross-domain Dreamer control

Combined robustness-oriented model and learning changes to train across diverse observation, action and reward regimes with fixed hyperparameters, including a Minecraft diamond-collection demonstration.

B+ · Audio modeling, latent dynamics and learning feedback

Assran et al.: V-JEPA 2 video prediction and robot planning

Combined self-supervised video representation prediction with action-conditioned post-training on robot trajectories, enabling image-goal planning experiments on robot arms without local task-specific training.

B+ · Vision, robotics, reasoning and inference systems

Carion et al.: SAM 3 promptable concept segmentation

Unified text/exemplar-prompted detection, segmentation and video tracking with decoupled recognition/localization, a scalable data engine and the companion SA-Co evaluation benchmark.

A- · Vision, robotics, reasoning and inference systems

Bardes et al.: V-JEPA video feature prediction

Learned visual representations from video through feature prediction without pixel reconstruction, text labels, negative examples or pretrained image encoders, evaluating frozen backbones on appearance and motion tasks.

B+ · Vision, robotics, reasoning and inference systems

OpenAI: gpt-oss open-weight reasoning and tool-use resource

Released open-weight expert reasoning models with quantized expert weights, variable-effort reasoning, tool-use training and accompanying inference implementations and tokenizers.

A · Vision, robotics, reasoning and inference systems

Siméoni et al.: DINOv3 Gram-anchored dense visual features

Scaled self-supervised image representation learning and introduced Gram anchoring to stabilize dense features during long training, with adaptable model sizes and resolution strategies.

A+ · Vision, robotics, reasoning and inference systems

OpenAI: o1 reinforcement-trained reasoning system

Trained language models with reinforcement learning for extended reasoning, reporting improvements with additional training and inference computation across coding and mathematical evaluations.

A · Optimization and inference scheduling

Yu et al.: Orca iteration-level generative serving

Scheduled autoregressive inference one iteration at a time and selectively batched operations, enabling finished requests to leave and new requests to enter active generation batches.

A · Optimization and inference scheduling

Jordan et al.: Muon momentum-update orthogonalization

Combined momentum with inexpensive approximate Newton–Schulz orthogonalization of matrix-valued hidden-layer updates, with empirical neural-network training evaluations.

B+ · Efficient foundation-model architecture and training

DeepSeek-AI: V4 compressed-attention long-context system

Combined compressed sparse and heavily compressed attention with manifold-constrained residual connections and Muon optimization in an openly released long-context expert-model family.

B+ · Efficient foundation-model architecture and training

NVIDIA: Nemotron 3 Nano hybrid reasoning-training resource

Trained and openly documented a hybrid Mamba-Transformer expert model with granular sparse routing and multi-environment post-training for reasoning and tool-use workloads.

B+ · Efficient foundation-model architecture and training

MiniMax: Lightning-Attention long-context expert system

Scaled a hybrid linear/softmax attention expert-model architecture with optimized parallel execution and communication overlap, releasing text and vision-language models for long-context tasks.

B+ · Efficient foundation-model architecture and training

MiniMax: CISPO and hybrid-attention reasoning training

Combined efficient hybrid-attention reasoning with CISPO reinforcement learning, which clips importance-sampling weights, and trained on reasoning and software-environment tasks.

B+ · Efficient foundation-model architecture and training

Lieber et al.: Jamba hybrid Transformer-Mamba experts

Interleaved attention and selective state-space layers with sparsely activated experts, studying architecture choices for a long-context language model with reduced inference-memory cost.

B+ · Language-model training and open research resources

Apple: efficient device/server foundation-model adaptation

Integrated device and server language models with mixed-bit compression, task adapters and post-training procedures including teacher-committee rejection sampling and mirror-descent-based preference optimization.

A- · Language-model training and open research resources

Falcon LLM Team: web-data language-model training resource

Developed open language-model checkpoints with a web-data curation pipeline and distributed cloud-training tooling, documenting data mixtures, architecture decisions and large-scale training.

B+ · Language-model training and open research resources

Cai et al.: InternLM2 conditional online preference training

Documented a long-context language-model training pipeline and conditional online RLHF designed to handle conflicting preferences and reward hacking, releasing intermediate model stages.

A · Text-guided speech generation and editing

Le et al.: Voicebox flow-matching speech infilling

Trained a non-autoregressive flow-matching model to infill speech from transcript and surrounding audio, enabling multiple synthesis and editing tasks through contextual conditioning.

B+ · Low-precision hybrid language-model training systems

NVIDIA: Nemotron 3 NVFP4 hybrid expert-training system

Implemented low-precision NVFP4 pretraining with latent-expert Mamba/attention hybrids and native multi-token prediction, then consolidated specialist agentic teachers in the Ultra post-training system.

A · Self-supervised visual representation learning

Bao et al.: BEiT masked visual-token prediction

Pretrained vision Transformers by predicting discrete visual tokens for masked image patches, transferring the learned encoder to image classification and segmentation.

A · Unified visual and vision-language pretraining

Wang et al.: BEiT-3 multiway vision-language pretraining

Introduced multiway Transformer blocks and a shared masked-modeling objective across images, text and paired modalities, supporting deep fusion and modality-specific encoding.

B+ · Sparse long-sequence modeling and distributed attention

Ding et al.: LongNet dilated distributed attention

Used dilated attention with exponentially growing receptive fields and sequence-partitioned execution to reduce long-sequence attention computation and communication.

A · Ternary quantization-aware language-model training

Ma et al.: BitNet b1.58 ternary-weight language-model recipe

Extended the binary-weight design with absolute-mean ternary quantization into negative, zero and positive values, paired with an adapted Transformer training recipe and eight-bit activations.

A · Reasoning-model training and inference control

Anthropic: hybrid reasoning budgets and tool-interleaved inference

Combined fast-response and reinforcement-learned extended-thinking modes in a model family with controllable thinking budgets, later extending the system to tool use during thinking and summarized long reasoning traces.

B+ · Serving-aware mixture-of-experts architecture

Elango et al.: LatentMoE compressed routed-expert computation

Projected routed payloads and expert computation into a lower-dimensional latent space while retaining routing decisions in the original representation, trading communication and weight traffic for expert capacity.

A · Data-dependent recurrent attention and GPU training

Yang et al.: hardware-efficient gated linear attention

Derived a chunk-parallel gated linear-attention form that permits data-dependent matrix-memory forgetting while using ordinary tensor-core operations for training.

B+ · Multimodal mixture-of-experts training

ERNIE Team: heterogeneous multimodal expert sharing

Built a heterogeneous expert architecture combining shared and modality-specific parameters, with a documented multimodal training/deployment toolkit and open model family.

B+ · Unified multimodal generation and elastic training

ERNIE Team: elastic unified multimodal expert training

Trained multimodal understanding and generation under a common next-group-of-tokens objective, with elastic depth, expert capacity and routing sparsity to support multiple deployment budgets from one run.

B+ · Native multimodal hybrid language-model training

Qwen Team: native vision-language hybrid training resource

Combined early multimodal fusion with alternating gated-delta and global attention layers in a sparse expert model family, releasing weights and implementation-facing architecture details.

B+ · Language-model training systems

Cohere: decentralized expert-track post-training and model merging

Alternated centralized instruction tuning with separately optimized capability experts, parameter merging and polishing to integrate multilingual, retrieval and tool-use capabilities in Command A; documented an interleaved local/global attention implementation.

B+ · Instruction-data generation and model alignment

Sudalairaj et al.: taxonomy-guided LAB synthetic instruction alignment

Combined a human-maintained task/knowledge taxonomy, teacher-generated instructions with quality filtering and multi-phase tuning to add skills and knowledge to pretrained chat models; powered the collaborative InstructLab workflow.

B+ · Open bilingual language-model research resources

01.AI: Yi bilingual foundation-model research resource

Documented and released bilingual pretrained/chat research models with cascaded data deduplication and filtering, manually verified instruction data, and context/depth adaptation experiments in one model-family resource.

B+ · Language-model training stability and open checkpoints

Yang et al.: Baichuan2 training-stability and checkpoint resource

Documented output-head normalization, maximum-logit regularization, elastic distributed-training choices and intermediate checkpoints for bilingual language-model training, enabling training-dynamics research.

B+ · Code language-model training resources

Guo et al.: DeepSeek-Coder project-level code research resource

Trained and released code models on deduplicated project-level repositories with dependency-aware code organization and fill-in-the-middle training, documenting a reusable code-generation and infilling pipeline.

A · Trainable sparse-attention algorithms

Yuan et al.: hardware-aligned Native Sparse Attention

Combined compressed-block context, selected fine-grained blocks and local attention in a trainable hierarchical sparse design, co-designed with GPU-friendly kernels for forward, backward and decoding workloads.

A- · Neural-network residual architecture

Xie et al.: doubly-stochastic constrained hyper-connections

Constrained multi-stream residual mixing through Sinkhorn-normalized nonnegative matrices and integrated fused kernels, recomputation and communication overlap to make expanded residual connections more stable at scale.

A · Distributed reinforcement-learning infrastructure

Sheng et al.: HybridFlow hybrid-controller RLHF execution

Combined single-controller orchestration with distributed model-worker execution and hierarchical dataflow APIs, plus actor resharding between training and generation through a hybrid engine.

B+ · Pretrained time-series forecasting

Ansari et al.: Chronos quantized-token probabilistic forecasting

Scaled and quantized time-series values into a fixed token vocabulary, pretrained language-model architectures with cross-entropy and sampled future trajectories for probabilistic forecasts; supplemented public data with Gaussian-process synthetic series.

B+ · Pretrained multivariate time-series models

Woo et al.: Moirai unified variable-dimensional forecasting

Developed a masked-encoder forecasting architecture for heterogeneous frequencies, variable numbers of channels and varying output distributions, trained on the accompanying LOTSA time-series collection.

A · Self-supervised image representation learning

Chen and He: SimSiam stop-gradient visual self-supervision

Showed that a predictor and stop-gradient operation can train a simple shared-weight Siamese representation learner without negative pairs, momentum encoders or unusually large batches.

B+ · Open speech-understanding systems

Mistral AI: Voxtral long-audio understanding and evaluation resource

Integrated chunked audio encoding and downsampled audio-language adaptation for long-audio conversations, released open weights and speech understanding/reasoning evaluation resources, and documented transcription-versus-understanding training tradeoffs.

B+ · Language-model preference optimization

Choi et al.: self-improving robust preference optimization

Jointly optimized a generation policy and a policy that improves its outputs through a regularized adversarial preference objective, deriving an offline supervised training formulation and evaluating iterative self-revision.

B+ · On-device model sparsity and inference

Hou et al.: instruction-conditioned structured parameter pruning

Jointly trained a prompt-conditioned sparsity predictor and language model to choose structured feed-forward parameter masks, keeping selected parameters fixed for an input or task to reduce repeated weight loading.

B+ · On-device foundation-model inference systems

Apple: flash-resident prompt-routed on-device foundation system

Stored a larger sparse model in flash and selected prompt-dependent expert subsets into DRAM, combining always-active shared weights, periodic expert reselection and task-dependent active capacity for on-device multimodal inference.

A · Multimodal instruction learning

Liu et al.: LLaVA visual instruction tuning

Used language-only teacher-generated visual instruction data and a vision-encoder/language-model connector to train an open multimodal instruction-following assistant.

B+ · Video modeling and physical-AI research resources

NVIDIA: Cosmos video-world-model development platform

Released an integrated video curation/orchestration pipeline, visual tokenizers and pretrained generative video models with examples of domain post-training for robot and driving research.

A · Few-shot learning architectures

Vinyals et al.: support-conditioned matching networks

Mapped labeled support examples and a query through learned representations and attention to predict unseen-class labels, training on episodes that mimic the one-shot test setting.

A · Optimization-based meta-learning

Nichol and Schulman: first-order initialization meta-learning

Repeatedly sampled a task, trained on it and moved a shared parameter initialization toward the resulting weights, learning an initialization for fast adaptation without differentiating through the inner optimization.

A · Distributed language-model serving

Zhong et al.: SLO-aware prefill/decoding disaggregation

Placed prefill and decoding on different GPUs and jointly selected per-phase resource allocation, parallelism and placement to improve goodput subject to first-token and per-output-token latency targets.

B+ · Omnimodal physical-AI modeling systems

NVIDIA: dual-tower omnimodal reasoning/generation integration

Integrated a causal autoregressive reasoner and a bidirectional diffusion generator through shared attention over text, vision, audio and action tokens, aligning differing media/action sampling rates on physical time.

A · Vision-language contrastive objectives

Zhai et al.: pairwise sigmoid language-image pretraining loss

Replaced globally normalized softmax image-text contrastive loss with pairwise sigmoid classification, decoupling the objective from global batch normalization and enabling efficient distributed scaling.

B+ · Efficient multimodal token integration

Meng et al.: cross-layer injection of grouped visual tokens

Distributed groups of visual tokens across aligned language/vision transformer layers through residual injection, allowing richer visual inputs without placing all tokens in the language input sequence.

A · Human-feedback alignment systems

Bai et al.: iterated helpful-and-harmless preference training

Applied preference modeling and RLHF to helpful/harmless assistants and iterated online human feedback with regularly refreshed preference and policy models, studying capability compatibility and reward–KL behavior.

A · Robot-action sequence tokenization

Pertsch et al.: frequency-space robot-action tokenization

Compressed continuous action chunks through discrete-cosine-transform-based tokenization before autoregressive learning, releasing a tokenizer trained across diverse robot embodiments and control rates.

B+ · Vision-language-action transfer training

Driess et al.: gradient-insulated continuous-action experts

Trained the vision-language backbone with discrete-action/text prediction while separately training a continuous flow-action expert, stopping the expert's gradients into the backbone to preserve useful representations.

B+ · Foundation-model expansion methods

Kim et al.: pretrained-layer depth up-scaling

Copied a pretrained transformer, removed complementary top/bottom layer blocks and concatenated retained layers before continued training, increasing depth while reducing discontinuity at the join.

A · Unified multimodal systems

Chameleon: early-fusion mixed-modal transformer training

Developed stable early-fusion training and mixed-modal alignment for a transformer generating interleaved discrete image/text tokens, with architectural normalization changes and a long-form mixed-modal evaluation.

B+ · Model merging

DARE: drop-and-rescale task deltas for model merging

Randomly removed task-delta entries, rescaled retained entries and combined homologous fine-tuned models with existing merging methods, studying when sparse deltas preserve measured abilities.

B+ · Unified multimodal action/world-model systems

Reka Rho-1: shared-state discrete/continuous omni-model integration

Integrated language/visual understanding and continuous image/video/action generation through two expert streams with shared attention/KV state, combining next-token and flow objectives in a research-preview system.

A · Language-model inference

StreamingLLM: attention sinks and rolling KV state

Kept initial attention-sink tokens alongside recent tokens in a fixed rolling KV cache, enabling stable streaming generation beyond the model's training context without fine-tuning.

B+ · Language-model inference

PyramidKV: layer-dependent KV cache budgets

Allocated different KV-cache budgets across layers based on observed information-funneling patterns, retaining more entries in lower layers.

A · Language-model inference

H2O: recent/heavy-hitter KV cache eviction

Combined recency and accumulated attention heavy hitters in a dynamic KV-cache eviction policy and evaluated its memory/inference tradeoff.

A · Diffusion acceleration

DMD: distribution-matching diffusion distillation

Distilled a one-step generator using the difference between target and synthetic score estimates plus paired-trajectory regression, matching distributions rather than only individual teacher paths.

A · Efficient visual-generation systems

SANA/SANA-Sprint: efficient linear diffusion and hybrid few-step integration

Integrated deep-compression autoencoding, linear diffusion attention, a decoder-only text encoder and Flow-DPM sampling/caption-selection choices for efficient high-resolution synthesis. Later Sprint combines continuous-time consistency and latent adversarial distillation with step-adaptive sampling and interactive ControlNet.

A · Efficient vision architectures

SqueezeNet: Fire-module small-model architecture

Designed squeeze/expand Fire modules and channel/filter allocation strategies to reduce parameters while maintaining measured ImageNet classification performance.

B+ · Open generative-audio research systems

Suno Bark: text-prompted generative audio research resource

Released a text-prompted generative audio system and code/model resources for multilingual speech and non-speech audio, documenting inherited GPT-style semantic/acoustic generation and EnCodec representation.

B+ · Speech-language model systems

Step-Audio: unified speech systems with generative data and reasoning adaptation

Released a unified speech/text interaction system with a synthetic speech-data engine, a distilled TTS model and instruction/control/tool-use training plus evaluation resources. Step-Audio2 adds a latent audio encoder and reasoning-centric reinforcement learning while integrating paralinguistic speech generation and audio/text retrieval.

B · Spoken dialogue alignment

Spoken dialogue alignment from live user interactions

Constructed content- and timing-related preference pairs from multi-turn spoken interactions using transcription, AI feedback and speech resynthesis, then applied offline preference alignment to full-duplex speech models.

B · Three-dimensional scene reconstruction

Surflo: global-state surface generation from unposed views

Compressed variable numbers of unposed RGB views into fixed-size global latent tokens and decoded oriented surface points using conditional flow matching, with photometric/depth guidance to reduce local inconsistency.

B · Generative-model evaluation

FID Lottery: training-seed and sampling-seed evaluation

Measured FID variability on a two-axis panel of training and generation seeds for hundreds of SiT image models and introduced per-cell guidance tuning and multi-training-seed reporting recommendations.

B · Interactive world models

MIRA: multiplayer action-conditioned world modeling

Trained a representation-autoencoder latent diffusion world model on RocketLeague gameplay with multiple player action streams, studying shared dynamics and targeted physical-behavior evaluations.

B · Efficient vision-language architectures

CASA: local text self-attention for visual fusion

Added local text-to-text attention within dedicated visual fusion layers, retaining cross-attention-like scaling while narrowing the tested performance gap to full visual-token insertion.

B+ · Language-model context compression

ARC-Encoder: portable continuous context compression

Trained an encoder to replace text embeddings with fewer continuous pooled representations and small decoder-specific mappings, supporting multiple unchanged decoders and compressed context extension.

B · Music transcription resources and training

MuScriptor: open multi-instrument music transcription

Combined synthetic pretraining, aligned real-music finetuning, reinforcement-learning post-training and instrument-presence conditioning in an open-weight multi-instrument transcription model.

A · Formal mathematics evaluation

miniF2F: cross-system formal mathematics benchmark

Assembled488 competition/course problem statements across formal systems with GPT-f baselines, enabling comparison of formal-to-formal proving systems on shared mathematical tasks.

B+ · Mathematical autoformalization data

MMA: multilingual formal-to-informal training data

Generated natural-language informalizations of Lean4 and Isabelle statements to build a large paired corpus, then finetuned and compared multilingual-formal-language autoformalizers.

B · Inference-time proof-search resource allocation

Cost-aware action routing for agentic Lean proof search

Separated lemma/proof generation from a learned control plane estimating future attempt success and cost from failed trajectories, choosing whether to retry or restart the decomposition.

B+ · Formal-proof engineering resources

Leanstral: open proof-engineering models and repository workflows

Released sparse Lean4-specialized agent models with language-server tooling and FLTEval repository tasks; the1.5stage describes CISPO reinforcement learning over multiturn proof/disproof and filesystem code-agent environments.

B+ · Compact language-model training

Ministral3: cascade pruning and pretrained distillation

Derived progressively smaller dense models by pruning and continued logit distillation through an intermediate teacher cascade, then post-trained visual instruction and reasoning variants.

B · Regional multimodal language-model adaptation

Phoenix-VL: localized multimodal training and evaluation resources

Adapted a pretrained multimodal model using curated regional/general replay data, long-context continued training and local multimodal/alignment data, introducing Singapore-focused evaluation and behavior frameworks.

B+ · Neural computational-fluid-dynamics surrogates

NeuralCFD / AB-UPT: geometry-separated anchored CFD surrogates

Evolved GP-UPT geometry-preserving encoding into anchored, multi-branch UPT decoders for surface/volume fields, including an explicit divergence-free output formulation; a later report evaluated existing architecture on SHIFT automotive/aerospace data.

B+ · Policy-conditioned safety classification

Shieldstral: policy-adaptive multimodal moderation

Unified heterogeneous moderation taxonomies into instruction/query/document yes-no tasks, training on curated and contrastively generated text/image data and using yes/no logits for policy-conditioned classification.

B+ · Physics-informed AI evaluation data

Emmi-Wing: three-dimensional transonic CFD benchmark

Generated roughly30thousand wing-geometry/inflow RANS simulations with surface and volume fields and evaluated learned surrogates for held-out geometry/condition lift-drag tradeoffs.

B · Neural plasma-turbulence simulation

GyroSwin: five-dimensional gyrokinetic plasma surrogates

Extended hierarchical Swin models to5D distribution functions using cross-dimensional attention/integration and channelwise mode separation, jointly predicting distributions, potentials and heat flux.

A+ · Distributed AI runtime systems

Ray: unified distributed task and actor execution

Built a dynamic task-graph runtime combining task and actor abstractions with a sharded fault-tolerant control store and bottom-up distributed scheduling for heterogeneous AI workloads.

B+ · Large-language-model optimization systems

Moonlight: update scaling and distributed Muon training

Added weight decay and adjusted parameter-update scales for large-model Muon, implementing ZeRO-style distributed orthogonalization and releasing Moonlight checkpoints with scaling experiments.

A · Distributed ML compiler systems

GSPMD: compiler propagation of tensor sharding

Inferred operator partitioning from limited tensor annotations and generated SPMD computation, supporting uneven/nested sharding, padding and halo exchange in XLA.

A · Neural-network generalization training

SAM: approximate neighborhood-loss minimization

Optimized an approximate min-max neighborhood-loss objective by perturbing weights along a first-order direction and computing an update gradient at the perturbed weights.

A · Large-scale AI orchestration systems

Pathways: asynchronous distributed accelerator dataflow

Used sharded asynchronous operators over futures and gang scheduling to decouple control-plane execution from dependent accelerator work under a single-controller programming model.

B+ · Language-model inference acceleration

Medusa: multihead drafts with tree attention

Added future-token prediction heads to a language-model backbone, with tree-attention verification, frozen-backbone or joint training and a typical-acceptance option.

B · Memory-efficient distributed training

UPipe: headwise-chunked context parallelism

Processed attention heads in staged chunks under a context-parallel schedule and used GQA-compatible out-of-order scheduling to reduce intermediate activation memory while preserving practical training throughput.

B+ · Distributed language-model reinforcement learning

OpenRLHF: Ray-based multi-model RLHF scheduling

Separated and scheduled RLHF model roles using Ray, vLLM and DeepSpeed, integrating large-model training and multiple alignment algorithms in an accessible framework.

B+ · Distributed language-model reinforcement learning

ROLL: sample-level rollout orchestration and resource mapping

Integrated parallel workers, sample-level rollout scheduling, environment/reward workers and automatic device mapping in a configurable RL training library for multi-domain and agentic workloads.

A · Language-model data curation

FineWeb family: ablated web curation and language-adaptive filtering

FineWeb documented and ablated filtering/deduplication for a large English web corpus and an educational subset; FineWeb2 adapted curation statistics by language and rebalanced globally deduplicated multilingual data using duplication and quality signals.

A · Multimodal dataset evaluation

DataComp: fixed-recipe multimodal dataset experiments

Provided candidate image-text pools, fixed CLIP training/evaluation recipes and compute-scaled tracks, with DataComp-1B demonstrating the importance of filtering under controlled training conditions.

A · Multimodal training resources

LAION family: CLIP-filtered image-text indexes at scale

LAION400M released image-URL/metadata pairs, CLIP embeddings and nearest-neighbor indexes; LAION5B expanded multilingual coverage and provided filtering signals and model-training studies.

A · Self-supervised representation learning

data2vec family: contextual targets and efficient masked self-distillation

Regressed contextual latent representations from an EMA teacher's full input using masked student views, applying one self-distillation objective across separate speech, image and text settings. data2vec2 skipped masked inputs, used a convolutional decoder and amortized teacher computation across several masked student views.

A · Self-supervised visual representation learning

I-JEPA: context-to-target image-block representation prediction

Predicted target-block embeddings from informative context blocks with a joint-embedding predictive architecture and multi-block masking, learning image features without handcrafted view-augmentation invariances.

A+ · Deep reinforcement-learning training

A3C and asynchronous neural actor-learners

Ran parallel actor-learners with asynchronous gradient updates to decorrelate online experience, developing asynchronous variants of value-learning and advantage actor-critic methods without relying on a replay buffer.

A · Neural-network optimization

ADADELTA: gradient and update RMS rescaling

Replaced AdaGrad's unbounded squared-gradient accumulation with a decaying average and used prior-update RMS over gradient RMS to form dimensionally matched coordinate updates.

A+ · Neural-network activation functions

GELU: Gaussian-CDF-weighted neural activation

Defined a smooth input-weighted activation through the expected action of an input-dependent stochastic identity/zero map, with Gaussian cumulative probabilities and empirical neural-network evaluations.

A · Neural-network activation functions

Sigmoid-weighted activation lineage: SiL/SiLd1 and Swish

Elfwing and colleagues studied sigmoid-weighted linear and derivative activations with eligibility-trace RL; Ramachandran and colleagues later evaluated the same self-gated form as Swish and a scaled-parameter variant in deep vision/language networks.

A · Neural-network activation and initialization

PReLU and rectifier-aware network initialization

Learned negative-side rectifier slopes jointly with network weights and analyzed initialization adapted to rectifier nonlinearities, studying deep image classifiers.

A · Deep-learning framework systems

MXNet: unified symbolic and imperative tensor execution

Integrated declarative computation graphs and imperative tensor operations under a dependency engine with memory reuse, automatic differentiation and distributed communication interfaces.

A · Distributed model compilation and training

GShard: compiler-driven sharding for sparse-expert models

Combined lightweight sharding annotations with XLA compiler support to express distributed computation, scaling multilingual sparse-expert Transformer training with automated partitioning.

A+ · Scientific-computing compiler infrastructure

Theano: symbolic differentiation and optimized array compilation

Compiled typed NumPy-like symbolic graphs through canonicalization, numerical-stability rewrites, specialization and CPU/GPU code generation, with symbolic differentiation; a later community report documents development.

A+ · Differentiable-programming compiler systems

JAX: high-level tracing of pure array subroutines

Traced annotated pure-and-statically-composed Python/NumPy subroutines into XLA computations while preserving dynamic Python orchestration and compatibility with Autograd transformations.

A+ · Deep value-based reinforcement learning

Double DQN: decoupled action selection and target evaluation

Adapted Double Q-learning to deep Q-networks by selecting next actions with the online network and evaluating them with a separate target network, reducing maximization overestimation in tested tasks.

A · General-purpose benchmark reinforcement-learning agents

Agent57: adaptive exploration and discount selection on Atari57

Combined stabilized value-learning parameterization with a bandit mechanism selecting exploration and discount settings, obtaining source-reported above-human baseline scores across all57 Atari games.

A+ · Goal-conditioned reinforcement learning

Hindsight Experience Replay: relabeling achieved goals

Replayed trajectories with alternative achieved goals and recomputed goal-dependent rewards, allowing off-policy goal-conditioned agents to learn from attempts that missed the requested goal.

A+ · General graph learning and quantum-property prediction

MPNN: unified learned messages and graph-level readout

Unified several existing graph models into learned message-passing/update and invariant readout phases, exploring variants on non-biological quantum-chemistry property prediction.

A · Graph attention expressivity

GATv2: query-dependent graph-attention ranking

Identified query-independent key-ranking restrictions of the original GAT score and changed the order of linear transformations/nonlinearity to enable dynamic attention.

A · Feed-forward neural-network normalization

Self-normalizing networks: SELU moment stabilization

Designed scaled exponential-linear activations and compatible initialization to attract layerwise activation mean/variance toward a stable region under an analyzed moment map.

B+ · AI-accelerator performance characterization

Citadel's microbenchmark characterization of the Graphcore IPU

Characterized the early IPU's tile-local SRAM, communication and arithmetic organization, publishing reproducible microbenchmark techniques and memory-bandwidth behavior under different load widths and block sizes.

A · Structured neural-network compression

Structured CNN filter pruning by weight magnitude

Ranked trained convolutional filters by absolute weight sums and removed corresponding feature maps and downstream kernels, producing smaller dense operations rather than isolated sparse weights.

B+ · AI training systems

AWS Neuron distributed LLM training on Trainium

Integrated inherited parallel-training methods with Trainium-aware mixed tensor-parallel degrees, automatic pipeline graph partitioning, delayed device materialization and asynchronous graph execution in Neuron/NxDT.

A · Neural-accelerator architecture

DianNao: memory-aware compact neural-network accelerator

Co-designed pipelined neural arithmetic with separate input/output/weight buffers and locality-aware tiling, reporting a compact65nm post-layout inference accelerator including external-memory cost analysis.

A · Distributed recommendation training

Neo/ZionEX: co-designed distributed recommendation training

Combined table/row/column/data-parallel embedding placement, fused sparse operators, hierarchical memory and a dedicated scale-out network in a PyTorch-based training stack for very large recommendation models.

A · Distributed machine-learning compilers

Unity: joint algebraic and parallelization search for DNN training

Represented computation and communication in parallel computation graphs, generated small algebraic/parallel substitutions from operator specifications, checked them with an automated prover and searched their compositions hierarchically.

B+ · Multi-GPU operator compilers

Mercury: remote-memory scheduling for multi-GPU operators

Introduced a loop-based communication IR treating remote GPU memory as schedulable storage, with parallelize, shift, shard and replicate transformations and autotuned multi-GPU operator schedules.

A · Multi-task recommendation

MMoE: task-specific gates over shared expert networks

Assigned a separate input-dependent gating network to each task while sharing expert subnetworks, letting different prediction towers use different mixtures of learned representations.

A · Sequential recommendation

BERT4Rec: masked bidirectional training for item sequences

Transferred bidirectional Transformer encoding and masked-item prediction to recommendation, then appended a mask at the history's end for next-item inference to address the training–prediction mismatch.

B+ · Industrial recommendation ranking

BST: target-aware behavior-sequence attention for click ranking

Added Transformer encoding of historical clicked items plus the candidate item and relative-time position features to an embedding/MLP ranker, combining the encoded sequence with user, item and context features.

A · Multi-interest recommendation

MIND: capsule-routed multi-interest retrieval at Tmall

Adapted dynamic routing to aggregate variable-length behavior embeddings into several interest vectors, using label-aware attention in training and independent nearest-neighbor queries for candidate retrieval.

B+ · Hybrid sequence-model architectures

B’MOJO: coupled fading and selected eidetic memory

Combined recurrent fading memory with a local attention window and innovation-selected stored tokens, expressing a family of hybrid state-space modules that can retrieve selected information beyond the recent context.

B · Retrieval-augmented recurrent inference

PICASO: composing precomputed SSM context states

Stored precomputed context states and transition factors, composed them algebraically and averaged compositions over permutations or cyclic rotations to reduce online context-processing costs.

A · Diffusion-based planning

Diffuser: trajectory denoising as guided planning

Learned a diffusion prior over state/action trajectories, guided reverse denoising with reward gradients or clamped constraints and executed sampled plans in a receding-horizon loop.

A+ · Learning to rank

RankNet: pairwise probabilistic neural ranking

Trained a scalar neural ranking function from document pairs using logistic score differences and cross-entropy loss, extending backpropagation to pairwise preferences while retaining individual-item scoring at inference.

A · Learning to rank

LambdaRank: metric-aware score-update rules for ranking

Specified document-score update signals using ranked positions and target retrieval measures, trained differentiable ranking models from these implicit-gradient rules and factored pairwise training contributions.

A · Sentence representation learning

SimCSE: dropout-based contrastive sentence embeddings

Used independently sampled dropout masks to create positive views of the same sentence, and used entailment positives and contradiction negatives in a supervised contrastive variant.

A · Information retrieval evaluation

BEIR: heterogeneous zero-shot retrieval evaluation

Standardized cross-domain retrieval evaluation over diverse query/document forms, relevance labels and tasks, comparing lexical, dense and reranking approaches beyond their training domains.

A · Code representation and generation

CodeT5/CodeT5+: identifier-aware code pretraining and modular code models

Added identifier tagging/recovery and text–code dual generation to T5-style pretraining, then extended the family with modular encoder/decoder use, mixed denoising/contrastive/matching/causal objectives and compute-efficient initialization from pretrained code LLMs.

A · Structured code representation learning

GraphCodeBERT: data-flow-aware masked code pretraining

Added extracted variable data-flow nodes to source/comment inputs, used graph-guided attention masks and trained code-edge and variable/token alignment tasks alongside masked language modeling.

B+ · Sentence representation learning

AnglE: complex-space angle objectives for text embeddings

Combined similarity-ordering and supervised contrastive objectives with complex-space angle optimization, using known duplicate sentences as positives rather than false in-batch negatives.

A+ · Language-understanding benchmarks

GLUE and SuperGLUE: shared multi-task language evaluation

Combined heterogeneous language tasks, evaluation protocols, diagnostic sets and reference systems into shared benchmarks; SuperGLUE expanded the task formats and difficulty after progress on GLUE.

A+ · Natural-language inference

SNLI and MultiNLI: large human-labeled entailment corpora

Collected entailment, contradiction and neutral hypotheses around text premises; extended caption-based SNLI with multi-genre written and spoken English and matched versus mismatched genre evaluation.

A · Search and question answering

MS MARCO: search-query reading-comprehension data

Released real anonymized Bing queries, retrieved web passages and human-written answers, including some questions with multiple answers or no answer, for reading-comprehension research.

A · Multi-document question answering

HotpotQA: multi-hop questions with supporting sentences

Collected Wikipedia paragraph-pair questions through bridge entities and entity comparisons, with sentence-level supporting-fact annotations to evaluate both answers and evidence selection.

A · Question-answering benchmarks

BoolQ: naturally occurring yes-or-no questions

Collected real search queries with Wikipedia evidence and human yes/no labels, building a dedicated paragraph-based task and studying transfer from textual entailment.

A · Reading-comprehension benchmarks

RACE: exam-derived English reading-comprehension benchmark

Collected English passages and multiple-choice questions from Chinese middle- and high-school examinations written by instructors, introducing a large reading-comprehension evaluation beyond automatically generated cloze questions.

A · Physical commonsense benchmarks

PIQA: textual tests of everyday physical commonsense

Collected physical goals with a valid solution and a plausible incorrect alternative, validated the examples and applied filtering to reduce readily detectable annotation artifacts.

A · Commonsense inference benchmarks

SWAG: adversarially filtered grounded event completion

Used video-caption contexts and language-model-generated alternatives, iteratively filtering easy negatives with stylistic classifiers and validating choices to build grounded next-event questions.

B+ · Long-context reasoning evaluation

BABILong: reasoning facts embedded in long distractor text

Embedded generated bAbI reasoning facts among ordered background book sentences, allowing controlled extension of context length while testing retrieval, fact chaining and other reasoning operations.

A · Sequence-model architectures

FNet: fixed Fourier mixing in language encoders

Replaced encoder self-attention with real-valued outputs of Fourier transforms over sequence and hidden dimensions, retaining feed-forward blocks and studying speed–accuracy tradeoffs.

A · Multilingual translation resources

M2M-100: mined many-to-many translation beyond English pivots

Combined mined parallel data across non-English language directions with shared and language-specific capacity studies, releasing a many-to-many translation model and reproducible data/evaluation workflows.

A · Cross-lingual evaluation

XNLI: aligned multilingual entailment evaluation

Collected new English premise–hypothesis evaluation examples using the MultiNLI protocol and professionally translated them into aligned multilingual sets for comparing cross-lingual sentence representations.

A+ · Machine-learning software

LIBSVM: reusable support-vector learning software

Documented a reusable training-and-prediction library for support-vector classification, regression and one-class learning, with interfaces and practical tools for applying the methods.

A+ · Statistical machine-translation software

Moses: factored statistical translation and open decoding tools

Built an open phrase-based translation toolkit with configurable linguistic factors, confusion-network decoding and memory-conscious phrase-table access, alongside training, tuning and evaluation workflows.

A · Object-detection training systems

YOLOv4/v7/v9: detector integration and auxiliary training pathways

Studied component/augmentation combinations for efficient detection, then developed aggregation-aware scaling and reparameterization, lead-guided auxiliary labels, and programmable-gradient auxiliary branches with generalized layer aggregation.

A+ · Object-detection methods

SSD: one-pass multi-scale detection with box priors

Predicted class scores and shared box offsets for predefined priors at several feature-map resolutions, integrating multi-category detection without a separate proposal-generation stage.

A+ · Adversarial generative learning

Wasserstein GAN and gradient-penalty training

Used a Lipschitz-constrained critic motivated by Wasserstein-1 duality, then replaced restrictive weight clipping with a sampled input-gradient penalty to improve practical adversarial training.

A+ · Conditional image generation

pix2pix and pix2pixHD: paired conditional image translation

Combined image-conditioned adversarial training with reconstruction and patch-based discrimination; the high-resolution extension added coarse-to-fine generation, multi-scale discriminators and discriminator-feature matching.

A · Score estimation

Sliced score matching: random-projection score objectives

Matched score differences along random directions and used integration by parts to obtain objectives computable with Hessian-vector products, including a variance-reduced form for scalable score estimation.

A · Continuous generative modeling

Stochastic interpolants: variational velocity and score learning

Specified paths between endpoint samples and learned probability-current velocities through quadratic regression objectives; extended the construction with latent noise to relate deterministic flows, scores and tunable diffusions.

S- · Flow-based probabilistic generative modeling

Variational inference with normalizing flows

Composed invertible transformations to enrich amortized variational posteriors and retain tractable change-of-variables density terms, including linear-cost planar and radial flow constructions.

A+ · Flow-based probabilistic generative modeling

NICE, Real NVP and Glow: coupling-based generative flows

Developed tractable invertible generative models through additive coupling, affine coupling with learned scale, and Glow's invertible1x1 channel mixing and ActNorm within multiscale architectures.

A · Flow-based probabilistic generative modeling

Inverse and masked autoregressive flows

Used triangular autoregressive transforms to enrich variational posteriors and construct flexible density estimators, exploiting complementary fast directions in IAF and MAF.

A · Flow-based probabilistic generative modeling

Neural spline flows with analytic invertibility

Parameterized monotonic rational-quadratic spline transforms inside coupling or autoregressive flows, increasing scalar-transform flexibility while retaining tractable derivatives and analytic inversion.

A · Flow-based probabilistic generative modeling

FFJORD: scalable continuous normalizing flows

Combined continuous-time invertible dynamics with Hutchinson trace estimation and adjoint-based training to scale log-density evaluation without triangular neural Jacobian restrictions.

A+ · Convolutional visual recognition

R-CNN: region proposals with convolutional features

Combined bottom-up region proposals with pretrained and detection-finetuned convolutional features and class-specific SVMs, demonstrating strong object detection and transferable region representations.

A · Convolutional visual recognition

ResNeXt: aggregated residual transformations

Introduced a homogeneous multi-branch residual block and cardinality as a model-design axis, with an equivalent grouped-convolution implementation for the selected bottleneck structure.

A · Convolutional visual recognition

Squeeze-and-Excitation channel recalibration

Added global spatial pooling and a bottleneck gating network to adaptively rescale convolutional feature channels, enabling SE-enhanced recognition architectures.

A · Convolutional visual recognition

Deformable ConvNets and modulated deformable modules

Learned input-dependent offsets for convolution and region pooling, then expanded deformable layers with modulation scalars and R-CNN feature-mimicking supervision to improve spatial adaptation.

A · Visual recognition datasets and evaluation

LVIS: long-tail instance segmentation and federated evaluation

Designed a large-vocabulary instance-segmentation dataset and per-category positive/negative evaluation subsets, enabling long-tail object recognition without exhaustive labeling of every image-category pair.

A+ · Visual recognition datasets and evaluation

Visual Genome: densely grounded scene graphs and language

Collected region descriptions, object/attribute/relationship annotations and question-answer pairs grounded to natural images, canonicalizing language concepts with WordNet to support structured vision-language research.

A+ · Visual recognition datasets and evaluation

ADE20K: detailed scene, object and part annotations

Created densely segmented natural-scene annotations with object instances, attributes and hierarchical object parts, supporting scene parsing beyond a small predefined object vocabulary.

A+ · Large-scale reinforcement-learning systems

OpenAI Five: scaled self-play for team Dota2

Scaled recurrent PPO self-play with distributed rollout/inference/optimization and continual-training infrastructure, producing a team agent that defeated Team OG in the documented2019 Dota2 setting.

A+ · Multiplayer imperfect-information game reasoning

Pluribus: multiplayer poker self-play and limited-depth search

Combined improved Monte Carlo CFR blueprint learning with depth-limited online search that permits multiple continuation strategies, defeating professional players in six-player no-limit poker experiments.

A+ · Imperfect-information multiagent learning

Counterfactual regret minimization in extensive-form games

Decomposed overall strategic regret into information-set counterfactual regrets, enabling locally maintained regret-matching updates and approximate-equilibrium computation in large imperfect-information games.

A+ · Imperfect-information multiagent learning

CFR+ and Cepheus: scalable near-equilibrium poker solving

Introduced clipped cumulative regret-matching updates and weighted averaging, then combined distributed compressed computation with CFR+ to essentially weakly solve heads-up limit Texas hold'em.

A · Imperfect-information multiagent learning

Neural fictitious self-play

Combined off-policy deep reinforcement learning of approximate best responses with supervised reservoir-memory learning of average behavior, supporting end-to-end imperfect-information self-play.

A · Imperfect-information multiagent learning

ReBeL: reinforcement learning and search over public beliefs

Reframed imperfect-information learning/search around public belief states, training value/policy functions using self-play subgame solving rather than treating hidden-world states as ordinary perfect-information leaves.

A · Imperfect-information multiagent learning

Policy-space response oracles and deep cognitive hierarchies

Grew empirical meta-games of policies by learning approximate best responses to policy mixtures, then applied meta-strategy solvers; a decoupled hierarchy reduced the full payoff-tensor bottleneck.

A · Multiagent game-learning systems

OpenSpiel: common game interfaces and learning algorithms

Provided a C++/Python framework spanning sequential/simultaneous and perfect/imperfect-information games, shared interfaces and algorithm implementations for reinforcement-learning and game-theoretic research.

A · Multiagent game-learning systems

For The Win: population-trained visual team play

Combined concurrent populations, two-tier optimization of internal reward schemes and multiscale recurrent representations to learn pixel-based QuakeIII capture-the-flag policies that cooperated and competed with unfamiliar teammates/opponents.

A · Imperfect-information multiagent learning

DeepNash: regularized Nash dynamics for Stratego

Combined regularized payoff-learning dynamics with model-free deep self-play, fine-tuning and test-time policy filtering to reach expert-level Stratego Classic performance without game-tree search or human demonstrations.

A+ · Language-grounded multiagent reasoning

CICERO: intent-grounded dialogue with strategic planning

Integrated human-data-trained intent-conditioned dialogue, human-regularized strategic planning and message filtering, achieving strong human-level performance in the reported online Diplomacy blitz league.

A · Multi-agent credit assignment

COMA counterfactual multi-agent policy gradients

Uses a centralized action-value critic and decentralized actors, marginalizing each agent's action while holding teammates' actions fixed to construct a counterfactual credit-assignment baseline.

A · Cooperative multi-agent reinforcement learning

QMIX monotonic joint-value factorization

Combines local action-value utilities through a state-conditioned monotonic mixing network so local greedy choices agree with the represented joint greedy choice.

A · Cooperative multi-agent reinforcement learning

QPLEX duplex-dueling multi-agent Q-learning

Uses duplex dueling and advantage-based mixing to represent the individual-global-max consistent value-function class while supporting decentralized greedy execution.

A · Multi-agent exploration

MAVEN committed multi-agent variational exploration

Conditions coordinated agent utilities on an episode-level latent variable and trains a hierarchical exploration policy with a variational mutual-information objective to distinguish joint behaviors.

A · Cooperative multi-agent reinforcement learning

MAPPO cooperative multi-agent PPO training recipe

Demonstrates strong cooperative-game performance using PPO with centralized agent-specific value inputs, value normalization, controlled data reuse, action masking and appropriate death masking.

A · Cooperative multi-agent actor-critic

FACMAC factored multi-agent centralized policy gradients

Learns a factored centralized critic and differentiates a joint current-policy action to coordinate actor updates; examines monotonic and nonmonotonic critic factorization in cooperative control.

B+ · Multi-agent action communication

Simplified Action Decoder for cooperative learning

Exposes an actor's unperturbed greedy action to teammates during centralized training so recurrent agents can decode action information without epsilon-greedy exploration blur; greedy execution removes that side channel at test time.

A · Zero-shot coordination

Other-Play symmetry-based zero-shot coordination

Trains against symmetry-transformed partners to reduce arbitrary convention dependence and improve zero-shot cross-play without pre-agreed symmetry-breaking labels.

A · Game-theoretic evaluation

Alpha-Rank evolutionary multi-agent evaluation

Ranks finite strategy profiles through the stationary distribution of a mutation-selection Markov chain, retaining intransitive cycles rather than forcing a scalar transitive dominance interpretation.

A · Multi-agent planning and learning

DORA no-press Diplomacy learning from scratch

Combines neural Nash-style value iteration, policy-proposal restrictions and double-oracle action discovery for self-play in large simultaneous-action no-press Diplomacy.

A · Human-compatible multi-agent planning

piKL and Diplodocus human-regularized planning family

piKL anchors search to imitation-learned policies through KL-regularized utilities; DiL-piKL distributes regularization strengths and RL-DiL-piKL trains Diplodocus for human-compatible no-press Diplomacy.

A · Human-AI coordination

Overcooked human-aware collaborative learning testbed

Introduces a simplified cooperative game testbed and compares self-play/population-based agents with agents trained or planned using behavior-cloned human models, including real-human collaboration tests.

A · Neural architecture search

DARTS differentiable architecture search

Relaxes discrete operation choices into softmax mixtures and approximates a train/validation bilevel objective with alternating weight and architecture-gradient updates before discretization.

A · Neural architecture search

ENAS shared-parameter neural architecture search

Uses a reinforcement-learned controller to sample subgraphs of a shared computation graph, alternating controller validation rewards with shared-weight training to reduce repeated child-model training.

A · Learned data augmentation

AutoAugment and RandAugment image-augmentation policy family

AutoAugment searches operation/probability/magnitude subpolicies using validation rewards; RandAugment replaces the separate proxy search with uniform sampled operations and a small count/magnitude parameter space.

B+ · Automated data augmentation

Fast AutoAugment density-matching policy search

Uses trained split-data classifiers and Bayesian policy exploration to find augmentation policies whose transformed examples match a learned data distribution, then retrains on the augmented full training set.

B+ · Automated data augmentation

Population Based Augmentation policy schedules

Applies population-based training to augmentation probabilities and magnitudes, yielding nonstationary schedules learned alongside child networks and transferred to larger training runs.

A · Hyperparameter optimization

BOHB model-based Hyperband optimization

Combines Hyperband's multi-fidelity allocation with multidimensional density-estimation guidance, using the largest sufficiently populated budget model and retaining random exploration.

A · Hyperparameter schedule search

Population Based Training of neural networks

Asynchronously trains a population, copies promising members' weights/hyperparameters and perturbs hyperparameters to discover schedules within continuing training runs.

A · Hardware-aware neural architecture search

ProxylessNAS direct target-task and hardware search

Uses binarized path gates and pairwise architecture updates to reduce supernetwork memory, with latency-model gradients or REINFORCE for hardware-aware search directly on target tasks.

A · Neural architecture search evaluation

NAS-Bench-101 tabular architecture-search benchmark

Precomputes repeated CIFAR-10 training metrics for roughly 423,000 graph-isomorphism-deduplicated cells under a fixed pipeline, enabling reproducible lookup-based NAS comparisons.

A · Neural network architecture search

Weight Agnostic Neural Network topology search

Evolves sparse network topologies while evaluating each with multiple values of one globally shared weight, reducing dependence on learned individual weight parameters.

B+ · Automated machine learning software

Auto-PyTorch tabular multi-fidelity AutoDL

Combines architecture/training configuration search, BOHB multi-fidelity budgets, portfolio warmstarts and post-hoc ensembling for tabular automated learning.

B+ · Automated machine learning software

TPOT tree-based learning-pipeline optimization

Represents general-purpose preprocessing, feature selection and classifier combinations as trees, and uses genetic programming with a complexity-aware Pareto variant to optimize pipelines.

A · Automated machine learning software

auto-sklearn meta-learning and ensemble-based AutoML

Warmstarts structured Bayesian configuration search using related-dataset meta-features and constructs an ensemble from previously evaluated models in a scikit-learn pipeline search space.

A · Probabilistic programming

Pyro effect-handler probabilistic programming

Embeds dynamic probabilistic models in Python/PyTorch with sample/parameter primitives and composable Poutine effect handlers, supporting scalable approximate inference.

A · Accelerated probabilistic programming

NumPyro composable effects and iterative compiled NUTS

Combines Pyro-style effect handlers with JAX transformations and replaces NUTS's recursive tree-building implementation by an iterative form suitable for end-to-end JIT compilation.

A · Differentiable probabilistic computing

TensorFlow Distributions and composable bijectors

Separates probability-distribution objects from deterministic volume-tracking transformations, with tensor batch/event semantics, differentiable operations and composable transformed distributions.

A · Automated machine learning software

AutoGluon-Tabular multilayer ensemble AutoML

Builds heterogeneous multilayer stack ensembles using original features and out-of-fold model predictions, repeated bagging and weighted ensemble selection for tabular learning.

A · Distributed learning infrastructure

Tune distributed model-selection and training interfaces

Separates trainable-model and trial-scheduler interfaces so intermediate reporting, checkpointing and runtime configuration changes support varied distributed search algorithms over Ray.

A · Reinforcement learning software

Dopamine compact reproducible deep-RL framework

Provides compact self-contained value-based RL agents, replay components, experiment runners and reproducibility-oriented infrastructure for algorithmic research and instruction.

A · Reinforcement learning environments

DeepMind Lab first-person 3D learning platform

Provides a configurable first-person 3D game-engine platform with pixel/depth/motion observations and navigation/action tasks for partially observable agent research.

A · Multi-agent learning infrastructure

PettingZoo unified multi-agent environments

Provides agent-iteration and parallel interfaces, common spaces/seeding and reusable tests/documentation for diverse multi-agent simulation environments.

B+ · Reinforcement learning simulation infrastructure

Jumanji scalable compositional JAX environments

Provides accelerator-native routing/packing/logic environments with customizable initial-state generators, reset/reward/viewer components and actor-critic baselines for scalable experiments.

A+ · Approximate Bayesian inference

ADVI transformed-space automatic variational inference

Transforms constrained continuous latent variables to unconstrained coordinates, selects Gaussian variational families and uses reparameterized automatic-differentiation gradients for generic optimization.

A · Scalable Gaussian-process computation

GPyTorch black-box matrix-matrix Gaussian-process inference

Reuses batched conjugate-gradient work to estimate solves, trace derivatives and log determinants using kernel matrix-matrix multiplication, paired with preconditioning and a PyTorch framework.

A · Probabilistic learning software

GPflow TensorFlow-backed Gaussian-process software

Combines Python object-oriented GP model interfaces with TensorFlow automatic differentiation, variational/sparse and sampling methods, contributing differentiable Cholesky and GPU triangular-solve support.

A+ · Bayesian hyperparameter optimization

Practical GP-based hyperparameter optimization

Studies covariance choices and integration over GP hyperparameters, expected-improvement-per-time acquisition and Monte Carlo fantasies for pending parallel evaluations.

A+ · Sequential learning and optimization

GP bandit UCB regret bounds through information gain

Relates Gaussian-process upper-confidence bandit cumulative regret to maximal sampling information gain, using kernel spectral structure to derive sublinear-regret results under the source's assumptions.

A · Learning optimization algorithms

Coordinatewise LSTM learned optimizers

Trains recurrent update rules across optimization tasks, sharing a coordinatewise LSTM's parameters while retaining separate hidden states to propose gradient-history-dependent parameter steps.

A · Amortized probabilistic function learning

Conditional and latent Neural Process family

Aggregates permutation-invariant context representations for conditional predictions; latent Neural Processes add a shared global latent to generate coherent function samples.

A · Hyperparameter optimization

Tree-structured Parzen estimators and Hyperopt

Models promising versus remaining conditional configurations with density estimators and expected-improvement selection; Hyperopt packages structured stochastic search spaces, interchangeable optimizers and persistent asynchronous trials.

A · Algorithm configuration

SMAC sequential model-based algorithm configuration

Extends sequential model-based configuration to categorical parameters and instance sets using random-forest performance models and aggressive incumbent/challenger intensification.

S- · Neural operators and scientific machine learning

Graph-kernel and Fourier neural operators

Learns parameterized maps between input and solution functions through shared integral-operator layers; GKN approximates kernels by graph message passing and Nyström sampling, while FNO parameterizes truncated Fourier modes for efficient grid evaluation.

A+ · Neural operators and scientific machine learning

DeepONet branch–trunk operator-learning architecture

Combines a branch network encoding sampled input functions with a trunk network encoding output locations, taking their learned feature inner product to approximate nonlinear operators.

A+ · Learned physical simulation

Graph Network Simulators and MeshGraphNets

Learns particle dynamics by graph encode–process–decode message passing, then extends this learned-simulation approach to irregular meshes using mesh-space/world-space edges and a predicted sizing field with a generic remesher.

A · Graph and geometric machine learning

E(n)-equivariant graph neural networks

Uses invariant distance-conditioned scalar messages and radial coordinate updates to preserve Euclidean rotation, reflection and translation equivariance without computing higher-order spherical-harmonic features.

A · Graph and geometric machine learning

SE(3)-Transformer equivariant attention

Combines invariant attention weights with equivariant tensor-field value messages to process 3D point clouds while respecting rigid rotations and translations.

A · Graph and geometric machine learning

LieConv continuous-data group convolutions

Lifts continuous coordinates into a Lie group and parameterizes convolution kernels through its Lie algebra, enabling local learned convolutions on irregularly sampled data.

A · Graph and geometric machine learning

Variational graph auto-encoders

Uses a graph-convolutional variational encoder and inner-product decoder to learn latent node variables and reconstruct graph links, with a deterministic graph-autoencoder variant.

A · Graph and geometric machine learning

DiffPool differentiable hierarchical graph pooling

Learns soft node-to-cluster assignments and coarsens features and adjacency through S-transpose Z and S-transpose A S, enabling hierarchical graph neural networks.

A · Graph and geometric machine learning

LINE first- and second-order network embeddings

Learns direct-edge and neighborhood-context embeddings using negative sampling and weight-proportional edge sampling, then combines separately trained proximity representations.

A · Graph and geometric machine learning

NetMF matrix-factorization view of network embeddings

Relates random-walk/negative-sampling embedding objectives to graph matrix factorizations and computes clipped log co-occurrence embeddings directly or with spectral approximation.

A · Scientific machine learning

Multi-grid tensorized Fourier neural operators

Jointly parameterizes spectral operator weights through low-rank tensor factorizations and predicts local domains with hierarchical coarse-to-fine global context, reducing parameter and memory costs in reported PDE tasks.

B+ · Scientific machine learning

NeuralOperator modular operator-learning library

Packages neural-operator architectures, spectral/integral layers, data processing, training, losses and memory-efficient tensorized/distributed workflows in a PyTorch-compatible library.

A · Scientific machine learning

Spherical Fourier neural operators

Uses spherical-harmonic convolutions rather than planar FFTs for operator learning on spherical geometry, with a differentiable spherical-harmonic implementation and reported stable atmospheric rollouts.

A · AI weather forecasting

Aurora transferable Earth-system foundation model

Pretrains a 3D Swin/Perceiver weather model on diverse forecast, analysis, reanalysis and climate data, then fine-tunes for weather, ocean waves and cyclone-track tasks in the expanded source version.

A · AI weather forecasting

Aardvark end-to-end observation-to-weather forecasting

Maps heterogeneous weather observations through learned state estimation, autoregressive forecasting and local prediction modules, permitting end-to-end adaptation without numerical-model initial states at inference.

A · AI weather forecasting

FuXi cascaded short-to-long-range weather prediction

Cascades separately fine-tuned forecast models for0–5,5–10 and10–15-day windows, using joint space-time embedding and a U-Transformer to reduce long-range autoregressive errors.

S- · Scientific machine learning

SINDy sparse identification of nonlinear dynamics

Regresses measured state derivatives onto a candidate nonlinear-function library using sparsity, including sequential thresholded least squares, to identify compact dynamical models.

A+ · AI interpretability, model editing and data attribution

Grad-CAM: gradient-weighted coarse localization for CNN predictions

Uses pooled class gradients to weight convolutional feature maps and produces a rectified localization map without changing or retraining the target CNN; Guided Grad-CAM combines it with a high-resolution backward visualization.

A · AI interpretability, model editing and data attribution

SmoothGrad: noise-averaged gradient sensitivity maps

Averages sensitivity maps over Gaussian perturbations of an input to reduce visually noisy saliency, and studies visualization choices and training-time noise.

A · AI interpretability, model editing and data attribution

TCAV: concept-vector directional sensitivity testing

Learns concept directions from positive and counterexample activations, measures output directional derivatives along these directions and aggregates their signs into class-level concept sensitivity.

A · AI interpretability, model editing and data attribution

Concept bottleneck models with editable intermediate concepts

Trains prediction through an explicitly supervised concept bottleneck using independent, sequential or joint losses, allowing predicted concepts to be corrected before the final output.

A · AI interpretability, model editing and data attribution

ROME and causal tracing for factual language-model edits

Uses corruption and restoration of internal activations to locate factual-recall pathways, then applies a constrained rank-one MLP update; CounterFact tests edited facts, paraphrases and nearby associations.

A · AI interpretability, model editing and data attribution

MEND: low-rank gradient-transform networks for local model editing

Learns small shared editor networks on factorized per-example gradients, producing targeted weight changes while training against edit-neighborhood and locality losses without modifying the base model before an edit.

A · AI interpretability, model editing and data attribution

Saliency sanity checks by parameter and label randomization

Introduces model-parameter and data-label randomization tests for explanation methods, revealing that some visually persuasive saliency procedures can ignore learned model or label structure.

A · AI interpretability, model editing and data attribution

Attention explanation stress tests with counterfactual weights

Tests correlations with gradient/erasure importance and searches permuted or adversarial attention distributions that preserve predictions in selected text classification, QA and inference models.

A · AI uncertainty, reliability and selective prediction

ODIN: temperature and input-perturbation OOD detection

Combines high-temperature softmax scores with small input-gradient perturbations to separate known and anomalous images while leaving the underlying classifier weights unchanged.

A · AI uncertainty, reliability and selective prediction

Energy-based OOD scoring and energy-bounded fine-tuning

Uses negative log-sum-exp of classifier logits as a non-probabilistic anomaly score and proposes margin-based fine-tuning to separate in-distribution and auxiliary-outlier energies.

A+ · AI uncertainty, reliability and selective prediction

Jackknife+ intervals from leave-one-out predictions and residuals

Forms prediction-interval endpoints from leave-one-out predictions at the new input paired with their held-out residuals, obtaining a distribution-free coverage guarantee for symmetric learning algorithms.

A · AI uncertainty, reliability and selective prediction

Weighted conformal prediction under covariate shift

Weights conformity-score quantiles by test-to-training covariate likelihood ratios, extending prediction coverage to a covariate-shift and weighted-exchangeability setting.

A · LLM factuality and grounded generation

Language Models (Mostly) Know What They Know

Studies answer-conditioned P(True) and trains a separate P(IK) value head from sampled correctness labels to estimate answerability before selecting a particular answer.

B+ · LLM factuality and grounded generation

Corrective Retrieval Augmented Generation

Scores retrieved documents with a learned relevance evaluator and routes among refined retrieval, web search and their combination before generation.

A · LLM factuality and grounded generation

Long-form factuality in large language models

Combines LongFact long-form prompts, search-augmented atomic-fact evaluation and F1-at-K using a preferred supported-fact count as a recall surrogate.

B+ · LLM factuality and grounded generation

Measuring short-form factuality in large language models

Short-form factuality benchmark with independently checked answers and explicit correct/incorrect/not-attempted judgments; later SimpleQA Verified filters redundancy, balances topics and reconciles sources.

B+ · Language-model representation control

Turner and colleagues: prompt-pair activation addition

Used activation differences elicited by contrasting prompts as inference-time steering vectors, showing selected changes to generated text without gradient-based fitting of the steering direction.

S- · Extremal combinatorics and Boolean complexity

Huang: induced hypercube degree bound and the Sensitivity Conjecture

A signed adjacency-matrix construction and eigenvalue interlacing give the sharp square-root maximum-degree lower bound for induced hypercube subgraphs with more than half the vertices. Via the known Gotsman–Linial equivalence, this proves polynomial relations between Boolean sensitivity, polynomial degree and block sensitivity.

S- · Geometric analysis and minimal surfaces

Marques and Neves: min–max proof of the Willmore conjecture

A canonical five-parameter family and Almgren–Pitts min–max methods prove the 2π² Willmore-energy lower bound for embedded closed positive-genus surfaces in the round three-sphere, with conformal Clifford-torus equality. The source explains how the Euclidean immersed-torus conjecture follows using existing nonembedded-surface bounds.

S- · Structural graph theory

Chudnovsky, Robertson, Seymour and Thomas: the strong perfect graph theorem

A finite simple graph is perfect exactly when it has neither an induced odd cycle of length at least five nor the complement of such a cycle. A structural decomposition of Berge graphs, together with exclusions for a minimal imperfect graph, yields the characterization.

S- · Equivariant stable homotopy theory

Hill, Hopkins and Ravenel: high-dimensional Kervaire-invariant-one nonexistence

An equivariant-bordism construction, detection theorem, 256-fold periodicity and a homotopy gap exclude Kervaire-invariant-one elements in the higher indexed dimensions. Combined with Browder's earlier restriction, the associated framed-manifold dimensions are limited to 2, 6, 14, 30, 62 and possibly 126 in this work.

S- · Operator algebras and mathematical quantum theory

Stinespring: dilation of completely positive maps

For a unital C*-algebra and a linear map into bounded operators on a Hilbert space, complete positivity is equivalent to representation as the compression V* pi(A) V of a *-representation on a larger Hilbert space. For a unital map the construction can make V an isometry.

A+ · Quantum many-body mathematical physics

Lieb and Robinson: a finite propagation-velocity bound for quantum spin systems

For translation-invariant finite-range interactions on a quantum spin lattice with finite-dimensional site spaces, the norm of a commutator between separated local observables becomes exponentially small outside a sufficiently fast space-time cone. The proof bounds dynamical influence independently of the chosen quantum state.

S · Matrix analysis and quantum information

Lieb and Ruskai: strong subadditivity of quantum entropy

For a finite-dimensional tripartite quantum state, the von Neumann entropies satisfy S(ABC)+S(B) <= S(AB)+S(BC). The proof uses operator trace inequalities and is accompanied by convexity of negative conditional entropy; the original text develops extensions through controlled finite-dimensional approximation.

S- · Algebraic coding theory and quantum information

Panteleev and Kalachev: asymptotically good quantum LDPC codes

Lifted products over nonabelian groups yield quantum LDPC code families with positive constant rate and minimum distance linear in block length. A related construction also yields classical locally testable LDPC codes with constant rate, relative distance, query complexity and soundness.

S- · Finite-field incidence geometry

Dvir: the polynomial method for finite-field Kakeya sets

For each fixed dimension, a subset of a finite vector space containing a full affine line in every direction has size at least a positive dimension-dependent fraction of the entire space. A low-degree polynomial vanishing on a too-small candidate set would force incompatible vanishing of its homogeneous components.

S- · Discrete and algebraic geometry

Guth and Katz: a near-linear lower bound for planar distinct distances

Every set of N distinct points in the Euclidean plane, for N at least two, determines at least cN/logN distinct nonzero distances for a universal positive constant c. The proof combines the Elekes-Sharir rigid-motion framework with three-dimensional line-incidence bounds, polynomial partitioning and ruled-surface geometry.

S- · Analytic and computational number theory

Helfgott: ternary Goldbach with Helfgott-Platt finite verification

Every odd integer greater than five is a sum of three primes. Explicit major- and minor-arc estimates and an optimized large sieve cover all sufficiently large integers; a rigorously verified finite range overlaps that analytic threshold and completes the result.

S · Linear algebra

Cayley: systematic square and rectangular matrix algebra

Cayley developed matrix addition, associative noncommutative composition, identity, inverses for nonzero determinant and transpose rules, and extended compatible composition to rectangular matrices. He stated the characteristic equation for arbitrary square order, explicitly demonstrated the two-by-two identity and reported verification in order three, using it to organize matrix powers and low-order examples.

S- · Transcendental number theory

Hermite’s proof that the number e is transcendental

Hermite constructed simultaneous rational approximations to exponentials and used their arithmetic structure to show that e satisfies no nonzero polynomial equation with integer, equivalently rational, coefficients. His treatment converts a putative integer-coefficient relation among distinct integral powers of e into integer linear forms that tend to zero. A nonvanishing determinant prevents all such forms from vanishing, yielding a contradiction.

S- · Partial differential equations and analytic local existence

Kovalevskaya: local analytic solutions of noncharacteristic PDE Cauchy problems

Kovalevskaya proved convergence of the recursively determined formal power series for analytic PDE Cauchy problems in the paper's normal, noncharacteristic forms. A coefficientwise majorant argument establishes the first-order system result; higher-order algebraic equations and specified coupled systems are reduced to this setting after selecting a simple root for the leading normal derivatives. Analytic initial data then determine a unique local analytic solution on that branch. She also exhibited heat-equation data whose formal time series has zero convergence radius, showing why solving for a lower-order time derivative alone is insufficient.

S- · Complex analysis and value distribution

Picard's omitted-value theorems for entire functions and isolated essential singularities

Picard proves that a nonconstant entire holomorphic function can omit at most one finite complex value. The October 1879 note strengthens this: a transcendental entire function assumes every finite value infinitely often, with at most one exception. The 1880 memoir supplies the detailed modular-function/monodromy proof and local extension: near an isolated essential singularity, a holomorphic function assumes every finite value infinitely often except possibly one; the corresponding meromorphic version permits at most two exceptional values on the sphere. These linked results are staged as one contribution family.

S- · Transcendental number theory

Lindemann: π is transcendental and the classical circle cannot be squared

Lindemann adapted Hermite's exponential-integral arithmetic to prove that π is not a root of any nonzero polynomial with rational coefficients. The proof uses symmetry among algebraic conjugates, integer or algebraic-integer relations that become too small, and a nonzero determinant; the application combines the exponential relation e^(iπ)=−1 with the algebraic hypothesis. Transcendence excludes exact squaring of a circle by a finite construction using only a compass and unmarked straightedge.

A+ · Complex analysis and meromorphic functions

Mittag-Leffler: constructing analytic functions with prescribed isolated singular parts

Mittag-Leffler's1884 memoir constructs a single-valued analytic function with prescribed singular parts at a countable isolated setQ, regular away fromQand its accumulation setQprime. Subtracting suitable finite Taylor/rational correction terms from each prescribed part makes their series locally uniformly convergent. Finite polynomial principal parts give the familiar meromorphic-function construction; entire functions of1/(z−a)allow isolated essential singular parts as well. Section 1also treats the stated connected-domain boundary formulation and describes the remaining freedom by addition of a regular function.

A+ · Complex analysis and approximation theory

Runge: rational approximation of single-valued analytic functions

Runge constructs rational approximations to a single-valued analytic function on a plane domain, converging uniformly on compact subsets away from its poles. Cauchy integrals on a nested square-grid exhaustion are replaced by finite rational sums; a pole-moving argument then relocates unwanted poles outside the approximation region. In particular, a holomorphic function on a domain can be locally uniformly approximated by rational functions without poles in that domain.

A+ · Finite groups, quotient groups and Galois theory

Hölder: invariant simple factor groups in finite-group composition series

Hölder proved that any two composition series of a finite group yield the same simple quotient groups up to isomorphism, order and multiplicity. He replaced the earlier invariance of numerical factor orders by invariance of the factor groups themselves, using quotient groups and an induction through intersections of distinct maximal normal subgroups. Applied to algebraic-equation chains, these simple factor groups give unavoidable constituents of the auxiliary equation groups, even when auxiliary irrationalities beyond the original roots are admitted under the paper's rationality-field conventions.

S · Commutative algebra and classical invariant theory

Hilbert: finite polynomial bases, terminating syzygies and finite invariant systems

Hilbert proved that a system of homogeneous polynomial forms in finitely many variables admits a finite subfamily generating every member by polynomial linear combinations. He supplied a separate integer-coefficient version, proved termination of successive minimal systems of relations in the stated polynomial setting, and applied the finite-basis mechanism together with invariant-producing differential operators to establish finite generation for the classical invariant systems treated in the paper. The argument turned finiteness questions about infinitely many forms into finite algebraic data.

A · Diophantine approximation and continued fractions

Hurwitz proves the sharp universal square-root-five rational-approximation bound

Hurwitz proves that every real irrational alpha has infinitely many rational approximations p/q with |alpha−p/q|<1/(sqrt(5)q²). The constant sqrt(5) in the denominator cannot be uniformly increased: irrationals whose continued fractions are eventually all 1, including the golden ratio and its integral fractional-linear equivalents, obstruct every larger constant.

S · Algebraic geometry and polynomial ideals

Hilbert: the homogeneous zero-set criterion behind the Nullstellensatz

Hilbert proved a homogeneous polynomial zero-set criterion: if a family of forms vanishes at every common zero of specified forms, then products of sufficiently many members of the vanishing family belong to the ideal generated by the specified forms. In particular, a sufficiently high power of any such form is a polynomial combination of the defining forms. This provides the central bridge from common zeros to ideal powers that became the Nullstellensatz, and supports his analysis of invariant systems.

S · Analytic number theory

Hadamard and de la Vallée Poussin: the prime number theorem

Independent analytic proofs established the asymptotic density of primes, in the weighted form θ(x)=Σ_{p<x}log p∼x and the familiar equivalent count form π(x)∼x/log x. Hadamard's 1896 paper proves the absence of zeta zeros on Re(s)=1 away from the pole, then obtains the asymptotic by a convergent smoothed contour integral and removes the smoothing. The same paper treats fixed reduced arithmetic progressions, with weighted density1/φ(k); de la Vallée Poussin's own Congress report states the corresponding weighted and counting asymptotics.

A+ · Geometry of numbers

Minkowski: volume forces a nonzero integer lattice point

Minkowski used translates of a half-scale centrally symmetric convex body to prove M^3 I<=8 for the minimum nonzero integer-lattice gauge M and unit-body volume I in three dimensions. Consequently a centered closed convex body of volume at least8 contains a nonzero integer lattice point. He connected the geometric bound with linear forms and simultaneous rational approximation.

S- · Algebraic number theory and local expansions

Hensel: prime-adic expansions as a new foundation for algebraic numbers

Hensel proposed replacing aspects of ideal-prime factorization by local prime-power expansions analogous to power-series expansions of algebraic functions. His announcement describes algebraic numbers through expansions with finitely many negative terms, distinguishes unramified and ramified local parameters, and relates the resulting places and orders of zeros or poles to prime-ideal divisibility and ramification. It sets out a prime-adic local viewpoint rather than giving a complete proof of the announced foundation.

A+ · Finite-group representations and invariant complements

Maschke: complete reducibility of finite complex linear groups

Maschke removed an earlier restriction from his criterion that a finite linear substitution group whose matrices have a fixed identically vanishing off-diagonal coefficient is intransitive, meaning transformable into separate blocks of variables. The decisive finite-group step starts with an invariant block and uses a positive invariant Hermitian form to eliminate the cross terms; the resulting unitary relations force the opposite off-diagonal block to vanish. Thus an invariant subspace in this complex finite-dimensional setting has an invariant complementary subspace, giving complete reducibility by iteration.

S- · Harmonic analysis and approximation theory

Fejér: arithmetic means restore convergence of Fourier expansions

Fejér proves that arithmetic means of the Fourier partial sums of a bounded integrable periodic function converge to its value at continuity points and to the average of its finite one-sided limits at a jump. A nonnegative normalized trigonometric kernel controls the nearby and distant parts of the integral. For a continuous periodic function the convergence is uniform, giving constructive trigonometric approximation; the note also explains how a convergent series of finite Fourier polynomials follows by telescoping the means.

S · Metric spaces and functional analysis

Frechet: abstract convergence, distance and compactness in functional calculus

Frechet organized functional calculus on sets of arbitrary objects by first axiomatizing convergence, then adding a symmetric separating distance and the triangle inequality. His framework transfers continuity and compactness arguments beyond Euclidean points. In the distance setting, he characterizes nonempty compact sets through boundedness and attainment of extrema of every real-valued continuous functional, and develops finite-small-cover criteria under his stronger normal-class assumptions.

S- · Harmonic analysis

Haar's dyadic orthogonal system with localized convergent expansions

Haar constructs a complete orthonormal system of localized dyadic step functions on [0,1]. In its specified natural order, Fourier-Haar expansions converge uniformly for continuous functions and almost everywhere for Lebesgue-integrable functions. The proof uses localized positive averaging kernels; dense recursive partitions yield related systems.

A+ · Matrix analysis and positive kernels

Schur proves that entrywise products preserve positive semidefiniteness

Schur proves that the coefficientwise product of two finite nonnegative Hermitian forms is again nonnegative. The proof factors one coefficient matrix into Gram terms and expresses the product form as a sum of nonnegative forms. He also bounds the product's characteristic roots using the extremal eigenvalues of one form and diagonal entries of the other, and derives a product-closure result for continuous nonnegative Hermitian kernels.

S- · Spectral theory and mathematical physics

Weyl: area controls the leading Dirichlet eigenvalue count

Weyl linked high Dirichlet eigenvalues of a planar domain to its area: for eigenvalues λ_n of −Δ ordered with multiplicity, n/λ_n tends to area/(4π). His1911note combines comparison inequalities for symmetric integral kernels with the Green-function singularity, reduction to squares and explicit square eigenvalues. It also states the analogous planar variable-coefficient leading term with effective area ∫k/p for the specified self-adjoint elliptic problem.

S- · Linear algebra and spectral theory

Frobenius: irreducible nonnegative matrices and their peripheral spectral cycle

Frobenius extends positive-matrix spectral theory to finite irreducible nonnegative matrices. The positive spectral radius is a simple eigenvalue with strictly positive left and right eigenvectors, while all eigenvalues on its spectral circle are simple and are the radius times a full cycle of roots of unity. The primitive case is characterized by a positive matrix power; sufficiently high powers are then positive. The same paper develops cyclic block structure and reduction into irreducible parts.

A+ · Measure theory and real analysis

Lusin: measurable functions are continuous on arbitrarily large closed subsets

In his French note, Lusin characterizes measurable real functions on [0,1] by continuity on a perfect nowhere-dense subset whose measure can be chosen greater than1−epsilon for every positive epsilon. Continuity is relative to that retained set. Using Egoroff's almost-uniform convergence result, the note shows that this C-property is preserved by pointwise or almost-everywhere limiting constructions and states the measurable-function characterization and converse.

A+ · Topology and continuous extension

Tietze extends bounded continuous functions from closed subsets of metric spaces

Tietze proves that a bounded real-valued continuous function on a closed subset of a Frechet classE—a metric space in the paper's explicit distance axioms—extends continuously to the whole space. The construction uses distance to the closed set and a distance-weighted upper envelope. Related majorization and decreasing continuous approximation results supply the same proof framework.

S- · Real analysis and geometric measure theory

Rademacher proves almost-everywhere differentiability of Lipschitz functions

Rademacher proves that a finite-dimensional Lipschitz function is totally differentiable outside a Lebesgue-null set. His original stronger sufficient condition uses a finite integrable upper local slope, and the paper connects almost-everywhere linearization to Jacobians and a change-of-variables formula for one-to-one transformations under its stated hypotheses.

S · Arithmetic geometry

Mordell: finite generation of rational points on genus-one curves

Mordell proved that rational solutions of the nonsingular genus-one cubic/quartic equations treated in his 1922 paper can all be generated from finitely many rational points by the classical chord/tangent and corresponding quartic constructions. For an elliptic curve over the rationals this gives finite generation of its rational-point group; infinite rational points can therefore have a finite generating set.

A+ · Functional and harmonic analysis

Marcel Riesz: log-convex bilinear bounds and restricted-exponent operator interpolation

For a fixed finite bilinear form, Riesz proves log-convexity of its norm in reciprocal-exponent coordinates α=1/p and β=1/r on0≤α,β≤1 with α+β≥1, including positive-weight versions. Via duality and Stieltjes–Lebesgue approximation this yields operator-norm log-convexity and endpoint interpolation for a compatible linear operator L^p→L^q in the region1≤p≤q≤∞: intermediate norms are bounded by the geometric interpolation of endpoint bounds.

S- · Harmonic analysis and probability

Bochner: continuous positive-definite functions on Euclidean space are Fourier transforms of finite positive measures

For finite-dimensional Euclidean R^k, Bochner proves that a bounded continuous complex function is positive definite exactly when it has a Fourier–Stieltjes representation f(x)=∫exp(i x·α)dV(α) with a nonnegative bounded distribution function. Positive definiteness is the nonnegativity of every finite quadratic form, not strict positivity. His uniqueness theorem identifies the distribution up to the original continuity-interval equivalence, corresponding to a unique finite positive Borel measure; its total mass is f(0).

A+ · Differential analysis and geometry

Sard: differentiability thresholds for null critical-value sets

For a C^q map from a region of R^m to R^n, Sard proves measure-zero results for the images of points where the derivative has less than maximal rank. If m>n, q≥m−n+1 gives zero n-dimensional Lebesgue measure; if m≤n, C^1 suffices for the rank-deficient image to have zero m-dimensional Hausdorff measure.

A+ · Ordinal analysis and number theory

Goodstein: termination through hereditary base change and ordinal descent

Goodstein connected natural-number descent processes to ordinal notation below epsilon zero. Writing numbers hereditarily in a base, replacing that base throughout the nested exponents by the next prescribed nondecreasing base, and subtracting one produces a process that eventually reaches zero. Replacing the finite base by omega assigns a strictly descending ordinal whenever the current number is positive. The paper relates these arithmetical processes to a restricted ordinal well-foundedness principle and develops finitary termination arguments for restricted ordinal heights.

S- · Enumerative combinatorics and group actions

Pólya's cycle-index substitution theorem for weighted orbit enumeration

For a finite permutation group acting on s positions and an inventory series f with finite nonnegative integer coefficients, the generating series of inequivalent configurations is obtained by replacing each cycle-index variable z_j with f(x^j,y^j,...). Fixed colour multiplicities are extracted coefficientwise; the proof counts cycle-constant fixed configurations and averages over the group.

A · Enumerative combinatorics and directed graphs

de Bruijn counts binary cycles containing every length-n word once

The number of cyclic binary sequences of length 2^n containing each binary word of length n exactly once is 2^(2^(n-1)-n). The proof relates these cycles to complete directed walks and shows that doubling a two-in/two-out network with m vertices multiplies its cyclic complete-walk count by 2^(m-1).

S · Mathematical logic and real algebra

Tarski: quantifier elimination and decidability of elementary real algebra

Tarski gave an effective procedure converting first-order real-algebra formulas built from polynomial equations, inequalities and logical quantifiers into equivalent quantifier-free formulas. For closed sentences this yields a terminating truth-decision method; coordinate translation gives a corresponding decision method for elementary Euclidean geometry.

S- · Convex analysis

Fenchel establishes symmetric convex conjugacy in finite dimensions

For a closed proper convex function on finite-dimensional Euclidean space, Fenchel's supremum construction gives a convex conjugate satisfying <x,xi> <= f(x)+f*(xi), with symmetric recovery of the original function by conjugation. Supporting hyperplanes connect equality to conjugate points without requiring differentiability.

A · Geometric and combinatorial inequalities

Loomis–Whitney: volume bounded by coordinate projections

Loomis and Whitney prove that the volume m of an open subset of R^n satisfies m^(n−1)≤m_1⋯m_n, where m_i is its (n−1)-dimensional coordinate projection measure. Their elementary induction and Hölder argument first establishes the corresponding cube-counting inequality N^(n−1)≤N_1⋯N_n. Axis-parallel boxes attain equality in the volume bound.

A+ · Order theory and combinatorics

Dilworth: finite-width chain decomposition of partially ordered sets

A partially ordered set of finite width k—no antichain of size k+1 and an antichain of size k—can be partitioned into k disjoint chains, and fewer chains cannot suffice. Dilworth proves the finite case and extends it to arbitrary finite-width ordered sets using a maximal principle. The paper applies the decomposition to set representatives and finite distributive-lattice embeddings.

A · Commutative algebra

Artin–Tate: finite-type intermediate-ring lemma

For commutative rings R⊂T⊂S with unit and R Noetherian, if S is a finitely generated R-algebra and a finite T-module, then T is a finitely generated R-algebra. Artin and Tate prove this by extracting a finite coefficient subalgebra and using Noetherian module finiteness, and give a short proof of Zariski's field lemma as an application.

S- · Probability and statistical decision theory

Chernoff: exponential tail rates and asymptotic test efficiency

Chernoff used the optimized exponential moment of a real random variable to bound tails of sums of independent identically distributed observations and identify their exponential decay rate. He then defined an asymptotic efficiency index for threshold tests between two simple hypotheses: the smallest fixed-positive-weight sum of the two error probabilities has a rate independent of that weight. Ratios of the logarithms of these indices compare asymptotic sample requirements.

A+ · Matrix analysis and majorization

Horn realizes majorized diagonals and characterizes rotation-matrix diagonals

For finite real vectors x and y, majorization of y by x, including equality of total sums, admits an orthostochastic realization y_i=sum_j U_ij^2 x_j with a real orthogonal matrix U. Consequently these conditions exactly characterize diagonals of Hermitian matrices with prescribed real eigenvalues, with real symmetric realization available. Horn also proves that diagonals of real determinant+1 orthogonal matrices form the convex hull of sign vectors with an even number of negative coordinates, deriving orthogonal and unitary diagonal characterizations.

S- · Linear algebra and matrix equations

Penrose: a unique generalized inverse defined by four matrix equations

Penrose characterized a unique generalized inverse X for every finite complex rectangular matrix A by AXA=A, XAX=X, (AX)*=AX and (XA)*=XA, with * the conjugate transpose. He gave an existence and uniqueness proof and used generalized inverses to express solvability and all solutions of AXB=C, as well as matrix projectors and a partial-isometry spectral decomposition.

A · Operating systems and concurrency

Corbató, Saltzer and Clingen: Multics—The First Seven Years

Multics was an attempt to make a computer a dependable shared utility. This paper explains how its designers connected goals such as continuous operation, controlled sharing and expandable capacity to implementation choices and years of experience. It also discusses revisions and incomplete goals. The contribution is an account of a working system and the lessons extracted from building it, rather than a claim that every feature of the original vision had been delivered.

A+ · Neural and deep learning

LeCun, Denker and Solla: Optimal Brain Damage

A trained neural network may contain weights that contribute little to its predictions. LeCun, Denker and Solla estimate the cost of removing a weight from how sharply the training error bends near the learned solution. They remove low-cost weights and retrain. Their experiments show why curvature can be more useful than simply keeping large weights, while also showing that a local approximation becomes less accurate when too many weights are removed at once.

A+ · Evaluation, safety and interpretability

Wolpert and Macready: no free lunch theorems for optimization

Could one search strategy be best for every optimization problem? Wolpert and Macready show why the answer changes when problems are averaged in a particular way. On finite search spaces, averaging uniformly over all objective functions removes the advantage of any strategy when performance depends on the values found after distinct queries. Practical success therefore depends on the structure of the problems encountered. This does not say that a useful optimizer, or a well-chosen benchmark, is impossible.

A+ · Probabilistic AI

Andrieu, Doucet and Holenstein: particle Markov chain Monte Carlo methods

Particle filters approximate hidden states using a finite collection of simulated possibilities. MCMC methods instead build a chain designed to preserve a target distribution. Particle MCMC connects the two by treating the random choices inside a particle filter as part of a larger mathematical state. This allows particle-based proposals to preserve the intended posterior exactly under stated assumptions, even with finitely many particles. Exactness of the stationary target still leaves a practical question: how quickly does the chain explore it?

A+ · Databases and information retrieval

Dewey: A Classification and Subject Index for Cataloguing and Arranging Books and Pamphlets of a Library

A growing library becomes hard to use if a book is identified mainly by the shelf where it happens to sit. Dewey links books to subjects using numbers that can be extended with extra digits. A subject index helps readers find the right number, while relative location lets a collection grow without renumbering every shelf. The first edition explains both the practical benefits and compromises of its hierarchy. The achievement is a reusable organization and retrieval method, not a neutral map of all knowledge.

S- · Precision measurement and instruments

Cavendish: experiments to determine the density of the Earth

The gravitational pull between ordinary laboratory objects is tiny. Cavendish made it measurable by suspending a light arm from a thin wire and observing how nearby heavy masses changed its position. Timing the arm’s oscillations helped connect the deflection to force. The experiment led to an estimate of Earth’s mean density, about 5.48 times that of water. The paper also examines air currents, temperature changes and other errors that could disturb such a delicate measurement.

A+ · Security and cryptography

Cohen: computer viruses, theory and experiments

Security is not only about whether a user can read a file. A program that a user trusts can alter another program, which can then spread the change further. Cohen develops this computer-virus model, relates spreading to information sharing and integrity policies, and reports controlled experiments on contemporary systems. The work helps explain why ordinary access controls can leave a different problem unsolved: deciding which information and programs should be allowed to change what.

A+ · Mathematics and statistics

Azuma: weighted dependent sums and asymptotic fluctuation control

Independent errors are easier to average than errors that depend on the past. Azuma studies sequences whose next increment has zero conditional mean, together with boundedness or conditional exponential-moment assumptions. These conditions control weighted sums and how their fluctuations grow. The paper gives convergence and iterated-logarithm upper bounds under explicit restrictions on the weights. This adds a route for studying dependent data without pretending that every dependent sequence behaves like independent noise.

S- · Condensed matter

Curie: magnetic properties of bodies at different temperatures

Heating a magnetic material can change far more than the strength of its attraction. Curie compares magnetic behaviour across materials and temperatures, looking for relations between weak magnetism, diamagnetism and ferromagnetism. For several weakly magnetic substances the magnetic coefficient varies approximately as the inverse of absolute temperature. Some ferromagnets approach this behaviour sufficiently far above their transformation temperature. The experiment gives later theories concrete patterns to explain, including exceptions and changes that a single simple formula misses.

B+ · Adversarial evaluation of language models

Chao and colleagues: iterative black-box model red-teaming with PAIR

Introduced an automated red-teaming workflow in which an attacker language model revises candidate requests using feedback from a target model and an evaluation model, enabling query-based stress testing without target-weight access.

A- · Language-model safety evaluation

Mazeika and colleagues: HarmBench standardized safeguard evaluation

Built a standardized framework combining curated harmful-behavior test cases, automated red-team method comparisons and response classifiers to evaluate robust refusal across language models under a common evaluation procedure.

A- · Language-model evaluation design

Perez and colleagues: model-written behavioral evaluations

Generated and filtered language-model evaluation datasets with language models and human relevance checks, using them to identify scaling and training trends in behaviors such as sycophancy and stated preferences.

A- · Language-model safety evaluation

Perez and colleagues: language-model-generated red-team tests

Used language models to generate adversarial test inputs and compared generation and learning strategies for finding undesirable target-model outputs, offering automated discovery as a complement to manual red-teaming.

B+ · Language-model social-bias evaluation

Parrish and colleagues: BBQ contextual social-bias evaluation

Constructed a question-answering benchmark contrasting ambiguous and disambiguated contexts to measure when model answers rely on social stereotypes rather than supplied information, using controlled templates and balancing.

B+ · Language-model safety evaluation

Souly and colleagues: StrongREJECT response-quality evaluation

Designed a benchmark and automated rubric that distinguish nominal non-refusal from a response that actually provides specific and convincing information, exposing overestimation in some automated red-team success measures.

S- · Ramsey theory and combinatorics

Hales–Jewett theorem: monochromatic combinatorial lines

Colour every word of a fixed length using a fixed finite alphabet. Hales and Jewett prove that, once the length is large enough, some family of words has one colour while the same nonempty positions vary together through the alphabet. This shared pattern is a combinatorial line. The theorem connects Ramsey-type regularity, arithmetic progressions and high-dimensional positional games.

S- · Combinatorics and discrete geometry

Erdős and Szekeres: monotone subsequences and unavoidable convex polygons

A long enough ordered list of distinct numbers must contain a long increasing or decreasing subsequence, even if that pattern is hidden among other entries. Erdős and Szekeres establish the sharp threshold (r−1)(s−1)+1 for an increasing subsequence of length r or a decreasing one of length s. Their related geometric argument shows that sufficiently many planar points in general position contain a convex n-gon, with the historical upper bound binomial(2n−4,n−2)+1.

A+ · Probability and quantitative limit theorems

Berry: explicit error bounds for normal approximation of independent sums

A bell curve may approximate a sum of independent random errors, but an approximation is more useful when its error is bounded. Berry gives a uniform bound on the difference between the cumulative distribution of a sum and its matching Gaussian distribution. His original estimate uses finite third absolute central moments and a maximum moment ratio; in the identically distributed case it gives an inverse-square-root rate in the number of terms. The work turns a limiting statement into a quantitative comparison.

S- · Extremal set theory

Erdős and Rado: finite sunflower bounds and cardinal Δ-system theorems

A large collection of small sets cannot remain completely unstructured. Erdős and Rado find a subcollection whose pairwise intersections are all the same common core: a Δ-system, also called a sunflower. Their paper gives finite bounds while distinguishing distinct sets from indexed repetitions, and treats an infinite-cardinal regime separately. The finite argument supplies a reusable tool for extracting regular structure from a complicated family of sets.

S- · Metric geometry and positive-definite functions

Schoenberg: Hilbert metrics characterized by positive-definite kernels

Can a table of distances come from points in a Hilbert space, where lengths and angles behave as in Euclidean geometry? In a separable setting, Schoenberg connects that question to the kernels exp(−s d²), for every positive s. These kernels must be positive semidefinite on every finite selection of points. The result links geometry to algebraic tests on distance tables and explains why suitable fractional powers of distances admit Hilbert-space embeddings.

S · Operator theory and quantum foundations

Gleason: projection measures have trace-operator form

Suppose probabilities are attached to subspaces of a Hilbert space, with probabilities adding across mutually perpendicular alternatives. Gleason proves that, for the stated real or complex separable spaces of dimension at least three, every finite nonnegative assignment of this kind comes from a positive trace-class operator. For total probability one, that operator is a density operator. The result characterizes a quantum probability rule from precise consistency assumptions; it does not establish the rule without those assumptions.

S · Probabilistic combinatorics and random graphs

Erdős–Rényi: giant-component phase transition in random graph evolution

Add edges at random to a graph with n labelled vertices, giving every graph with the same number N of edges equal probability. Erdős and Rényi identify a change as N/n approaches a fixed density c. For fixed 0<c<1/2 the largest connected component has logarithmic order. For fixed c>1/2, one giant component contains a positive fraction of all vertices with probability tending to one. This is an asymptotic transition in a specified random model, rather than a rule for every finite network.

S · Number theory and Diophantine approximation

Roth: optimal rational-approximation exponent for algebraic irrationals

Some irrational numbers can be approximated extraordinarily well by fractions. Roth proves a sharp limit for real algebraic irrationals: for any fixed positive epsilon, only finitely many reduced fractions p/q satisfy |alpha−p/q|<q^(−2−epsilon). At exponent two, every irrational still has infinitely many good approximations. His proof closes the rational-approximation exponent gap left by earlier work without supplying a general computable list of all exceptional fractions.

S- · Ring theory and finite fields

Wedderburn: every finite division ring is commutative

Multiplication need not commute in every algebra: quaternion multiplication is a familiar counterexample. Wedderburn’s 1905 theorem says that a finite associative division ring cannot have that behaviour. If each nonzero element has a multiplicative inverse and the set is finite, multiplication must commute, making the structure a finite field. The paper presents several arguments and acknowledges Dickson’s alternative proof; it is separate from the later structure theorem for semisimple algebras.

S · Real analysis and category methods

Baire: category and countable nowhere-dense sets in a real interval

Can a whole interval be assembled from countably many sets that leave a gap inside every smaller interval? Baire proves that it cannot. His 1899 thesis gives a nested-interval argument and introduces first and second category, a way to distinguish topologically small sets from a whole real interval. The framework also describes where suitable discontinuous functions remain continuous. It is a foundational principle about countable exceptional sets, rather than a statement about their total length.

S- · Real functions and descriptive hierarchy

Baire: pointwise-limit function classes and the first-class characterization

A sequence of continuous functions can settle point by point into a discontinuous limit. Baire classified functions by repeated pointwise limits and characterized the first class on a real interval through continuity of the restricted function on every perfect subset. His thesis distinguishes successive classes and gives a rational/irrational class-two example. A 1900 paper supplies a shorter sufficiency proof on a finite-dimensional closed cube, while explicitly acknowledging Lebesgue’s reduction of several variables to one.

S · Complex analysis and normal families

Montel: compactness and omitted-value criteria for holomorphic families

An unruly list of complex differentiable functions can contain a well-behaved subsequence. Montel’s 1907 compactness criterion extracts a locally uniformly convergent subsequence from a locally uniformly bounded holomorphic family. His 1912 work adds a different route: a holomorphic family that omits two shared distinct finite values is normal, allowing a subsequence to diverge uniformly to infinity. These criteria turn questions about many functions into questions about one limiting function.

S · Measure theory and integration

Fubini and Tonelli: valid reduction of multiple Lebesgue integrals to iterated integrals

Adding the rows of a table or its columns gives the same total. Infinite integrals need conditions before the analogous swap is valid. Fubini’s 1907 paper establishes equality between a Lebesgue double integral and either iterated integral for an integrable function, with exceptional sections handled almost everywhere. Tonelli’s 1909 nonnegative criterion can establish integrability from a finite iterated integral. The two papers form one evolving theorem family, not a joint publication.

S- · Additive number theory and Waring's problem

Hilbert: a finite number of kth powers suffices for every positive integer

Every positive integer is a sum of a bounded number of squares, but what happens for cubes, fourth powers or any other fixed exponent? Hilbert proves that each positive integer exponent has its own finite bound on the number of positive-power summands needed for every positive integer. His 1909 proof turns an integral identity into finite rational identities and then integer representations. It establishes existence for all exponents, without finding the least possible bound.

S · Set theory and foundations

Zermelo: well-ordering an arbitrary set using a choice function

A well-order gives every nonempty subset a first element. Zermelo showed how a simultaneous choice of one element from each nonempty subset can yield such an order on an arbitrary set. His 1904 letter compares compatible partial well-orders and combines them until the whole set is covered. The choice principle is an explicit assumption. Erhard Schmidt is acknowledged for the choice-assignment idea, while Zermelo is the printed author of the proof.

S · Analytic number theory and uniform distribution

Weyl: testing equidistribution by exponential sums and applying it to polynomials

A deterministic sequence can spread around a circle as evenly as interval lengths predict. Weyl’s exponential-sum criterion tests this by asking whether each nonzero integer frequency cancels out on average. His 1916 paper applies the method to polynomial sequences with an irrational nonconstant coefficient and to multidimensional settings under the stated independence conditions. Even distribution is a long-run frequency statement; it does not make the sequence independent, random or perfectly balanced after a fixed number of terms.

S · Quantum many-body theory and superfluidity

Bogoliubov: collective excitations of a weakly interacting Bose condensate

Weakly interacting atoms can move collectively in a way that individual free particles cannot describe. Bogoliubov’s 1947 approximation replaces the difficult interacting Bose gas near a condensate by elementary quasiparticle excitations. The resulting spectrum is sound-like at small momentum and approaches free-particle behaviour at large momentum under the stated interaction assumptions. The transformation supplies a reusable microscopic framework, while the original explicitly builds on earlier Bose-gas and Landau superfluidity ideas.

S- · Quantum many-body theory; dilute Bose gases

Lee–Huang–Yang: dilute hard-sphere Bose energy, excitations and correlations

Lee, Huang and Yang used a pseudopotential calculation to connect the wave functions, excitations, condensate depletion and pair correlations of a dilute hard-sphere Bose gas. The 1957 paper recovers the beyond-mean-field energy correction, explicitly crediting its earlier Lee–Yang derivation, and calculates low-lying collective excitations at the stated order. Its value is the linked microscopic calculation, not a claim that every density regime of liquid helium has been solved.

S- · Low-dimensional statistical physics

Berezinskii: algebraic order and vortex physics in two-dimensional planar systems

A two-dimensional system can have slowly decaying correlations without settling into conventional long-range order. Berezinskii’s 1970 and 1971 theoretical work, published in English translation in 1971 and 1972, develops this low-temperature picture for planar systems. The follow-up connects vortices to a logarithmically interacting gas and describes stiffness and superfluid response. It also corrects an earlier phase criterion. Later Kosterlitz–Thouless theory, universal-jump results and experiments remain separate contributions.

S- · Quantum electrodynamics and dispersion forces

Casimir–Polder: retardation changes atomic dispersion interactions

Electromagnetic influences take time to travel between atoms. Casimir and Polder calculated how that delay changes dispersion interactions: at large separation the two-atom energy falls as the inverse seventh power of distance, rather than the nonretarded inverse sixth power. Their 1948 paper also treats a neutral atom near an ideal conducting plane, with a different distance law. These are quantum-electrodynamic predictions under stated approximations, separate from Casimir’s two-plate calculation and from later measurements.

S- · Magnetic-resonance physics / spectroscopy methods

Pulse-response Fourier-transform magnetic-resonance spectroscopy

Instead of slowly scanning one resonance frequency at a time, Ernst and Anderson applied short radio-frequency pulses, recorded the combined time response and used a Fourier transform to recover the spectrum. Their 1966 magnetic-resonance paper combines a pulse-response model, coherent accumulation, filtering, numerical processing and an experimental comparison. It demonstrates a practical sensitivity and recording-time advantage under the stated conditions, rather than claiming that a Fourier transform alone improves every noisy measurement.

A- · Quantum optics and statistical physics

Klaers and colleagues: photon Bose-Einstein condensation in a microcavity

Light ordinarily disappears into a cavity’s walls as the system cools, rather than piling into its lowest-energy mode. Klaers and colleagues used repeated absorption and re-emission in a dye-filled microcavity to thermalize an effectively two-dimensional photon gas. They observed a strongly occupied ground mode, thermal spectral wings, a threshold with the expected geometry dependence and condensation away from the pump spot. Together these observations support photon Bose–Einstein condensation in the reported pumped, lossy regime.

A · Disordered quantum systems and quantum gases

Two controlled cold-atom routes to spatial matter-wave localization

Two independent 2008 teams used cold atoms to observe spatial localization of matter waves under controlled conditions. Billy and colleagues released a dilute cloud into a one-dimensional laser-speckle potential and measured stationary exponential density wings. Roati and colleagues used an almost non-interacting potassium condensate in a quasiperiodic optical lattice, testing transport and spatial and momentum profiles. Their different experimental routes probe disorder-related localization; they are one result family here, with two separate source bylines.

A- · Ultracold-atom quantum simulation and strongly correlated matter

Mazurenko and colleagues: finite-size antiferromagnetism in a cold-atom Hubbard simulator

Mazurenko and colleagues arranged cold fermionic atoms in a square optical lattice and measured antiferromagnetic spin correlations across a finite region of roughly eighty sites. A quantum gas microscope resolved individual sites, while comparisons with numerical models helped estimate temperature and interpret the correlations. The experiment created a useful low-temperature Hubbard-model simulator. It did not establish finite-temperature long-range order in an infinite two-dimensional system or solve the full doped-Hubbard phase diagram.

S- · Quantum dynamics and mathematical physics

Zener: transition law for an ideal linear two-level crossing

Two interacting quantum energy levels can avoid crossing even when their uncoupled energies would meet. Zener solved an ideal two-state crossing model to show how the rate of change affects the chance of a non-adiabatic transition. With constant coupling V and a linear uncoupled energy difference of slope s, the asymptotic probability is exp(-2*pi*V^2/(hbar*abs(s))). Slow and fast passages can therefore have very different outcomes.

S · Classical mechanics and statistical physics

Clausius: the mechanical virial relation for bounded stationary motion

Particles can keep moving while obeying a simple long-run energy balance. Clausius related the time-averaged kinetic energy of bounded stationary motion to a force-position quantity he called the virial. His mechanical derivation keeps a time-boundary term before taking a periodic or long-time average. For central pair forces and uniform external pressure, it connects microscopic motion with the pressure-volume term.

S · Thermodynamics and low-temperature free-energy limits

Nernst: a low-temperature heat hypothesis constraining thermodynamic equilibrium

Measurements of heat do not by themselves determine the maximum work a process can deliver: an integration constant remains. Nernst proposed a low-temperature hypothesis to supply the missing constraint for processes involving pure condensed substances. The work and energy curves approach a common tangent near absolute zero. Combined with thermal measurements and specified approximations, this made equilibrium calculations more constrained and became a foundation of later low-temperature thermodynamics.

S- · Quantum foundations and operator uncertainty

Robertson relates two standard deviations to the mean commutator

Quantum uncertainty can be expressed as a relation for many pairs of observables. Robertson connected their standard deviations, which measure the spread of repeated outcomes, to the magnitude of the expected commutator: Delta A times Delta B is at least one-half of abs(<AB-BA>). The familiar position-momentum case becomes one example of this general relation, alongside angular-momentum components.

S- · Atomic spectroscopy and empirical laws

Balmer: an empirical integer formula for the hydrogen spectral series

Four measured lines in the hydrogen spectrum fit a surprisingly compact number pattern. Balmer expressed their wavelengths using a common scale b times m^2/(m^2-4), with integer m=3,4,5,6. He then compared the extension of that pattern with additional violet and ultraviolet observations. This was a useful empirical rule before an atomic theory explained why those numbers appeared.

A+ · Magneto-optics

Kerr: magnetization-dependent polarization in reflected light

Magnetizing an iron mirror changes the polarization of light reflected from it. Kerr compared light extinction and the effects of reversing magnetization, changing incidence and rotating the polarizing apparatus. His 1877 and 1878 papers established a family of reflection effects, including changes that cannot be described simply as rotation of a still-linear polarization.

S- · Physical optics

Brewster: connecting the polarizing angle to refractive index

The angle at which reflected light is most strongly polarized is connected to refractive index. Brewster compared transparent materials and related the tangent of the polarizing angle to their index. He also connected this angle with a right angle between reflected and refracted rays. The work turned a qualitative optical effect into a quantitative relation that can be checked with geometry and material properties.

S · Statistical physics / electrical fluctuations

Johnson–Nyquist electrical thermal noise: measurement and equilibrium theory

An electrical conductor can produce measurable random voltage even when no signal is being sent through it. Johnson measured this thermal noise and investigated how it depends on resistance, temperature and the measuring circuit. Nyquist gave an equilibrium explanation: in the classical regime, a resistor has voltage mean-square contribution 4kTR per unit ordinary-frequency bandwidth. The two separate papers connect an observed limit of sensitive electronics with thermal statistical physics.

S- · Probability and extremal set theory

Erdős: sharp real sign-sum anti-concentration and Sperner extension

For real coefficients |x_i|≥1, at most binomial(n,floor(n/2)) of the2^n signed sums fall inside any open interval of length2. Erdős obtains the sharp bound through Sperner's antichain theorem, removes a logarithmic loss for complex-coefficient disk concentration up to an absolute constant, and proves the associated bound by the r largest binomial coefficients for longer intervals and families without an(r+1)-element inclusion chain.

S- · Quantum foundations and quantum speed limits

Energy variance bounds on quantum evolution

Mandelstam and Tamm related the energy spread of an isolated quantum system to the rate at which an observable changes: ΔH ΔR ≥ (ℏ/2)|d⟨R⟩/dt|. Applying this to the projector onto the initial pure state gives a survival probability of at least cos²(ΔH t/ℏ) up to πℏ/(2ΔH), hence a lower bound on the time to reach an orthogonal state. They also extended the observable inequality to statistical mixtures.

S · Magnetic resonance and coherent spin dynamics

Hahn: nuclear spin echoes and relaxation measurements

Hahn observed nuclear induction echoes after separated radiofrequency pulses and explained how pulse-induced rephasing restores a macroscopic signal from an inhomogeneously dephased ensemble. Echo amplitudes provided measurements of spin relaxation, while a third pulse produced stimulated and secondary echoes. Bloch-equation analysis related the observed decay to relaxation and, in liquids, molecular diffusion through field gradients.

S · Matrix and spectral theory

Schur triangularizes every complex matrix by a unitary change of basis

Schur proves that every finite square complex matrix is unitarily similar to a triangular matrix whose diagonal lists its eigenvalues with algebraic multiplicity. He derives sum |lambda_j|^2 <= sum |a_ij|^2, with equality exactly when a unitary change of basis diagonalizes the matrix, and related bounds on the real and imaginary parts of the eigenvalues.

A+ · Number theory and probability

Copeland–Erdős normality of prime and sufficiently dense integer concatenations

For a strictly increasing positive-integer sequence whose counting function eventually exceeds N^theta for every theta<1, concatenating its base-b representations gives a b-normal real. This proves the prime-concatenation example and the sums-of-two-squares example using the stated counting estimates.

S- · Approximation theory

Bernstein's binomial-expectation polynomial approximation method

For every continuous F on[0,1], the explicit polynomials B_nF(x)=sum_{k=0}^n F(k/n) binom(n,k)x^k(1-x)^(n-k) converge uniformly to F. The original derives this construction as the expected payout from n Bernoulli trials, using continuity and a small tail probability.

S- · Approximation theory

Faber's obstruction to universal uniform polynomial interpolation

For every prescribed triangular array of distinct interpolation nodes in a real compact interval, some continuous function fails to be uniformly approximated by its Lagrange interpolation polynomials. Faber proves the corresponding periodic trigonometric obstruction and derives unbounded interpolation-operator norms, using a constructive continuous-function argument.

S- · Approximation theory and real analysis

Remez sharp polynomial bound from control on a subset of prescribed measure

For a real polynomial p of degree at most n, bounded by k on a measurable subset E of an interval S of length l with measure at least lambda=theta*l, 0<theta<1, the interval supremum is at most k*T_n(2/theta-1). Shifted Chebyshev polynomials on an endpoint interval of length lambda attain the bound.

A · Fixed-point theory

Kakutani's direct common-fixed-point proof and congruent-group generalization

Kakutani gave a direct averaging proof of Markov's common-fixed-point theorem for a commuting family of continuous affine self-maps of a nonempty compact convex subset of a locally convex topological vector space. He also formulated a common-fixed-point theorem for an affine congruent group preserving such a set, with applications to almost-periodic means and an alternative route to Banach's extension theorem.

A+ · Embodied-AI simulation infrastructure

AI2-THOR: an interactive indoor simulation interface for visual AI

An image can show a closed refrigerator, but it cannot reveal what changes when a robot opens it. AI2-THOR connects a simulated indoor world to a Python controller: an agent requests an action, the world applies its rules, and the agent receives a new image and structured information. The 2017 account describes 120 rooms across four household settings, with objects that can be opened, picked up or otherwise manipulated. This makes sequences of perception and action repeatable without requiring a physical robot for every experiment. Its contribution here is the documented simulation resource and interface, separate from the earlier image-target navigation algorithm developed with the platform.

A · Goal-conditioned visual reinforcement learning

Image-target navigation with shared visual representations

Instead of naming a destination, a robot can be shown a photograph of the place it should reach. Zhu and colleagues combine that target image with the current camera view in a shared Siamese network, which processes both inputs using related parameters. An actor–critic policy then chooses movement commands. Sharing representations across destinations allows experience from one route to help another. The paper tests target changes, adaptation to new simulated rooms and a small real-room robot experiment. The distinctive contribution is the goal-conditioned navigation method; the simulator resource and inherited actor–critic and visual-recognition components retain their own credit.

A · Embodied question answering and hierarchical agents

IQA: asking questions that require an agent to look and act

“Is there an apple in the refrigerator?” cannot always be answered from the first camera image. The agent may need to move, open the door and remember what it saw. Gordon and colleagues introduce an interactive question-answering task and a hierarchical system that divides planning, navigation, detection, manipulation and answering. A spatial memory stores observations at locations rather than forcing a single recurrent state to remember everything. Their IQADATA resource supplies automatically generated existence, counting and spatial-relation questions in simulated kitchens. The contribution combines this task design with the specific memory and controller architecture, without separately counting the underlying AI2-THOR engine.

A+ · Machine-learning domain-specific compilation

Tensor Comprehensions: turning tensor formulas into tuned GPU kernels

A new neural-network operation may be easy to write as a formula yet slow to implement efficiently. Tensor Comprehensions provides a compact language for array calculations and a compiler that rearranges their loops, combines operations and specializes code for tensor shapes. An autotuner tries implementation choices and caches useful results. The work connects a high-level mathematical description to CUDA kernels and integrates with PyTorch and Caffe2 through ATen. Its contribution is this language, compiler and tuning pipeline, building on earlier polyhedral compilation, Halide and numerical libraries rather than replacing their authorship.

A · Automated feature engineering

Deep Feature Synthesis: constructing predictors from related tables

A prediction problem often begins with several connected tables: customers, purchases and individual items, for example. Useful inputs may include a customer’s purchase count or the average price of their items, rather than just one table column. Kanter and Veeramachaneni describe Deep Feature Synthesis, which composes transformations and aggregations along table relationships. Their Data Science Machine combines these generated features with selection, preprocessing, model fitting and tuning. The result is a reusable way to automate part of feature construction; “deep” refers to composed features, not necessarily a deep neural network.

A+ · Adaptive-depth sequence architectures

Universal Transformers: repeatedly refining an attention-based state

A standard Transformer applies a sequence of distinct layers. A Universal Transformer instead reuses a transformation across processing steps, allowing its representation to be refined repeatedly. Self-attention lets positions exchange information during that refinement. An adaptive-computation variant can allocate different numbers of steps to different positions. Dehghani and colleagues investigate this combination on language, reasoning and algorithmic tasks. The contribution is the recurrent-depth architecture and its tested variants, rather than the invention of attention, Transformers or adaptive computation themselves.

A+ · Physics-based character animation

DeepMimic: learning simulated movement from example clips

A simulated character can reach a target while moving in an implausible way. DeepMimic combines a task reward with a reward for matching a reference motion, so the policy learns both what to accomplish and how to move. Random starting points within a motion and early termination of unsuccessful attempts help training reach difficult parts of a skill. The work demonstrates dynamic movements and several ways to combine skills. Its contribution is this practical imitation-and-task learning approach, using existing reinforcement-learning machinery rather than introducing PPO itself.

S- · Dexterous robot manipulation

Dactyl: transferring learned in-hand reorientation to a physical robot

The same simulated hand can behave differently when friction, object weight or motor delay changes. OpenAI’s Dactyl work trains across deliberately varied simulations so a recurrent control policy can handle more than one idealized set of conditions. A separately trained vision system estimates an object’s pose from three cameras. The researchers deploy the resulting system on a Shadow Dexterous Hand for block and prism reorientation, while documenting drops, mechanical failures and a remaining simulation-to-reality gap. Credit belongs to the original human research and engineering team, its scoped system and the inherited components it uses.

S- · Robotics simulation and numerical control tools

MuJoCo: a physics engine designed for control optimization

Designing a controller can require evaluating millions of possible movements. MuJoCo makes those repeated physical calculations a central design concern. Todorov, Erez and Tassa combine generalized-coordinate multijoint dynamics, contact-response methods, model compilation and parallel evaluation in an engine aimed at model-based control. The 2012 paper explains both its computational structure and alternative contact formulations. Its contribution is the specific engine and control-oriented approach; prior rigid-body algorithms and later tools built on MuJoCo retain separate credit.

A · Robot learning and remote demonstration infrastructure

RoboTurk: collecting simulated robot demonstrations with a phone

A person can demonstrate a robot-arm movement by moving a smartphone while watching a video stream. RoboTurk connects that familiar input to cloud-hosted robot simulations through low-latency communication. The 2018 platform collects a pilot set of more than 2,200 successful demonstrations and studies whether those examples help reinforcement learning explore sparse-reward tasks. Its contribution is the teleoperation and collection pipeline with its documented learning use, separate from the earlier ideas of imitation learning, WebRTC and PPO.

A+ · Continuous-control benchmark infrastructure

DeepMind Control Suite: comparable continuous-control tasks

A reinforcement-learning result is easier to interpret when the task, observations and reward have a consistent definition. The 2018 DeepMind Control Suite supplies a collection of continuous-control tasks, Python interfaces and baseline evaluations built on MuJoCo. It separates physical domains from task objectives and uses a common reward scale for most benchmark tasks. This makes it easier to compare learning curves and inspect failure cases. The contribution here is the original benchmark resource and interface design, not the invention of MuJoCo or the algorithms evaluated with it.

A+ · Reinforcement-learning representation learning

UNREAL: auxiliary learning tasks that improve a control representation

A game-playing agent learns more than a final score when it also practices useful auxiliary tasks. UNREAL adds pixel-change control, reward prediction and replayed value learning to an A3C agent, sharing parts of the visual and recurrent representation. These extra learning signals help the agent use its experience more effectively in the reported Labyrinth and Atari experiments. The contribution is the combined auxiliary-learning architecture and its finite evaluation, building on existing actor–critic, replay and off-policy methods.

A- · Model-based value prediction

Predictron: predicting value through an abstract internal rollout

A model need not paint every future image to estimate whether a situation is promising. The Predictron learns an internal sequence of abstract states, rewards and discounts, combines predictions at several depths and trains them against return targets. Its internal states need to support useful value predictions rather than reproduce the visible environment exactly. Silver and colleagues test the approach on maze-related predictions and simulated pool. The contribution is this learned value-prediction architecture and its training design.

A · Model-based reinforcement learning

Value Prediction Networks: planning with abstract rewards and values

An observation-based planner tries to predict what it will see after an action. A Value Prediction Network instead learns action-option-dependent changes in an abstract state and predicts rewards, discounts and future values. It can expand several possible options and back up their estimated returns without generating future images. Oh, Singh and Lee combine this lookahead with multistep learning and evaluate it in a collection task and selected Atari games. This adds controlled planning to the abstract-value approach, rather than re-awarding the earlier uncontrolled Predictron.

A+ · Reinforcement-learning evaluation and generalization

CoinRun: separating training levels from generalization tests

An agent may master its training game levels yet struggle with a new layout. CoinRun makes this gap measurable by generating many levels and comparing performance on training sets of different sizes with zero-shot test performance. Cobbe and colleagues use the benchmark to study network size, regularization and visual augmentation, and show that substantial overfitting can persist even with many training levels. The contribution is the 2018 evaluation resource and its controlled comparisons; earlier generalization studies and the algorithms being tested retain separate credit.

A+ · Measure theory and convergence

Pointwise convergence becomes uniform after a small exceptional set is removed

Imagine that each point of an interval settles toward its own final value, but different points settle at different speeds. Egoroff shows that, for measurable functions converging almost everywhere on a finite interval, one can remove a set with arbitrarily small positive measure and obtain uniform convergence on what remains. Uniform means that one sufficiently late stage works for every retained point. Severini had developed the small-exceptional-set mechanism in a 1910 study of convergent orthogonal-function expansions. Egoroff's 1911 note gives the general measurable-sequence statement. The two original papers form one historical contribution family, with separate author roles.

S- · Metric Diophantine approximation

Khintchine: an integral decides how often typical numbers have very close fractions

Fractions approximate irrational numbers, but how often can they meet a chosen accuracy target? Khintchine's 1924 theorem gives a threshold for almost every real number. In the original statement, a positive continuous function f specifies the error bound f(q)/q for denominator q, and x f(x) must decrease. If the improper integral of f diverges, almost every number has infinitely many fractions meeting that bound. If it converges, almost every number has only finitely many. Continued fractions connect the divergent case to earlier estimates of Bernstein. The contribution is this original metric threshold, rather than a claim about every particular irrational.

A+ · Metric number theory and continued fractions

Khintchine: a common geometric mean hidden in almost every continued fraction

A continued fraction represents a number through successive positive integer partial quotients. Individual quotients can fluctuate greatly, yet Khintchine proves that their geometric mean approaches the same absolute constant for almost every number. A more general theorem handles nonnegative functions of the quotients with a specified growth bound; applying it to their logarithms gives the geometric-mean result. The proof uses quantitative estimates of how widely separated quotients approach independence. This makes a precise long-run regularity visible inside irregular-looking expansions. The result strengthens the author's earlier boundedness estimate rather than repeating it.

A+ · Metric number theory and continued fractions

Khintchine and Lévy: the typical exponential growth of continued-fraction denominators

Successive convergents of a continued fraction have denominators q_n. These control both the size of the fractions and their approximation accuracy. Khintchine proves that the nth root of q_n approaches a common absolute constant for almost every number. His argument compares the full denominator ratio with a finite block and controls the truncation error. In a separate paper, Lévy identifies the constant as exp(pi squared divided by 12 log 2). Lévy explicitly credits Khintchine's existence result in a later-added note. This record preserves the existence and evaluation contributions as one result family, rather than inventing a joint paper.

S- · Approximation theory and completeness of function systems

Müntz and Szász: when a sparse collection of powers still approximates every curve

Ordinary polynomials use all whole-number powers. What happens if most powers are unavailable? For increasing positive real exponents p_n, Müntz shows that finite combinations of 1 and x raised to those powers approximate every continuous function on [0,1] exactly when the sum of 1/p_n diverges. Szász later simplifies the proof and extends its scope to complex exponents. When their real parts stay above a fixed positive constant, he obtains an exact corresponding criterion. The contribution identifies a boundary between complete and incomplete approximation systems, building on Weierstrass and Bernstein's question.

A · Metric number theory and constructive specification

Sierpiński and Lebesgue: specifying a number with balanced digits in every base

A normal number has the expected long-run frequencies of digit blocks; absolute normality requires this in every integer base. Borel had already shown that almost every number has this property. Sierpiński supplies an elementary exceptional-interval argument and specifies one such number using the infimum of a carefully defined complement. Lebesgue's companion article explains a complementary selection method using nested decimal intervals and a controllable bound on the lengths excluded. Their papers bridge a bare existence statement and the specification of an individual example. They are separate works in one historical contribution family.

S- · Approximation theory

Jackson: a quantitative speed for approximating Lipschitz functions by polynomials

Weierstrass guarantees that a continuous curve can be approximated by polynomials, but does not give one useful speed for all continuous curves. Jackson adds a regularity condition: the change in the function must be bounded by a constant times the change in its input. For such a Lipschitz function on a compact interval, he constructs polynomials of degree at most n whose largest error is bounded by a constant divided by n. His route first smooths the curve with a fourth-power sinc kernel, then replaces that kernel by a polynomial while tracking error and degree. This supplies a quantitative approximation capability.

S- · Complex analysis

Fabry: sparse coefficients can block analytic continuation around an entire circle

A power series may converge inside a circle while its function can still be continued beyond part of that circle. Fabry develops coefficient and sign-change criteria that can rule this out at every boundary point. His 1896 paper includes explicit quantitative sparsity conditions on the nonzero powers, with the finite positive convergence radius normalized to one. One such condition requires successive exponent gaps, divided by the logarithm of the exponent, to grow without bound. These results enlarge the known families of functions whose convergence circle is a natural boundary, building on Hadamard's earlier work.

S · Harmonic analysis / maximal operators

Hardy and Littlewood: controlling the largest local averages

An average can hide a short burst. What if one looks around every point and chooses the interval with the largest average? Hardy and Littlewood show how to control these maximal averages in one dimension. Their rearrangement comparisons lead to an Lp norm bound p/(p−1) for the one-sided average, when p is greater than one. For their two-direction endpoint-interval maximal function, the corresponding integral bound is twice that factor raised to p. A finite-interval endpoint result also explains why an extra logarithmic integrability condition can control the maximal average when ordinary integrability alone cannot.

S- · Probability / stationary processes

Khintchine: describing stationary fluctuations through a spectrum of frequencies

A fluctuating signal may look irregular while its average and its pairwise correlation remain stable over time. Khintchine builds a theory for this second-order stationary setting. For a real normalized process with the required mean-square continuity, the correlation is a cosine average over a probability distribution of frequencies. He also constructs a process for any such correlation. The distribution can contain individual frequency atoms as well as continuous parts. Using this representation, he studies long-run averages and the separation of persistent oscillations from a continuous-spectrum remainder. Bochner's earlier Fourier representation is an explicit mathematical input.

S · Functional analysis / orthogonal expansions

Riesz and Fischer: a home for limits measured by average squared error

A sequence of curves can settle down in average squared error without settling at every point. Fischer proves that, on a finite interval, a sequence that is Cauchy in this mean-square sense has a square-integrable mean-square limit. Riesz shows that every square-summable list of coefficients can be realized against an arbitrary normalized orthogonal sequence; Fischer independently obtains this using completeness. Together these results connect functions with infinite lists of coordinates. If the orthogonal system is complete, the correspondence describes the whole function space, with functions differing only on a set of measure zero treated as the same.

S- · Integral equations and positive kernels

Mercer: expanding a positive kernel into uniformly convergent building blocks

A kernel assigns a number to each pair of positions. For a real continuous symmetric kernel on a finite closed interval, Mercer connects positivity of its integral quadratic form to nonnegative determinants of all finite sampled kernel matrices. He then proves that a positive-type kernel can be expanded into products of normalized eigenfunctions, with absolute and uniform convergence across the entire closed square. In modern notation each product is weighted by an integral-operator eigenvalue. Integrating along the diagonal gives the associated trace sum. This turns positivity into a strong, controlled expansion rather than simply assuming that an expansion converges uniformly.

A+ · Real analysis

Darboux: a derivative can be discontinuous and still skip no intermediate slope

A derivative measures slope. It is tempting to assume that slopes must change continuously, but this is false. Darboux proves a different constraint: if a finite derivative exists at every point of an interval, it takes every value between any two of its values. The proof subtracts a line with an intermediate slope. The resulting function has an interior extremum, where its derivative vanishes, so the original derivative takes the desired slope. The same paper gives examples showing why this intermediate-value property can survive even when the derivative is discontinuous.

S- · Complex analysis

Hurwitz: why complex zeros survive a locally uniform limit

Approximating a complex analytic function is useful only if its important features remain controlled. Hurwitz proves that when holomorphic functions converge uniformly near every interior point to a limit that is not identically zero, their zeros track the zeros of the limit locally. Around an isolated zero of multiplicity r, choose a small boundary containing no limit zero. All sufficiently late approximants then have exactly r zeros inside, counted with multiplicity. The original paper develops this general tool before using it for Bessel functions and explicitly includes polynomial partial sums of a power series.

A+ · Functional analysis and infinite matrix summability

Schur: when testing against every bounded sequence forces norm convergence

An infinite matrix can turn one sequence of numbers into another. Schur asks when it turns every bounded input into a convergent output. The answer requires the rows to settle coordinate by coordinate and their absolute tails to become uniformly small. Equivalently, the absolute row sums must approach the absolute sum of the limiting row. If the tails remain uncontrolled, his proof builds a bounded test sequence that makes the outputs oscillate. In modern sequence-space language, this gives the Schur property: a weakly convergent sequence of absolutely summable sequences also converges in its norm.

A+ · Functional analysis and summability

Banach and Saks: choosing a subsequence whose running averages settle in norm

A bounded sequence of functions need not approach one function, even if none of its terms grows without limit. Banach and Saks show that in Lp(0,1), for a finite exponent p greater than one, one can select a subsequence whose ordinary arithmetic averages do converge in norm. Their argument first uses an earlier compactness result of F. Riesz to obtain a weakly convergent subsequence, then carefully selects later terms to control partial-sum growth after the weak limit is subtracted. A step-function construction transfers the result to the corresponding space of summable numerical sequences.

A+ · Long-context sequence architectures

Titans: updating a neural memory while reading

A language model can keep a long conversation in its prompt, but attending to that growing text becomes costly. Titans explores another route: a small neural memory learns key–value associations while the sequence arrives. Larger prediction errors produce stronger memory updates, while momentum and adaptive decay help balance recent information with older content. Behrouz, Zhong and Mirrokni combine this changing memory with attention in three different architectures. The contribution is the specified test-time memory design and its reported language and long-context experiments, building on fast weights and earlier test-time training.

A · Recurrent sequence-model design

MIRAS: choosing how a neural memory learns and retains information

Two memory systems can read the same text yet preserve different details. MIRAS makes four design choices explicit: the memory architecture, the objective used to learn associations, the rule for retaining old information and the learning algorithm. The researchers use this perspective to construct Moneta, Yaad and Memora, including variants based on robust losses and different regularizers. Their experiments compare language modeling, recall and other tasks. The contribution is this organizing framework and its demonstrated new variants, rather than invention of associative memory or the optimization tools it combines.

A+ · Continual-learning architectures and optimization

Nested Learning and Hope: memory components that update at different rates

Some information should change quickly, while other knowledge should persist. Nested Learning organizes a model and its learning procedures as interacting optimization processes with different contexts and update rates. Its Continuum Memory System uses several memory components on different schedules. Hope combines that system with a self-referential extension of Titans, allowing parts of its memory processing to adapt while data arrive. The contribution here is the specified multi-timescale memory and Hope design with its reported computational demonstrations, beyond the earlier Titans and MIRAS families.

B+ · External agent memory

PlugMem: turning experience into reusable facts and procedures

An agent that rereads every past action can waste its attention on details that no longer matter. PlugMem extracts two kinds of reusable knowledge: propositions describing facts and prescriptions describing how to accomplish a goal. These connect back to the experience from which they were derived. A retrieval stage selects relevant knowledge, and a reasoning stage condenses it for the agent’s current task. Yang and colleagues test the same basic module on conversational memory, multi-hop questions and web tasks. The contribution is this knowledge-centered memory pipeline and its scoped evaluation.

B+ · External agent memory

MEMORA: keeping an overview without losing the details

A short project summary is easy to search, but may omit the number or exception needed to answer a later question. Xia and colleagues pair a primary abstraction with concrete memory content, then add cue anchors that offer several ways to find the same entry. Their retrieval policy can refine a query, explore connected entries or stop. The work tests whether this combination improves answer quality on conversational-memory benchmarks. Its contribution is the external abstraction-and-cue representation and the specified retrieval methods, distinct from the neural Memora model introduced within MIRAS.

A- · Nonparametric test-time learning

EvoLib: retaining useful skills across test-time problems

Solving a problem can produce a useful procedure or reveal a mistake worth avoiding. EvoLib stores these as modular skills and reflective insights in an evolving library. A new problem retrieves candidate abstractions, the model attempts a solution, and the system updates which abstractions are sampled. Its weighting mechanism considers both immediate usefulness and whether an item helped produce a useful successor. The researchers test this no-weight-update approach on mathematics, coding and interactive tasks. The contribution is the evolving-library algorithm, with its reported comparisons and ablations.

A · Experience-based agent memory

ReasoningBank: learning reusable strategies from successes and failures

An agent may repeatedly make the same mistake even when a previous attempt exposed it. ReasoningBank turns self-judged successful and failed trajectories into short strategy records with a title, description and content. Later tasks retrieve relevant records, and new experiences add further lessons. Memory-aware test-time scaling, or MaTTS, compares parallel attempts or uses sequential refinement to obtain richer experience. Ouyang and colleagues test the combined approach on web navigation and software issues. The contribution is the particular strategy-memory and scaling method, not the general idea that failures can teach useful lessons.

A+ · Language-model context management

MemGPT: managing a conversation beyond the immediate prompt

A language model has limited room for the text it reads at once. MemGPT treats that room as an actively managed workspace rather than the whole memory. The agent can move information between its working context and external stores, search earlier material, handle capacity warnings and continue through tool calls. Packer and colleagues demonstrate this design on conversations and document tasks. The contribution is the explicit virtual-context management architecture and its tested interactions, inspired by operating-system memory management without claiming to invent external storage or retrieval.

A+ · Retrieval-augmented generation

GraphRAG: building community summaries for questions about a whole collection

Finding one relevant paragraph is different from asking what themes run through thousands of documents. GraphRAG extracts entities and relationships, groups them into communities and prepares summaries at several levels. A question can then draw on these summaries through a map-and-reduce process that combines partial answers. Edge, Trinh and colleagues demonstrate the approach on large text collections. The contribution is this graph-and-community summarization pipeline for collection-wide questions, separate from earlier retrieval, community-detection and language-model methods.

B+ · External conversational memory

Mem0: incrementally selecting and updating conversational memories

A long-running assistant may need a few relevant facts rather than an entire conversation history. The 2025 Mem0 paper describes extracting candidate memories, finding related stored items and deciding whether to add, update, delete or ignore each candidate. A graph variant also stores relationships. The researchers report conversational-memory results and query-time costs. The contribution is the specified incremental memory pipeline and its source-bound evaluation, rather than a certification of the current commercial product or ownership of the models it uses.

B+ · External agent memory

A-Mem: connecting and revising notes for an agent

Useful information is not always found by searching for the exact words used when it was stored. A-Mem turns incoming experiences into notes with keywords, tags, contextual descriptions and embeddings. The system finds related notes, creates links and can revise earlier descriptions as new information arrives. Xu and colleagues test this linked-note design across several language models on conversational-memory tasks. The contribution is the specific agent memory construction and evolution method, inspired by human linked-note practices rather than inventing those practices.

A · Hierarchical retrieval-augmented generation

RAPTOR: retrieving both details and summaries from a document tree

A question may need a precise paragraph or an overview spread across several sections. RAPTOR groups document chunks, summarizes the groups and repeats this process to build a hierarchy. Retrieval can consider text from different levels, rather than relying only on the original chunks. Sarthi and colleagues evaluate the design on several question-answering datasets. The contribution is this recursive clustering-and-summary retrieval method, building on existing embeddings, clustering and language models rather than counting each inherited component as a new discovery.

A- · Conversational-memory evaluation

LongMemEval: testing whether assistants can use a long interaction history

An assistant might remember one fact yet miss a later correction, confuse dates or answer a question whose premise is false. LongMemEval creates a structured evaluation of these abilities. Its questions require extracting information, reasoning across sessions and time, handling updates and abstaining when evidence is absent. Wu and colleagues combine curated questions with long interaction histories and study memory indexing, retrieval and reading choices. The contribution is the evaluation resource and its scoped design analysis, rather than an achievement by any model tested on it.

A · Multi-hop information retrieval

HippoRAG: following a retrieval graph to connect distant evidence

A multi-hop question can require facts that are far apart in a collection. HippoRAG extracts a graph from passages, links related entities and uses a personalized PageRank procedure to spread relevance from the query’s entities. It then maps that signal back to passages for the answering model. Gutiérrez and colleagues test the combination on multi-hop question answering. The contribution is the specified graph-based retrieval system and its evaluation; the memory analogy is inspiration for a computing method, not a new biological discovery.

B+ · Graph-augmented retrieval

LightRAG: using both local details and broader graph relationships

Searching for one entity and asking about a collection-wide relationship require different clues. LightRAG uses a graph of extracted entities and relationships alongside vector retrieval, with lower-level entity keys and higher-level relation keywords. It combines relevant graph information with original text chunks to help generate an answer. Guo and colleagues also describe merging new material into the index. The contribution is this dual-level retrieval and incremental indexing design, separate from GraphRAG and earlier graph and vector methods.

A · Adversarial image generation

GigaGAN: scaling a fast generator without losing editable image styles

Generating an image in one network pass is attractive, but simply making a GAN wider can destabilize training. GigaGAN combines a bank of filters selected for each example, attention between image regions and words, and training signals at several image scales. A base generator makes a small image, and a separate text-conditioned upsampler adds resolution. Kang and colleagues demonstrate billion-parameter-scale adversarial generation and editable latent representations. The contribution is this specified architecture and its reported experiments, building on GANs, StyleGAN, CLIP and earlier attention and dynamic-filter methods.

A- · Adversarial image generation

StyleGAN-T: making text-conditioned GANs larger and easier to steer

A GAN can turn a random seed into an image quickly, but open-ended text adds a much harder conditioning problem. StyleGAN-T revises the synthesis network and discriminator, incorporates pretrained visual and text features, and alternates generator training with adaptation of the text encoder. Per-prompt truncation moves a latent sample toward a typical sample for that prompt, trading variety for alignment. Sauer and colleagues demonstrate the combined design at large scale. The contribution is the specific adversarial image system, rather than invention of its inherited GAN or pretrained representation components.

B+ · Adversarial image generation

GALIP: adapting a frozen vision model for fast adversarial image generation

A large pretrained model can supply useful visual features without being retrained from scratch. GALIP places frozen CLIP representations inside both sides of a text-conditioned GAN. Small trainable components translate text and noise into suitable visual features, while a companion discriminator combines information from several layers. Tao and colleagues test this bridge design on image-generation tasks. The contribution is this integration and its reported experiments; the pretrained model, adversarial learning and earlier conditioning techniques retain their separate credit.

A+ · Geometric computer vision

DUSt3R: predicting a shared 3D map from two photographs

Matching photographs usually starts by finding image correspondences and estimating cameras. DUSt3R instead predicts a three-dimensional point for each pixel in two images, expressing both maps in the first camera’s coordinate frame. A learned confidence signal weights the predictions, and a later alignment procedure combines overlapping pairs. Wang and colleagues show how this representation supports depth, matching and camera estimation. The contribution is the learned pointmap formulation and its multi-view alignment method, building on existing transformer pretraining and supervised geometry data.

A · Geometric computer vision

MASt3R: using 3D predictions to find stronger image matches

Two pixels may look similar yet refer to different objects. MASt3R extends DUSt3R by learning local image descriptors together with three-dimensional geometry. A sampled reciprocal-neighbor search and coarse-to-fine matching procedure then find correspondences efficiently. Leroy, Cabon and Revaud use these matches in localization and reconstruction pipelines. The contribution is the geometry-aware descriptor and matching design with its reported evaluation, distinct from DUSt3R’s earlier pointmap contribution and from inherited contrastive learning and camera solvers.

A- · Dynamic-scene computer vision

MonST3R: reconstructing a moving scene from a video

A moving object violates the assumption that every image shows the same fixed world. MonST3R adapts DUSt3R to predict a pointmap for each time step, using posed videos and depth labels to train its decoder and prediction heads. A later procedure combines these maps with camera smoothness and optical-flow checks over regions estimated to be static. Zhang and colleagues demonstrate dynamic-scene geometry and camera estimation. The contribution is this time-dependent pointmap adaptation and video alignment system, rather than a new award for the inherited DUSt3R model.

A- · Geometric reconstruction and rendering

Splatter Image: predicting an object as an image-shaped set of 3D Gaussians

A single picture hides most of an object’s back and sides. Splatter Image uses a two-dimensional image network to predict a small colored three-dimensional Gaussian for each input pixel. Their positions, shapes and opacity together form a renderable object representation. A multi-view extension combines predictions using relative camera poses. Szymanowicz, Rupprecht and Vedaldi demonstrate fast object reconstruction and rendering. The contribution is this image-shaped Gaussian prediction design, building on earlier Gaussian rendering rather than inventing that representation.

A · Geometric reconstruction and rendering

LRM: learning to reconstruct an object from one image at scale

A model can learn likely three-dimensional structure from many examples, then propose a new object quickly. LRM combines a pretrained image encoder with a camera-conditioned transformer that predicts three feature planes. A small neural renderer reads these planes to produce views or support mesh extraction. Hong and colleagues train this image-to-3D system on a large synthetic-and-real multi-view corpus. The contribution is the scaled reconstruction architecture and its demonstrated object generalization, with separate credit for inherited image features, transformers and neural rendering.

A · Geometric reconstruction and rendering

pixelNeRF: predicting new views using image-aligned features

A neural radiance field describes how a scene looks along viewing rays, but fitting one from scratch for every object can be slow. pixelNeRF conditions this description on features extracted from input images. Each three-dimensional query is projected into the input camera, where the network samples nearby image features; features from several posed images can be pooled. Yu, Ye, Tancik and Kanazawa train across scenes to learn useful object priors. The contribution is this image-conditioned radiance-field method, separate from the original NeRF formulation.

S- · Quantum information and coding

Calderbank, Shor and Steane: quantum codes from nested classical codes

Compatible nested binary linear codes produce a quantum code whose bit- and phase-error syndromes can be corrected without measuring the encoded information. The construction corrects arbitrary errors on a bounded number of physical qubits and gives asymptotically positive-rate families for a small fixed correctable error fraction.

A+ · Quantum communication and entanglement

Bennett et al.: distilling noisy entanglement for faithful teleportation

Local operations coordinated by classical messages can distill fewer high-quality entangled pairs from many imperfect two-qubit pairs whose singlet fidelity exceeds one half. The work introduces two-way recurrence purification and seeded asymptotic breeding, providing entanglement that can support faithful teleportation across a noisy link.

S- · Quantum information theory

Bennett et al.: connecting one-way entanglement distillation and quantum error correction

The work relates one-way entanglement purification to quantum channel coding and shows that free forward classical messages do not increase unassisted quantum capacity. For Bell-diagonal states and their associated generalized depolarizing channels, the reversible state-channel construction identifies one-way distillable entanglement with quantum capacity.

S- · Models of quantum computation

Raussendorf and Briegel: universal computation by measurements on cluster states

A sufficiently large prepared cluster state supports universal quantum computation through adaptive single-qubit measurements. The construction realizes wires, arbitrary one-qubit rotations and controlled gates, while tracking measurement-dependent Pauli byproducts with classical processing.

S · Quantum error correction and finite symplectic geometry

Gottesman and Calderbank et al.: the stabilizer framework for quantum codes

Commuting Pauli operators with a consistent joint eigenspace define quantum coding spaces. Their commutation and coset structure supplies error syndromes and an algebraic correction criterion, unifying earlier CSS constructions and enabling additional quantum codes. Gottesman and the separate Calderbank-Rains-Shor-Sloane paper develop complementary formulations.

S- · Quantum information and entanglement theory

Peres and Horodeckis: partial-transpose and positive-map separability criteria

Every finite-dimensional bipartite separable state has positive partial transpose. The Horodecki positive-map characterization proves that this necessary test is also sufficient for 2x2 and 2x3 systems; in general separability is equivalent to positivity after applying every positive map to one subsystem.

S- · Quantum information and entanglement distillation

Horodeckis: explicit PPT-entangled states and undistillable bound entanglement

Paweł Horodecki constructed explicit entangled states with positive partial transpose in 3x3 and 2x4 dimensions using a range criterion. The 1998 Horodecki paper proves that distillability requires a negative partial transpose: PPT states remain PPT under tensor powers and local operations with classical communication, hence these entangled states cannot be distilled into singlets.

S- · Quantum information and channel capacities

Hastings: minimum-output entropy and Holevo additivity counterexample

A probabilistic construction gives finite-dimensional quantum channels E and a complex-conjugate partner with minimum output von Neumann entropy strictly below the sum of the individual minima on their tensor product. Combined with the inherited equivalence of additivity questions, this disproves general Holevo single-letter additivity and shows that entangled block inputs can matter for classical communication.

S- · Quantum information and entanglement measures

Wootters: exact entanglement-of-formation formula for arbitrary two-qubit states

For every two-qubit density matrix rho, its convex-roof entanglement of formation equals h2((1+sqrt(1-C^2))/2), where C=max(0,lambda1-lambda2-lambda3-lambda4) and the ordered lambda values are the square roots of the eigenvalues of rho times its spin flip. An optimal decomposition exists with at most four pure states.

A- · Neutron stars and X-ray astronomy

NICER pulse-profile analyses constrain the mass and radius of PSR J0030+0451

Two analyses of NICER X-ray pulse profiles for the millisecond pulsar PSR J0030+0451 inferred its mass, radius and emitting-region geometry. Under their selected models, Riley and colleagues reported an equatorial radius of 12.71 +1.14/−1.19 km and mass of 1.34 +0.15/−0.16 solar masses; Miller and colleagues reported 13.02 +1.24/−1.06 km and 1.44 +0.15/−0.14 solar masses. These quoted marginal uncertainties are 68% credible intervals.

A+ · Atomic and molecular physics / laser cooling

Direct laser cooling of an SrF molecular beam

Shuman, Barry and DeMille used laser light to cool the sideways motion of a beam of strontium monofluoride molecules. Changing the light detuning and magnetic field produced different Doppler and Sisyphus cooling patterns in the observed fluorescence. Their simulations estimated a transverse temperature of about 5 millikelvin in the Doppler regime and about 300 microkelvin in the Sisyphus regime.

A+ · Atomic and molecular physics / laser cooling and trapping

Three-dimensional magneto-optical trapping of SrF molecules

Barry and colleagues confined strontium monofluoride molecules in a three-dimensional magneto-optical trap. Reversing the trapping conditions and observing the response of displaced clouds helped test whether the trap supplied a restoring force. The authors estimated about 400 molecules and reported a 56 ± 4 millisecond lifetime in the stated conditions.

A · Atomic and molecular physics / polyatomic laser cooling

Sisyphus laser cooling of a triatomic SrOH molecular beam

Kozyryev and colleagues used Sisyphus laser cooling to reduce the sideways motion of a beam of strontium monohydroxide, a molecule containing three atoms. They used vibrational repumping and changed the laser detuning to distinguish cooling from heating. The 2016 author preprint gives an estimated final transverse temperature of about 700 microkelvin; the 2017 published article gives about 750 microkelvin.

A+ · Atomic and molecular physics / polyatomic laser cooling and trapping

Magneto-optical trapping and subsequent sub-Doppler cooling of CaOH molecules

Vilas and colleagues confined calcium monohydroxide molecules in a radiofrequency magneto-optical trap and measured the response of the cloud after a push. They estimated 20,000 ± 5,000 trapped molecules. After switching off the trapping field, a separate optical-molasses stage cooled the sample to 110 ± 4 microkelvin.

A- · Atomic and molecular physics / laser cooling

Three-dimensional optical molasses cools CaF molecules below the Doppler limit

Truppe and colleagues trapped calcium monofluoride molecules, then switched the trap field off and applied three-dimensional optical molasses. Expansion images gave a temperature of 52 ± 2 microkelvin for the stated measurement, below the relevant Doppler limit. The work improved access to colder molecular samples.

A · Atomic and molecular physics / single-particle trapping

Single laser-cooled molecules are trapped and imaged in an optical tweezer array

Anderegg and colleagues loaded individual calcium monofluoride molecules into five optical tweezers and used fluorescence to identify occupied sites. In the reported setup, the average loading probability was about 34% per trap; the authors obtained 92% detection fidelity under optimized imaging conditions. The team also studied loss associated with collisions.

A- · Atomic and molecular physics / conservative trapping and cooling

Laser cooling remains effective for molecules held in an optical dipole trap

Anderegg and colleagues showed that laser cooling could remain effective while calcium monofluoride molecules were held by light in an optical dipole trap. Simultaneous cooling increased the number loaded by up to a factor of five, and a heating-and-recooling test brought the trapped sample back to about 60 microkelvin.

A+ · Gravitation and relativity

Cassini radio-frequency test of solar-system space curvature

Bertotti, Iess and Tortora analyzed multifrequency radio signals sent to and from the Cassini spacecraft near the Sun. Their 2003 fit reported the post-Newtonian parameter γ = 1 + (2.1 ± 2.3) × 10⁻⁵, consistent with the general-relativistic value within the reported uncertainty.

A+ · Quantum foundations and measurement theory

Frauchiger and Renner formulate an incompatibility among three rules for quantum agents

Frauchiger and Renner proposed a thought experiment in which four agents reason about one another using quantum theory. The authors argue that three stated rules about certainty, consistency and individual outcomes cannot all hold in their protocol. The example has prompted continuing debate about how quantum descriptions apply to observers.

B+ · Condensed matter physics

Spin–lattice model for the phonon Hall effect in paramagnetic dielectrics

Sheng, Sheng and Ting proposed a spin–lattice model for the phonon Hall effect in a paramagnetic dielectric. They used a model of acoustic phonons and magnetic ions to calculate a sideways thermal response and compared aspects of that response with earlier measurements.

A- · Condensed matter physics

Phonon band topology and the thermal Hall response

Zhang and colleagues described a model phonon Hall response using the geometry of phonon bands. In their two-dimensional lattice model, band touchings and changes of topological band numbers can occur as an effective field varies.

A · Condensed matter physics

Energy magnetization corrections to thermal transport

Qin, Niu and Shi developed formulas for energy magnetization and explained how circulating equilibrium currents affect thermal transport coefficients. In a noninteracting anomalous Hall example, the corrected calculation avoids a low-temperature divergence and recovers the expected relation between electrical and thermal response.

S- · Astrophysics

The large redshift of the radio source 3C 273

Maarten Schmidt identified broad spectral lines of the radio source 3C 273 as redshifted emission lines, with a common shift of about 0.158. The result made a distant, exceptionally luminous object a compelling interpretation and helped establish quasars as a new class of astronomical object.

B+ · Neutrino interactions and precision beta spectroscopy

KATRIN constrains additional neutrino interactions through the tritium beta spectrum

The KATRIN collaboration fitted an effective description of additional neutrino interactions to about four million electrons recorded in its second tritium measurement campaign. The analysis found no significant spectral distortion beyond its reference model and reported confidence regions for selected light- and heavier-neutrino interaction parameters. It extended endpoint spectroscopy to interaction searches using an existing experimental dataset.

B+ · Quantum optics and conditional weak measurements

A post-selected optical measurement yields negative conditional atomic-excitation response

Angulo and colleagues measured the small phase shift of an off-resonant probe caused by resonant light passing through a cold rubidium cloud. Comparing probe traces with and without a later photon detection isolated the inferred contribution of an extra transmitted photon. For longer, narrower-band pulses, its integrated response had the opposite sign to the average-photon response. The authors interpreted this result as evidence for a negative conditional atomic-excitation time related to anomalous group delay.

B+ · Matter-wave coherence and atom–molecule association

Molecular diffraction supports phase doubling and reactive pair correlations

Nagata and colleagues used optical-lattice diffraction to probe coherence during association of cesium atoms into molecules. They reconstructed a molecular spatial phase close to twice the imprinted atomic phase, with a small correction from unequal reaction couplings. Molecular momentum populations also yielded a negative parity and a positive entanglement witness within their coherent symmetric-pair model. This extends earlier population-oscillation evidence to phase transfer and reactive pair correlations.

B+ · Molecular quantum gases and finite two-dimensional condensation

Density response supports a finite two-dimensional condensate of bosonic dimers

Zhang, Chen and colleagues associated Bose-condensed cesium atoms into weakly bound, rotationally excited Cs2 molecules in a finite two-dimensional trap. Molecular density responses to calibrated potentials agreed with thermal and high-density Bose-gas equations of state. The inferred temperature and phase-space density supported a molecular condensate in the predicted superfluid regime. Suppressed collisional loss allowed local equilibration studies and measurements of dissociation near the resonance. The 2020 preprint preceded the 2021 publication.

A- · General relativity and small-body motion

A geodesic limit for sufficiently small self-gravitating bodies

Ehlers and Geroch proved a geodesic-limit theorem that permits a small body to carry its own gravitational field. Around a prescribed timelike curve, their hypotheses require arbitrarily localized nonzero bodies satisfying the dominant energy condition, with metrics and connections arbitrarily close to a smooth background. Under those conditions the limiting curve must be a geodesic of that background. The proof also applies to a conserved symmetric matter tensor satisfying the same support and energy conditions.

A- · Condensed matter / quantum geometry and nonlinear transport

Quantum-metric-related nonlinear electrical transport in antiferromagnetic MnBi2Te4

Two independent experiments reported low-temperature second-order electrical responses in even-layer antiferromagnetic MnBi2Te4 whose signs reverse with prepared antiferromagnetic order. Gao and colleagues engineered black-phosphorus interfaces and supported a predominantly nonlinear Hall response through symmetry, conductivity scaling and frequency-mixing controls. Wang and colleagues measured transverse and longitudinal nonlinear responses in four- and six-layer devices, including current-direction-dependent DC resistance. Their models attribute major contributions to energy-weighted quantum-metric geometry.

A- · Condensed matter physics / antiferromagnetic thermoelectric transport

Large anomalous Nernst response and transverse heat transport in Mn3Sn

Independent teams measured a sizable, hysteretic transverse thermoelectric response in the noncollinear antiferromagnet Mn3Sn near room temperature despite its small net magnetization. Ikhlas and colleagues reported a remanent Nernst signal of about 0.35 microvolt per kelvin at 300 K in one crystal. Li and colleagues additionally measured anomalous thermal Hall transport and found its ratio to electrical Hall transport approximately consistent with the Wiedemann–Franz value over their measured high-temperature magnetic phase. Berry-curvature calculations and transport comparisons supplied an interpretation of the response.

B+ · Atomic and fundamental physics / leptonic-atom microwave spectroscopy

Muonium Lamb-shift and isolated excited-state hyperfine spectroscopy

The Mu-MASS collaboration used a low-energy muon beam, carbon-foil muonium production and microwave-induced depletion of metastable atoms to measure the muonium n=2 Lamb shift. Ohayon and colleagues reported 1047.2±2.3(stat)±1.1(syst) MHz. Janka and colleagues then measured the isolated 2S1/2,F=0 to 2P1/2,F=1 transition at 580.6±6.8 MHz, deriving a Lamb shift of 1045.5±6.8 MHz and, together with the earlier transition measurement, a 2S hyperfine splitting of 559.6±7.2 MHz. The later line-shape analysis also identified a contribution from muonium in the n=3 excited state.

B+ · Atomic and fundamental physics / unstable-atom microwave spectroscopy

Pulsed-beam muonium hyperfine spectroscopy and time-domain Rabi analysis

The MuSEUM collaboration demonstrated near-zero-field muonium ground-state hyperfine spectroscopy at J-PARC using a pulsed muon beam and detectors designed for high event rates. Kanda and colleagues reported a frequency-scan result of 4463.302±0.004 MHz. Nishimura and colleagues developed an analysis of the time-dependent Rabi signal that jointly fits frequency detuning and microwave-field strength, and applied it to later data to obtain a zero-density hyperfine interval of 4,463,301.61±0.71 kHz, with the quoted uncertainty statistical. Their simulations identified conditions in which concentrating measurements at a suitable detuning could improve statistical precision.

B+ · Atomic theory / bound-state quantum electrodynamics

Analytic arbitrary-mass pure-recoil corrections for two-fermion atomic S states

Adkins, Gomprecht, Li and Shinn obtained analytic pure-recoil energy corrections at order (Zα)^6 for Coulombic S states of two spin-1/2 particles, retaining the full dependence on their mass ratio. Their calculation combines nonrelativistic-QED contributions with relativistic matching integrals expressed through harmonic polylogarithms, and gives both spin-averaged and hyperfine corrections. The result connects unequal-mass systems such as muonium to the equal-mass positronium limit and identifies corrections to earlier mass-ratio expansions.

B+ · Atomic and fundamental physics / positronium microwave spectroscopy

Positronium fine-structure spectroscopy and diagnosis of asymmetric resonance lines

Gurung and colleagues used laser-prepared metastable positronium, microwave transitions and annihilation-time detection to study the n=2 fine structure. Their 2021 analysis reported 18,501.02±0.57(stat)±0.323(syst) MHz for the 2³S₁ → 2³P₀ interval, approximately 4.2 standard deviations above its cited QED prediction under that error budget. The J=1 and J=2 spectra revealed asymmetric lines. A subsequent model by Akopyan and colleagues showed that frequency-dependent microwave reflections could produce shifts of several MHz, including shifts of apparently symmetric lines, exposing a systematic uncertainty beyond the earlier budget.

B+ · Atomic and fundamental physics / positronium spectroscopy

Positronium microwave field diagnostics and fine-structure measurement with a redesigned apparatus

Sheldon and colleagues observed that the apparent positronium 2³S₁ → 2³P₂ transition frequency changed when a free-space microwave horn was rotated, even when the spectral lines showed little measurable asymmetry. They then measured the interval in a redesigned waveguide apparatus with reduced chamber reflections, reversed microwave directions and a retroreflected excitation laser. Averaging the two directions gave 8627.94±0.30(stat)±0.91(syst) MHz, within 1.3 standard deviations of the cited QED value. These experiments established practical diagnostics for microwave-field distortions while retaining a substantial unresolved direction-dependent systematic error.

B+ · Atomic and fundamental physics / positronium beam methods

Production and characterization of an energy-tunable continuous metastable positronium beam

Newson, Babij and Cassidy produced a continuous beam containing metastable 2³S₁ positronium through charge-exchange collisions between positrons and xenon. Two position-sensitive detectors measured the beam profiles, and microwave-induced 2³S₁ → 2³P₂ transitions reduced the surviving count rate, identifying the metastable component. With flight-decay and saturation corrections, the authors estimated a metastable fraction of up to about 10% of the positronium beam under their chosen conditions. The measured beam properties and a preliminary single-waveguide spectrum supported its proposed use in separated-field spectroscopy.

B+ · Atomic and fundamental physics / precision muonium spectroscopy

Microwave measurement of the muonium 2S–2P3/2 interval

Blumer and colleagues measured the muonium 2S₁/₂–2P₃/₂ interval using microwave-induced depletion of a metastable beam and coincidence detection of Lyman-alpha photons. Five muonium scans with different powers, moderator gases and propagation directions gave 9871.0±7.0 MHz. Hydrogen reference measurements and simulated microwave fields supported the line-shape analysis. Combining the result with an earlier Lamb-shift measurement yielded an inferred 2P fine-structure interval of 10918.2±7.4 MHz.

B+ · Atomic and fundamental physics / optical spectroscopy and velocity-sensitive detection

Pulsed positronium 1S–2S spectroscopy with Rydberg field-ionization detection

Heiss and colleagues combined pulsed two-photon positronium 1³S₁ → 2³S₁ spectroscopy with excitation of surviving 2S atoms to the 20P Rydberg state and subsequent field ionization. Time-of-flight detection supplied velocity-distribution information for joint fits of spectral profiles and Doppler shifts. Two experimental runs gave a combined interval of 1,233,607,210.5±49.6 MHz, about 40 parts per billion. The second run added an optical frequency comb and a pulse-by-pulse laser-chirp measurement.

B+ · Particle physics / quantum correlations

Hyperon decay angular correlations and model-assisted Bell-like tests

The BESIII Collaboration measured proton–antiproton angular correlations in J/psi radiative decays producing Lambda–anti-Lambda pairs. An amplitude analysis separated spin-singlet contributions from backgrounds, and the corrected angular distribution agreed with the singlet-state model. Selected decay geometries supported a Bell-like comparison for massive particles; the authors reported a 5.2-sigma Clauser–Horne-type comparison under their reconstruction and statistical assumptions.

B+ · Condensed matter / moire electronic phases

Local magnetic imaging and gap estimates in fractional Chern insulators

Redekop and colleagues used a nanoscale SQUID sensor to image magnetic fringe fields in twisted MoTe2 devices at 1.6 kelvin. Density-dependent magnetic features appeared near several fractional fillings, while spatial reconstruction mapped magnetization and disorder across the devices. Assuming the Chern number inferred from earlier transport, the reconstructed magnetization change near filling −2/3 implied a local thermodynamic gap of about 7 meV. The work supplied local magnetic evidence complementary to transport and optical studies of fractional Chern insulators.

B+ · Condensed matter / topological electronic imaging

Local imaging of insulating bulk and conducting fractional-Chern edges

Ji and colleagues used exciton-resonant microwave impedance microscopy to image a dual-gated twisted MoTe2 device at zero magnetic field. Near fillings −2/3 and −3/5, spatial maps showed a suppressed bulk response surrounded by enhanced edge response, supporting the expected bulk–edge structure of fractional Chern insulators. A light-activated monolayer WS2 top gate enabled microwave access while retaining electrostatic control. Density and displacement-field scans followed the evolution between bulk-insulating, edge-enhanced and metallic regimes.

A · Condensed matter analogues / disorder and topology

Disorder induces topological responses in photonic lattices and atomic wires

Two independent experiments probed the predicted topological Anderson regime, where adding disorder can produce topology. Stützer and colleagues observed directional edge propagation emerging in a previously trivial, detuned array of helical optical waveguides. Meier and colleagues engineered disordered hopping between atomic momentum states and measured a mean chiral displacement whose finite-time evolution supported disorder-driven topology. Their complementary platforms showed how controlled disorder can create, as well as destroy, topological responses.

A+ · Condensed matter theory / disorder and topology

Disorder can create a topological insulator in quantum-well models

Li, Chu, Jain and Shen predicted a disorder-induced topological regime in numerical models of HgTe quantum wells, including wells whose clean band structure was not inverted. Calculated conductance plateaus and spin-resolved transmission supported conducting helical edges. Groth and colleagues explained how disorder, together with quadratic momentum terms in the effective Hamiltonian, can reverse the topological mass. Their effective-medium calculation accounted for the weak-disorder onset in finite samples and distinguished it from the strong-disorder localization transition.

S- · Condensed matter theory / quantum spin constraints

Higher-dimensional spin constraints rule out a unique ground state with a size-independent gap

Hastings extended the Lieb–Schultz–Mattis argument to higher-dimensional local quantum spin systems by combining separated twists with locality estimates. For the specified lattice families with a half-odd-integer spin per transverse column, a unique ground state has an excitation gap bounded by a constant times log(L)/L. Nachtergaele and Sims later gave a detailed rigorous proof with explicit geometric, interaction and symmetry hypotheses. The result restricts the possible low-energy structure of these many-body systems.

A+ · Condensed matter theory / one-dimensional interacting particles

One-dimensional filling constraints connect electron counting to low-energy excitations

Yamanaka, Oshikawa and Affleck used a nonperturbative twist argument to connect filling and translation symmetry to low-energy excitations in one-dimensional interacting electron systems. The construction fixes the momentum of a low-energy state, including a Kondo-chain counting relation that includes localized spins. Tasaki later supplied a self-contained local-twist extension: under the stated density-fluctuation and correlation conditions, local operations construct orthogonal low-energy states, and arbitrarily many such states occur below any fixed positive energy threshold in sufficiently large systems.

A+ · Condensed matter theory / crystalline many-body constraints

Non-symmorphic crystal symmetries obstruct trivial insulators at selected integer fillings

Parameswaran, Turner, Arovas and Vishwanath extended filling constraints on insulating states to non-symmorphic crystals, whose symmetries combine point operations with fractional translations. A flux-threading argument shows how a conserved charge can change screw or glide quantum numbers even when the filling per cell is an integer. This rules out a unique symmetry-preserving trivial insulator at selected integer fillings, sharpening the usual fractional-filling obstruction. The paper connects the constraint to band connectivity and gives spin and boson applications.

A · Condensed matter theory / symmetry and interacting insulators

Filling constraints extend to interacting spin-orbit coupled insulators

Watanabe, Po, Vishwanath and Zaletel derived electron-filling constraints for symmetry-preserving, gapped, short-range-entangled insulators while allowing spin-orbit coupling and charge fluctuations. A Schmidt-state argument uses charge conservation and time reversal rather than conserved spin. A second approach places the system on suitable compact flat geometries to strengthen the constraints. Together these methods give necessary filling conditions for all230three-dimensional space groups, with stronger restrictions for non-symmorphic groups.

A+ · Condensed matter theory / spontaneous symmetry breaking

Finite-size towers connect symmetric quantum ground states to spontaneous symmetry breaking

Koma and Tasaki related long-range order in symmetric finite-volume quantum states to families of low-energy states and symmetry-breaking infinite-volume ground states. They constructed charge-ladder trial states for local lattice Hamiltonians with a continuous symmetry. Under additional algebraic and discrete-symmetry assumptions, their excitation-energy bound scales as M squared divided by the number of sites, where M labels the charge displacement. Suitable linear combinations yield infinite-volume ground states with nonzero order parameters. A separate result establishes ergodic broken-symmetry limits for a discrete-symmetry setting with an isolated low-energy doublet.

A- · Condensed matter theory / gaps and incompressibility

A neutral excitation gap forces zero charge susceptibility in local quantum matter

Watanabe connected a gap within a fixed conserved-charge sector to the static response of that charge at zero temperature. For local quantum systems with a U(1) symmetry, a subregion charge fluctuation creates a neutral variational excitation. The boundary cost of this excitation forces charge fluctuations per volume to vanish when the neutral gap stays positive. Combining this with a susceptibility bound gives zero charge susceptibility, without translation symmetry or a quasiparticle description. The result clarifies part of the connection between magnetization plateaus and neutral-excitation constraints.

A- · Condensed matter and field theory / equilibrium currents

Gauge-based Bloch argument constrains equilibrium particle currents and chiral transport

Yamamoto extended the Bloch argument against spontaneous ground-state particle currents using the conserved U(1) vector current and a spatial phase variation. This formulation covers relativistic as well as nonrelativistic settings and clarifies why a homogeneous chiral magnetic transport current cannot be an equilibrium ground-state current in the thermodynamic limit. The paper contrasts this with a maintained chiral imbalance that supports a nonequilibrium current, and with an axial current that can represent spin polarization rather than forbidden vector transport.

S- · Condensed matter theory / one-dimensional symmetry-protected phases

Symmetry-protected entanglement degeneracy characterizes the Haldane phase

Pollmann, Turner, Berg and Oshikawa characterized the Haldane phase through an even degeneracy of its entire entanglement spectrum. Their matrix-product-state analysis relates this degeneracy to how symmetry acts on the Schmidt states. Bond-centered inversion, time reversal or the dihedral group of spin rotations can each protect the nontrivial structure. This identifies the phase even when conventional string order or zero-energy physical edge states are absent. Numerical spin-chain examples and a symmetry-preserving bond-weakening process illustrate the distinction from a trivial phase.

S- · Condensed matter theory / stability of topological phases

Topological quantum order remains stable under sufficiently weak local perturbations

Bravyi, Hastings and Michalakis established a conditional stability result for certain topologically ordered quantum spin systems under sufficiently weak local perturbations. For their class of commuting-projector Hamiltonians, the low-energy spectral band remains separated from higher excitations under the stated conditions.

S- · Cosmology / inflationary fluctuations

Primordial three-point correlations in single-field inflation

Maldacena calculated leading three-point correlations of primordial scalar and tensor fluctuations in a single-field inflation model. He related a limit in which one wavelength is much longer than the others to the scale dependence of the two-point spectrum.

B+ · Condensed matter and quantum materials

Angular negative magnetoresistance in TaAs

Huang, Zhao and colleagues measured angle-sensitive negative longitudinal magnetoresistance in TaAs single crystals, alongside quantum oscillations and Hall transport. They interpreted the narrow aligned-field signal as evidence consistent with a chiral anomaly in a Weyl semimetal.

A+ · Condensed matter and superconductivity

High-temperature superconducting signatures in compressed sulfur hydride

Drozdov, Eremets and colleagues reported sharp resistance transitions, field dependence, isotope shifts and a magnetic response in compressed sulfur hydride, with a reported magnetic onset near 203 K at about 155 GPa. They interpreted the findings as high-temperature superconductivity and proposed a hydrogen-rich phase as the likely source.

B · Fluid dynamics and turbulence

Turbulent-band growth and splitting in channel-flow simulations

Xiong and colleagues simulated pressure-driven channel flow in wide periodic domains and followed localized disturbances into oblique turbulent bands. Their calculations showed band growth, break-up and splitting; near the lower end of their tested range an isolated seed could grow while interactions could still cause turbulence to decay. At higher Reynolds numbers splitting supported spreading in the finite simulations.

S- · Astronomical instrumentation and stellar measurements

Optical stellar intensity interferometry of Sirius

At Jodrell Bank Hanbury Brown and Twiss tested optical intensity interferometry on Sirius, observing a decrease in correlated intensity with projected baseline. A later participant account reproduces four observational signal-to-noise values and reports a best-fit angular diameter of 7.1 ± 0.55 milliarcseconds after a theoretical limb-darkening correction.

S- · Gravitational-wave astronomy

GW170817: gravitational waves from a binary-neutron-star inspiral

The LIGO Scientific Collaboration and Virgo Collaboration reported GW170817, a long gravitational-wave inspiral signal detected by the two LIGO instruments and localized using Virgo data. Its masses and coincident electromagnetic observations support a binary-neutron-star interpretation, opening gravitational and electromagnetic study of the same compact merger.

B+ · Particle astrophysics and dark matter

LZ dark-matter searches: conventional limits and an extended-energy recoil candidate

The LZ collaboration combined 2022 and 2023–24 exposure in a conventional low-energy WIMP search, reporting no excess over expected backgrounds and setting model-dependent interaction limits. A later analysis of the overlapping 2023–24 data extended the recoil window and found one event compatible with a high-energy nuclear recoil; its model scan reported 2.6 sigma global and at most 3.4 sigma local tension with background.

B+ · Superfluidity and quantum fluids

Temperature-dependent pinning and depinning of a single superfluid vortex

Donev, Hough and Zieve used a vibrating wire to follow a single partially attached vortex in superfluid helium. In their rougher cell, pinning became more frequent as temperature rose; a smoother cell showed much less pinning. Varying the wire motion changed the observed decay, and the authors proposed excitation of Kelvin waves as a mechanism that helps a vortex unpin.

B+ · Atom interferometry and gravitation

Simultaneous rubidium and potassium atom-interferometer test of free fall

Albers and colleagues compared the free-fall acceleration of simultaneously operated rubidium-87 and potassium-39 matter-wave interferometers. After correcting estimated systematic shifts, they reported an Eötvös ratio of −1.9 × 10⁻⁷ with combined standard uncertainty 3.2 × 10⁻⁷, consistent with equal acceleration within that uncertainty.

S- · Experimental particle physics

UA1 and UA2 collider observations of W and Z bosons

In 1983, two collaborations at CERN’s proton–antiproton collider reported evidence for the charged W and neutral Z bosons. UA1 and UA2 separately observed high-energy electrons with missing energy consistent with W decay. Later that year, UA1 reported electron and muon pairs near the expected Z mass and UA2 reported electron-pair events consistent with Z decay. The measurements supplied direct evidence for particles predicted by electroweak theory.

S- · Experimental particle physics

Fermilab observes a 9.5 GeV dimuon resonance

In 1977 Herb and colleagues observed a strong 9.5 GeV enhancement in opposite-sign dimuons from 400 GeV proton–nucleus collisions. In a subsequent analysis with approximately 26,000 dimuon events, Innes and colleagues reported two narrow peaks around 9.4 and 10.0 GeV, while treating a possible third near 10.4 GeV as unestablished.

A- · Plasma and fusion physics

Wendelstein 7-X tests optimized stellarator energy confinement

The Wendelstein 7-X team used pellet-fuelled 2018 stellarator discharges to test whether magnetic-field optimization reduced neoclassical energy transport. A team report describes one high-performance discharge with 4.5 MW heating and about 0.23 s energy confinement. From measured density and temperature profiles and modeled transport, the authors infer that similarly scaled less-optimized configurations would have required more heating to sustain the profiles. In a separate longer discharge, stable detached divertor operation with particle exhaust was maintained for over 26 seconds at 5 MW.

S- · Low-temperature and condensed-matter physics

Giauque and MacDougall demonstrate refrigeration by adiabatic demagnetization

Giauque and MacDougall demonstrated cooling by adiabatically demagnetizing gadolinium sulfate. In their 1933 report, a sample beginning near 1.5 kelvin reached an indicated 0.25 kelvin. The method first magnetizes a material while heat escapes, then reduces the field after thermal isolation; its magnetic susceptibility provides temperature information.

A+ · Condensed matter and neutron scattering

Neutron spectroscopy measures lattice vibration dispersion in aluminium

B. N. Brockhouse and A. T. Stewart used neutron spectroscopy on a single crystal of aluminium to probe lattice vibrations. In Brockhouse’s later account, energy-resolved neutron groups measured at different crystal orientations yielded phonon frequency and wave vector through conservation relations. Subsequent measurements and comparison with other laboratories produced dispersion curves along selected symmetry directions and exposed limitations in simple interatomic-force models.

A · High-energy astrophysics

X-ray and gamma-ray pulsations identify Geminga as a neutron-star pulsar

An X-ray observation identified coherent pulsations with a period near 237 milliseconds from the source associated with Geminga. A subsequent EGRET analysis found gamma-ray pulses at the same period, linking the earlier high-energy gamma-ray source to a pulsar. A later NASA account reproduces a pulse-phase profile from the gamma-ray observations and attributes the X-ray and gamma-ray measurements to different teams.

A- · Stellar and galactic astrophysics

Gaia identifies a massive dark companion in the BH3 binary

Gaia’s preliminary astrometric binary solution identified a metal-poor giant in an approximately 11.6-year orbit around an unseen massive companion. Gaia radial velocities and ground-based spectroscopy supported the orbital solution. Assuming the visible star’s modeled mass and a single dark companion, the team inferred a companion mass of 32.70±0.82 solar masses and identified a dormant black hole as the simplest explanation.

A · Astrophysics

Gaia BH1: a Sun-like star orbiting a massive dark companion

Gaia DR3 astrometric selection and follow-up radial-velocity spectroscopy identified a Sun-like star with a massive, optically dark companion. The version-1 joint orbital fit estimated a companion mass of 9.78 ± 0.18 solar masses and a period of 185.63 ± 0.05 days, supporting a dormant black-hole interpretation.

A- · Observational cosmology

BOSS detects an acoustic peak in the Lyman-alpha forest

Using spectra of 48,640 quasars from BOSS DR9, the analysis measured the three-dimensional correlation of Lyman-alpha forest transmission at mean absorber redshift about 2.3 and identified a peak near the expected baryon acoustic scale. This extended the acoustic-distance method to an intergalactic absorption tracer at high redshift.

S · Radio astronomy

Ewen and Purcell detect galactic hydrogen at the 21-centimeter line

Ewen and Purcell observed radio emission from neutral hydrogen in the Milky Way near the 21-centimetre wavelength. Their 1951 report describes a signal concentrated near the Galactic plane, with a measurable frequency shift consistent with relative motion. The result gave radio astronomers a way to study hydrogen beyond regions visible in ordinary light.

S- · Exoplanetary astrophysics

Pulsar timing reveals a planetary system around PSR B1257+12

Arecibo timing of pulses from the millisecond pulsar PSR B1257+12 revealed periodic deviations consistent with two planetary companions, reported by Wolszczan and Frail in 1992. A later participant report describes an additional lower-amplitude periodicity and a fit to the predicted mutual perturbations of the two larger planets, strengthening the planetary interpretation. A 2003 timing analysis by Konacki and Wolszczan used a longer data span and an interaction model to infer the masses and inclinations of the two larger planets.

A+ · High-energy atmospheric physics

Terrestrial gamma-ray flashes observed from orbit

The BATSE instrument on the Compton Gamma Ray Observatory detected brief, hard gamma-ray flashes from directions below the local horizon. The participant report describes at least a dozen events, time profiles and locations, with confirmation by another instrument on the same observatory.

B+ · Gravitational-wave astrophysics

Conditional neutron-star radius and tidal-deformability inference from GW170817

A Bayesian reanalysis of the GW170817 gravitational-wave signal constrained the binary tidal deformability and inferred an approximately common neutron-star radius. Under a shared equation-of-state approximation, electromagnetic location and distance, and three mass priors, the authors reported radius posteriors centered near 10.8 km; their appended erratum corrected the comparison of models with and without the common-equation-of-state constraint.

A · Observational cosmology

CMB gravitational lensing detected through WMAP and radio-galaxy cross-correlation

Smith, Zahn and Doré reconstructed a noisy gravitational-lensing potential from WMAP temperature maps and cross-correlated it with radio-source counts from the NVSS survey. They reported a 3.4σ lensing signal including their modeled systematic errors, an early observational detection of CMB lensing.

A+ · Observational cosmology

Planck reconstructs the CMB lensing potential and its power spectrum

The Planck Collaboration reconstructed a noisy sky map of the cosmic microwave background lensing potential from the first 15 months of temperature data and estimated its power spectrum. Combining the relevant angular scales, the authors reported a lensing signal above 25σ and an approximately 4% constraint on the fiducial spectrum amplitude; cross-correlations with other tracers were also measured.

A+ · Two-dimensional magnetism

Ferromagnetism in a monolayer of chromium triiodide

Polar magneto-optical Kerr microscopy of exfoliated chromium triiodide revealed hysteresis and remanent out-of-plane magnetization down to a single atomic layer. The authors reported an approximately 45 K monolayer ordering temperature and a distinct suppressed low-field signal in bilayer samples, consistent with antiferromagnetic interlayer alignment.

A · Two-dimensional magnetism

Field-sensitive magnetism in few-layer Cr₂Ge₂Te₆

Kerr microscopy of thin Cr₂Ge₂Te₆ flakes revealed a strong thickness and magnetic-field dependence of the magnetic response. Measurements reached bilayer thickness; six-layer samples showed a small remanent Kerr signal, and the characteristic temperature inferred from bilayer response increased from about 28 K to 44 K as the applied field increased from 0.065 T to 0.3 T.

B+ · Stellar astrophysics

Broadband photometry of the cool companion Gliese 229B

Following the 1995 discovery of the cool companion Gliese 229B, Matthews and colleagues measured and reassessed its broadband emission from 0.8 to 10.5 micrometres, revising earlier near-infrared photometry affected by scattered light from the primary star. The observed bands imply a luminosity of (4.9 ± 0.6) × 10⁻⁶ solar luminosities.

B+ · Condensed matter physics

Graphene transport reveals a mesoscopic analogue of strong-field pair creation

Schmitt and colleagues studied transport in six encapsulated graphene devices and reported conductance consistent with a one-dimensional Klein–Schwinger electron–hole pair-creation model near current saturation. Across the device series, a fitted linear extrapolation was approximately 0.18 mS, close to the model’s 0.186 mS value.

B+ · Low-temperature physics

Multiple-frequency tests of anomalous rotation in bulk solid helium

Eyal, Mi, Talanov and Reppy measured bulk solid helium with double- and triple-mode torsional oscillators, separating a dominant frequency-dependent period shift from a smaller extrapolated frequency-independent contribution in some samples. They considered the latter a possible supersolid signature and proposed further discriminating tests.

B+ · Particle physics

CAST searches for solar axions with helium-filled and vacuum helioscopes

CAST used a solar-tracking magnet to search for axion-to-photon conversion. A 2012 helium-buffer run improved limits in selected mass regions near 0.2 and 0.4 eV. Its 2013–2015 vacuum run found no significant excess and reported a 95% upper coupling limit of 0.66 × 10⁻¹⁰ GeV⁻¹ for masses below about 0.02 eV.

B+ · Neutrino physics

Borexino constrains a mantle geoneutrino contribution

Borexino analyzed 3262.74 days of data and obtained a fitted geoneutrino signal of 47.0 terrestrial neutrino units, with approximately 18% total uncertainty under its assumed thorium-to-uranium ratio. Incorporating a model for the local and broader lithosphere, the authors reported a nonzero mantle contribution at 99% confidence.

A+ · Cosmology

BICEP/Keck and Planck foreground analysis and primordial B-mode constraints

A 2015 joint analysis of BICEP2/Keck and Planck polarization maps found substantial Galactic dust contribution to the observed B-mode power and set a model-dependent limit r at pivot 0.05 per Mpc below 0.12 at 95% confidence. A later BICEP/Keck analysis adding 2016–2018 data and using WMAP and Planck maps reported r below 0.036 at 95% under its stated foreground and cosmological model.

A · Observational cosmology

SARAS 3 tests a reported cosmic-dawn absorption profile

The SARAS 3 radiometer measured a sky-averaged radio spectrum and compared it with the absorption profile previously reported by EDGES. With the paper’s foreground and calibration model, its fit disfavoured the earlier best-fitting profile at 95.3% confidence; the authors also tested the wider set of profiles allowed by EDGES.

A · Observational cosmology

EDGES reports a low-frequency sky-averaged absorption profile

Bowman and colleagues reported a fitted absorption-like feature in EDGES low-band radio observations centred near 78 MHz, with a best-fitting width near 19 MHz and amplitude around 0.5 K. The authors interpreted it as a possible redshifted hydrogen signal from cosmic dawn.

A · Observational cosmology

HERA constrains early-universe 21 cm fluctuations

HERA analyzed 94 selected nights of Phase I observations and reported 95% upper limits on the dimensionless 21 cm brightness-temperature fluctuation power of 457 mK² at redshift 7.9 and wave number 0.34 h/Mpc, and 3,496 mK² at redshift 10.4 and 0.36 h/Mpc. The analysis also explored implications for astrophysical heating under specified models.

A- · Observational cosmology

Galaxy ages trace the cosmic expansion history

Jimenez, Verde, Treu and Stern used the upper age envelope of selected SDSS galaxies to estimate the low-redshift expansion rate, finding H₀ = 69 ± 12 km s⁻¹ Mpc⁻¹ in their 2003 analysis. Simon, Verde and Jimenez subsequently combined selected galaxy spectra, including previously analyzed objects and new survey data, to estimate H(z) at nine redshifts and fit a parameterized dark-energy potential; the resulting potential was consistent with a constant within the stated uncertainties.

A+ · Observational astrophysics

A predicted gravitationally lensed supernova image reappears

After four images of supernova Refsdal were observed in 2014 behind galaxy cluster MACS J1149.5+2223, five modeling teams used existing imaging and spectroscopy to construct seven lens models and predicted an additional image. Hubble observations on 11 December 2015 revealed a new source at the predicted location, interpreted as that fifth image. Its early brightness and timing allowed a blind comparison with prior lens-model predictions. A later blinded analysis of the extended light curves reported an SX–S1 delay of 376.0 days with a 16th–84th percentile interval of approximately −5.5 to +5.6 days, using a weighted combination of four fitting methods.

A- · Condensed-matter physics

Complementary X-ray evidence of charge order competing with superconductivity in underdoped cuprates

In 2012 Chang and colleagues used nonresonant hard X-ray diffraction on an underdoped YBa₂Cu₃O₆.₆₇ crystal to identify incommensurate lattice-modulation peaks associated with charge order; the peak weakened below the superconducting transition and increased under an applied magnetic field. Separately, Ghiringhelli and colleagues used resonant soft X-ray scattering near the Cu L₃ edge on underdoped Y- and Nd-based 123 cuprates, identifying a quasi-elastic charge-associated peak near 0.31 reciprocal lattice units. Its intensity and correlation length rose on cooling toward the superconducting transition and fell below it, supporting competition between the measured charge correlations and superconductivity.

S- · Optical physics

Temporal soliton mode locking in a nonlinear optical microresonator

Herr and colleagues reported pulse formation in a continuously driven magnesium-fluoride optical microresonator. Discrete transmission steps and a low-noise radio-frequency beat accompanied different optical spectra. Frequency-resolved optical gating reconstructed a single pulse of about 200 femtoseconds and resolved multiple pulses in other states. Coupled-mode simulations and an approximate driven nonlinear Schrödinger solution associated these states with temporal cavity solitons. The 2013 revised author version added an independent single-shot pulse-spacing check and described tuning and stability of the soliton states.

B+ · Gravitational-wave astrophysics

GW150914 ringdown overtone fits and their statistical dispute

Isi and colleagues fit damped black-hole oscillation models to GW150914 data beginning near the waveform peak and reported evidence for a short-lived overtone together with a fundamental mode. A 2022 reanalysis by Cotesta and colleagues found much weaker overtone support and sensitivity to start time and noise. In 2023 Isi and Farr identified timing and analysis-duration problems in that reanalysis; Carullo and colleagues repeated their analysis with changes, reporting improved agreement for some estimates while maintaining that Bayesian evidence remained weak.

A+ · Gravitational physics

Planetary radar measurements test the solar gravitational time delay

Shapiro and colleagues tested the extra round-trip delay of radar signals passing near the Sun using planetary echoes. Their 1968 preliminary analysis combined orbital modeling with Mercury and Venus observations and reported agreement with the general-relativistic delay within the estimated experimental uncertainty. A later 1971 analysis combined further Haystack and Arecibo measurements and fitted a delay scale of about 1.02 relative to the general-relativistic prediction of 1, with an estimated 0.05 uncertainty including systematics.

A+ · Condensed-matter physics

Real-space imaging of a skyrmion lattice in a thin magnetic film

Yu and colleagues used Lorentz transmission electron microscopy to image magnetic textures in a thin Fe₀.₅Co₀.₅Si film. Under a perpendicular magnetic field, they observed a hexagonal arrangement of swirling in-plane magnetization with roughly 90-nanometre spacing, and tracked its change with field and temperature. A two-dimensional spin-model Monte Carlo calculation supplied a comparison for the observed phase diagram.

A+ · Condensed-matter physics

Superconductivity in layered iron oxypnictide LaOFeP

Kamihara and colleagues reported superconducting behavior in the layered iron oxypnictide LaOFeP. At low temperatures the electrical resistance fell to the measurement limit and the material became diamagnetic; a fluorine-doped sample had a higher transition temperature.

A+ · Condensed-matter physics

Superconductivity near 55 K in fluorine-doped samarium iron oxypnictide

Ren and colleagues reported superconducting signatures in fluorine-doped samarium iron oxypnictide. Electrical resistivity began its transition at 55.0 kelvin and reached the reported zero-resistance level at 52.6 kelvin; magnetic susceptibility showed an onset of diamagnetic response at 54.6 kelvin. These observations extended the experimentally explored transition-temperature range of the layered iron-arsenide family.

S- · Astrophysics

Direct imaging of the HR 8799 planetary system

Marois and colleagues used high-contrast near-infrared imaging at Gemini and Keck to resolve three faint companions of HR 8799. Multi-epoch positions supported common motion with the star and apparent orbital motion, while their colors and luminosities, together with a young system age and evolutionary models, supported planetary-mass interpretations. A later five-author report added images and measured motion of a fourth, closer companion, HR 8799 e.

A+ · Astrophysics

A planetary microlensing event detected by OGLE and MOA

Bond and colleagues analyzed an event independently observed by the OGLE and MOA surveys. Both light curves showed a roughly seven-day deviation from a single-lens profile, including a caustic feature. Their binary-lens fit favored an extreme mass ratio of about 0.0039, supporting a planetary companion to the foreground lens. A later Hubble analysis reported excess blended light and a color-dependent centroid shift consistent with a main-sequence lens star, and combined those data with the microlensing fit to estimate the system properties.

B+ · Condensed Matter Physics

Electron escape from liquid-helium bubble states at a free surface

Rayfield and Schoepe introduced a tunneling interpretation of their earlier measured electron escape from liquid helium in 1971, fitting temperature-dependent trapping data to infer bubble-state properties. In a detailed 1973 study they measured temperature and electric-field dependences in helium-3, helium-4 and mixtures. Their semiclassical model described the reported pure-liquid trends while the mixture results remained anomalous.

B+ · Nuclear Physics

Nuclear transparency in pion electroproduction

Clasie and collaborators measured pion electroproduction on deuterium, carbon, aluminium, copper and gold targets over momentum transfers squared of approximately 1.1–4.7 (GeV/c)². Their extracted nuclear transparency and its target-mass dependence varied with momentum transfer, in better agreement with the specific calculations incorporating color transparency than with the displayed conventional calculations.

A+ · Astrophysics

Parker Solar Probe observes structured slow solar wind and magnetic reversals

During its first 2018 solar encounter, Parker Solar Probe measured slow solar wind with rapid, large magnetic-field reversals, velocity enhancements and plasma waves. Bale and colleagues compared the in-situ measurements with coronal field models and extreme-ultraviolet maps, associating the sampled stream with a small equatorial coronal hole. Their measurements reveal a highly structured near-Sun wind and motivate further study of its acceleration and heating.

A+ · Astrophysics

Infrared day–night brightness mapping of HD 189733b

Knutson and colleagues used the Spitzer Space Telescope to measure an 8-micrometre phase curve of the transiting hot Jupiter HD 189733b over slightly more than half an orbit. They inferred a modest day–night brightness contrast and an eastward offset of the brightest hemisphere, consistent with atmospheric transport of heat. A regularized longitudinal-slice fit gave a coarse brightness map rather than a spatially resolved picture.

A+ · Astrophysics

COBE observations of the cosmic infrared background

Hauser and colleagues analyzed ten COBE DIRBE infrared bands after modeling local foregrounds, reporting isotropic residuals consistent with a cosmic infrared background at 140 and 240 micrometres and upper limits at shorter wavelengths. Fixsen and colleagues used COBE FIRAS spectra and three foreground-separation approaches to estimate the far-infrared background spectrum from 125 to 2000 micrometres, finding consistency with the DIRBE measurements within their stated calibration uncertainties.

A- · Astrophysics

A candidate gravitational microlensing event toward the Large Magellanic Cloud

The MACHO collaboration monitored approximately 1.8 million Large Magellanic Cloud stars and reported a brightening event whose two-color light curve was broadly consistent with gravitational microlensing. Its fitted amplification and approximately month-long characteristic time illustrated the observational search for compact lensing objects suggested by Paczyński.

A- · Astrophysics

A candidate microlensing event toward the Galactic bulge

The OGLE team reported a candidate microlensing event toward the Galactic bulge after surveying approximately 650,000 stars. The selected star brightened and returned to its previous level; a single-lens model fit its light curve with an estimated Einstein-radius crossing time of 23.8 ± 0.9 days. This was a separate direction and event from contemporaneous Large Magellanic Cloud searches.

A- · Condensed Matter Physics

Raman and neutron evidence for unusual magnetic excitations in α-RuCl3

Sandilands and colleagues measured a broad Raman continuum and anomalous phonon line shapes in α-RuCl3. In a separate neutron study, Banerjee and colleagues reported magnetic ordering and an excitation spectrum whose broad component persisted above the ordering temperature. Both teams compared their observations with predictions for proximity to a Kitaev spin-liquid regime.

S- · Optics and photonics

Self-referenced optical comb controls pulse-to-pulse carrier-envelope phase

Jones and colleagues used an octave-spanning mode-locked laser spectrum and self-referencing to stabilize the pulse-to-pulse carrier-envelope phase and the optical frequency comb. They checked relative phase control with a time-domain cross-correlator and measured a rubidium optical reference against a microwave clock.

B+ · Observational astrophysics

A new transient source appears in the Fomalhaut debris system

Kalas and colleagues reported a new compact source in 2023 Hubble images of the Fomalhaut debris system and compared it with an earlier source first reported in 2008. They interpreted the new source and the earlier object as light scattered by dust from separate planetesimal collisions. In 2020 Gáspár and Rieke had reanalysed the earlier Fomalhaut b observations, interpreting the source as an expanding collision-generated dust cloud. The original 2008 report measured the earlier compact source in 2004 and 2006 Hubble images and presented it as an exoplanet candidate. In a 2013 analysis of 2010 and 2012 Hubble images, Kalas and colleagues recovered the earlier source and revised the orbital interpretation using four observing epochs.

B+ · Atomic interferometry and gravitation

A horizontal atom gradiometer tests gravity while suppressing beam-steering noise

Biedermann and colleagues built a horizontal, dual-cesium-atom interferometer and reduced differential noise caused by beam steering through air by enclosing the optical path at low pressure. Moving nearby source masses modulated the measured gravity signal; the authors reported a proof-of-concept sensitivity corresponding to a relative statistical precision of 3 × 10⁻⁴ for a gravitational-constant measurement.

B+ · Quantum optics and atomic ensembles

Cold atoms store and retrieve weak light pulses carrying orbital angular momentum

Veissier and colleagues used electromagnetically induced transparency in cold cesium atoms to store and retrieve weak light pulses in two opposite orbital-angular-momentum modes. Mode-selective detection showed that the retrieved light retained the input mode labels; the authors also tested an equal-weight spatial-mode input. In a later related experiment, Nicolas and colleagues measured coherence and performed tomography on stored orbital-mode qubits, reporting fidelities above a benchmark that accounts for weak coherent inputs and the measured retrieval efficiency.

A+ · Extragalactic astronomy and cosmology

JWST spectroscopy identifies two luminous galaxies at redshifts near 14

Carniani and collaborators used JWST/NIRSpec spectroscopy and NIRCam imaging to examine two early galaxy candidates. Both spectra show strong continuum breaks interpreted as Lyman-alpha breaks, yielding model-fitted redshifts near 14.32 and 13.90 in the first author preprint; the brighter object is spatially extended in the imaging. In a later ALMA follow-up, Schouws and colleagues detected a far-infrared oxygen line from the brighter source and obtained a more precise, consistent redshift.

A+ · Condensed matter theory and topological materials

Predicted topological electronic phases in 1T′ transition-metal dichalcogenide monolayers

Qian, Liu, Fu and Li used first-principles electronic-structure and edge-state calculations to predict nontrivial band topology in six distorted 1T′ transition-metal dichalcogenide monolayers. They calculated a field-driven topological phase transition for monolayer MoS₂ and proposed a layered field-effect device exploiting the predicted edge channels.

S- · Cosmology and cosmic microwave background

Planck full-mission cosmic microwave background cosmological parameter analysis

The Planck Collaboration combined final full-mission cosmic microwave background temperature and polarization power spectra with its lensing reconstruction to constrain parameters of the spatially flat six-parameter base Lambda-CDM model. For the combined Planck TT,TE,EE+lowE+lensing likelihood, the paper gives H0 = 67.36 ± 0.54 km/s/Mpc and matter fraction 0.3153 ± 0.0073, at 68% confidence.

A- · Planetary physics and gravitation

Juno gravity motivates model-dependent Jupiter interior profiles with a dilute core

Wahl and colleagues compared numerical interior structure models against Jupiter’s even gravitational moments from Juno’s first two close orbits. In their model families an extended heavy-element-enriched core, mixed with hydrogen and helium, can improve agreement with the measurements; the authors explored how equations of state and envelope composition change the inferred core and gravitational moments.

A · Gravitational lensing and stellar physics

Astrometric microlensing measures the mass of white dwarf Stein 2051 B

Sahu and colleagues used Hubble observations of the apparent positional shift of a background star as the nearby white dwarf Stein 2051 B passed in front of it. Fitting the astrometric microlensing model and parallax gave a lens mass of 0.675 ± 0.051 solar masses, providing a comparison point for white-dwarf mass–radius models.

B+ · Dark matter detection and particle astrophysics

DAMA/LIBRA annual modulation and a later same-target COSINE-100 test

DAMA/LIBRA phase 2 reported an annual modulation of low-energy single-hit events in six annual cycles, with an exposure of 1.13 tonne-years. A phase-fixed 1–6 keV fit gave 0.0105 ± 0.0011 counts per day per kilogram per keV. A later COSINE-100 analysis with an independent sodium-iodide detector reported a phase-fixed 1–6 keV electron-equivalent amplitude of 0.0017 ± 0.0029 over 6.4 years of operation and compared its results with DAMA/LIBRA. Two additional annual cycles extended the phase-2 dataset to eight cycles and 1.53 tonne-years; the independent COSINE comparison used this later DAMA analysis.

A- · Graphene superlattices and quantum magnetotransport

Brown–Zak quantum oscillations persist above room temperature in graphene superlattices

Transport measurements in aligned graphene–hexagonal-boron-nitride superlattices revealed oscillations periodic in inverse magnetic field that remained visible at 373 K in fields of a few tesla. Their principal maxima followed one flux quantum per integer number of superlattice cells, with a period largely independent of carrier density. Comparison with misaligned devices, capacitance measurements and magnetic-miniband modelling supported an interpretation through recurring Bloch states rather than thermally resolved Landau gaps.

A- · Single-electron charging and mesoscopic electrometry

An electron box reveals gate-controlled quantization of average island charge

Lafarge and colleagues used a capacitively coupled single-electron-transistor electrometer to measure charge changes in a small metallic electron box. Varying the gate voltage produced the sawtooth response expected when the island exchanges electrons in discrete units, with thermal rounding that agreed with a charging-energy model above about 100 mK. The experiment resolved charge quantization in an equilibrium solid-state circuit, including an electron-periodic response when its aluminium electrodes were superconducting.

A- · Superconducting parity and two-electron charge quantization

Electron parity controls charge addition to a superconducting island

Lafarge, Joyez and colleagues used Coulomb-blockade electrometry to measure how electron-number parity changes the free energy of a small superconducting island. In one device, unequal widths of successive charge steps gave the temperature-dependent cost of an unpaired electron. A later device with a larger superconducting gap relative to its charging energy showed charge steps of two electrons at low temperature and field; increasing either restored intermediate or single-electron steps.

A- · Time-resolved single-electron charging and tunnelling

An electrometer resolves individual electron-charge jumps on a metallic island

Lafarge and colleagues monitored a metallic island connected to a reservoir through four tunnel junctions. A coupled single-electron-transistor electrometer resolved discrete potential jumps as individual electrons entered or left the island, with charge remaining fixed between resolved events. Gate sweeps produced a hysteretic charge staircase. The measured switching rate greatly exceeded the simple cotunnelling prediction, exposing a limitation relevant to proposed precision charge-transfer devices.

A- · Ultracold quantum gases and collective atom–molecule dynamics

Density-enhanced collective oscillations couple atomic and molecular condensates

Zhang, Nagata and colleagues observed collective atom–molecule reaction dynamics in an ultracold cesium gas near a narrow Feshbach resonance. After rapid molecule formation and heating, the atomic and molecular populations oscillated for several milliseconds. Higher condensate densities produced faster oscillations. The density scaling and an approximately 20 percent molecular fraction supported a model dominated by coherent three-body recombination. The family was first reported in 2022 and published in 2023.

A · Relativistic field theory and classical particle limits

Tracking stress-energy connects small bodies to geodesic and Lorentz-force limits

Geroch and Weatherall introduced a stress-energy tracking condition that connects smooth extended bodies to point-particle limits. A conserved collection satisfying the dominant energy condition and tracking a timelike curve contains a rescaled sequence converging to a point-mass distribution; the curve is therefore geodesic. A charged extension with uniformly bounded charge-to-mass ratio yields a Lorentz-force limit. Applications characterize optical limits of source-free Maxwell fields and distinguish fixed-parameter Klein–Gordon packets from classical limits allowing their mass parameter to vary.

A- · Nonequilibrium photonic matter and dissipative dynamics

Long-lived switching and hysteresis in a driven microwave cavity chain

Fitzpatrick and colleagues drove a fabricated72-cavity superconducting microwave chain and observed an abrupt transmission change, hysteresis and stochastic switching between long-lived metastable states. Dwell-time statistics gave switching times up to about 60 ms. In a two-state rate model, the inferred slow decay rate reached roughly 10 Hz, far below intrinsic photon and qubit decay rates. Broadband emission and photon bunching further distinguished the regimes. These finite-device observations provided evidence for an approach to a dissipative phase transition.

A · Particle physics / low-emittance muon beams

Radiofrequency acceleration of cooled positive muons to 100 keV

Aritome and colleagues combined thermal-muonium production, laser ionization and electrostatic extraction with a radiofrequency quadrupole to accelerate positive muons to 100 keV. Time-of-flight signals appeared with both resonant laser excitation and radiofrequency power, and quadrupole scans measured the transverse beam emittance. The reported horizontal and vertical normalized emittances were about 0.85 and 0.32 pi millimetre milliradian, respectively, more than two orders of magnitude below simulated incoming-beam values.

A- · Fundamental physics / trapped antimatter and precision spectroscopy

Fast subthermal cyclotron preparation and improved antiproton spin readout

Latacz and the BASE team implemented a double-Penning-trap procedure that repeatedly thermalizes an antiproton’s modified cyclotron motion and measures its energy, stopping when a cold state is found. They reported preparation below an energy-equivalent temperature of 200 millikelvin in about 500 seconds, with a measured thermalization time constant of 4.7±0.4 seconds. A colder prepared antiproton showed clearly separated spin-transition signals, improving nondestructive spin-state identification.

A- · Atomic and fundamental physics / remote ion cooling

Remote sympathetic cooling of a trapped proton through a superconducting circuit

Bohman and the BASE team sympathetically cooled a single proton by coupling it through a superconducting resonant circuit to laser-cooled beryllium ions in a separate Penning trap about nine centimetres away. Frequency spectra and controlled remote heating demonstrated energy exchange. Measurements of energy-dependent proton frequency shifts then showed a temperature reduction reaching 14.4±0.7 kelvin, relative to an effective circuit-noise temperature near 17 kelvin. The experiment extended sympathetic cooling beyond direct short-range Coulomb coupling.

A · Atomic and fundamental physics / muonium spectroscopy

Precision two-photon measurement of the muonium 1s–2s interval

Meyer and colleagues measured the muonium 1s–2s interval using counterpropagating two-photon laser excitation, photoionization and muon detection. Pulse-by-pulse laser diagnostics, an iodine frequency reference and deuterium control measurements supported the analysis of 99 muonium events. After correcting to the hyperfine centroid, they reported a transition frequency of 2,455,528,941.0±9.8 MHz. Comparisons with bound-state quantum electrodynamics provided conditional determinations of the positive-muon mass and constraints on the muon–electron charge ratio.

A- · Atomic and fundamental physics / precision positronium laser spectroscopy

Continuous-wave two-photon positronium 1S–2S spectroscopy with coincidence detection

De Sousa Borges and colleagues measured the positronium 1³S₁ → 2³S₁ interval with continuous-wave two-photon excitation and photoionization by the same laser. Coincidence detection of the released positron and two annihilation photons suppressed background; 1124 selected events from about 12 days supported a transition frequency of 1,233,607,224.1±6.0 MHz, or 4.9 parts per billion. They also developed an approximate semi-analytical line-shape model and compared its fitted centres with their Monte Carlo model and the measured spectrum.

A- · Condensed matter physics / correlated moiré electronic transport

Fractional spin-Hall transport and low-field symmetry diagnostics in twisted MoTe₂

Kang and colleagues measured local and nonlocal transport in small-angle twisted MoTe₂, finding connection-dependent conductance plateaus consistent with integer and fractional spin-Hall edge transport. At filling 3, the inferred edge contribution was near 3e²/(2h). Follow-up measurements on the same transport device resolved a finite hysteretic Hall response below about 20 mT, despite an almost zero response at larger fields. Magnetic circular dichroism in a nearby region supplied complementary evidence of spontaneous time-reversal symmetry breaking, narrowing interpretations of the fractional state.

A- · Particle physics / collider spin correlations

Parton-level top-quark spin entanglement near production threshold

The CMS Collaboration extracted a top-quark spin-entanglement witness from opposite-charge dilepton events in 13 TeV proton collisions, using 36.3 inverse femtobarns of 2016 data. In the selected threshold region, a profile-likelihood analysis corrected for detector effects gave D = −0.480 with total uncertainties of +0.026 and −0.029. This crossed the D = −1/3 separability-witness boundary with an author-reported significance of 5.1 sigma under a signal model including a predicted toponium contribution. The measurement supplies a separate detector and parton-level determination alongside the earlier ATLAS result.

A- · Particle physics / collider spin correlations

High-mass top-quark entanglement and full spin-matrix measurement

The CMS Collaboration measured all 15 top-quark polarization and spin-correlation coefficients in lepton-plus-jets events from 13 TeV proton collisions, using 138 inverse femtobarns of 2016–2018 data. In events with top-pair mass above 800 GeV and absolute scattering-angle cosine below 0.4, the fitted correlation matrix gave an entanglement witness of 2.03 ± 0.15, above the separability boundary of 1 with an author-reported significance of 6.7 sigma. A complementary angular estimator supported the same high-mass result. The measurement extended collider spin-entanglement evidence beyond the production-threshold regime.

A+ · Condensed matter / symmetry-protected electronic transport

Double quantum spin-Hall transport in twisted bilayer WSe2

Kang and colleagues combined local and nonlocal transport with penetration-capacitance measurements in twisted bilayer WSe2. Near hole fillings 2 and 4, local resistances approached h/(2e²) and h/(4e²), while nonlocal responses and bulk incompressibility supported one and two pairs of helical edge channels. The transport changed much more strongly under in-plane than out-of-plane magnetic fields, consistent with approximate spin-conservation protection of a double quantum spin-Hall phase at filling 4.

A · Condensed matter / moiré superconductivity

Superconductivity in twisted bilayer WSe2

Separate experiments by Xia and Han and colleagues and by Guo and colleagues observed superconducting transport in twisted bilayer WSe2. In a 3.65-degree device, Xia and Han and colleagues found zero resistance near half-band filling, a BKT transition near 180 mK and an electric-field-tuned boundary toward a correlated insulator. In a distinct 5.0-degree device, Guo and colleagues found zero resistance, nonlinear current response, a BKT scale near 395 mK and a 50-percent normal-resistance transition near 426 mK. The latter superconducting pocket lay adjacent to anomalous metallic transport interpreted as magnetic reconstruction.

A- · Condensed matter / correlated topological bands

Ferromagnetism and tunable topology in the second moiré band of MoTe2

Separate experiments by Park and colleagues and by Fan Xu and colleagues used magnetotransport and magnetic circular dichroism to study the second moiré band of twisted bilayer MoTe2. Both found ferromagnetic responses near three holes per moiré cell and magnetic-field-induced Chern states. Park and colleagues compared twist angles and observed a high-field Chern-number −2 state near filling −2. Fan Xu and colleagues mapped intermediate-angle devices and found an additional resistance upturn near filling −5/2 that was strongly suppressed by perpendicular field.

A- · Condensed matter / magnetic and excitonic correlations

Fermi-surface reconstruction and a high-field re-entrant insulator in twisted WSe2

Ghiotto, Wei, Song and colleagues mapped longitudinal and Hall transport in a 4.2-degree twisted bilayer WSe2 device. They found an enhanced low-field Hall response away from exact half filling, consistent with reconstructed small Fermi pockets. Near one hole per moiré cell, a low-field correlated insulator gave way to metallic transport around 5 T and a second insulating region above about 24 T. Temperature dependence, Hall sign changes and Landau-level trajectories motivated interpretations in terms of antiferromagnetic reconstruction and a high-field Ising excitonic insulator.

A · Condensed matter / moiré topology and thermodynamics

Twist-tuned multiband topology mapped by local compressibility in bilayer WSe2

Foutty, Kometter and colleagues used a scanning single-electron transistor to map electronic compressibility in small-angle twisted bilayer WSe2. Near a local twist angle of 1.23 degrees, insulating gaps at one and three holes per moiré cell followed magnetic-field trajectories corresponding to Chern number +1, while the even-filling gaps had total Chern number zero. Measurements across regions with different twist angles revealed a narrow topological window, and the probe-induced displacement field switched the one-hole state between topological and trivial responses. The work linked local thermodynamic measurements to tunable multiband topology in a semiconductor moiré system.

A- · Quantum physics / nonequilibrium thermodynamics

Early quantum work-distribution measurements in NMR and a trapped ion

Two teams developed complementary experimental routes to quantum work statistics. Batalhão and colleagues mapped a driven carbon nuclear spin’s work characteristic function onto a hydrogen-spin interferometer and reconstructed forward and backward work distributions. An and colleagues measured initial phonon statistics, prepared corresponding number states and inferred driven transitions of a trapped ytterbium ion from sideband signals. The experiments compared reconstructed work statistics with quantum fluctuation relations; the ion study reported Jarzynski estimates consistent with zero dissipated-work bias over three temperatures and three drive durations.

A · Atomic physics / one-dimensional quantum gases

Spin-dependent phase separation in a one-dimensional Fermi gas

Liao, Rittner and colleagues measured spin-resolved density profiles of an attractively interacting lithium-6 gas confined to an array of narrow tubes. Unlike the paired central region familiar from three-dimensional experiments, their partially polarized core was surrounded by paired or fully polarized wings as the spin imbalance changed. The measured radii mapped a phase-separation diagram and were compared with finite-temperature thermodynamic Bethe-ansatz calculations. The experiment supplied a controlled setting in which theories predict one-dimensional FFLO-like pairing correlations.

A+ · Ultracold gases / local thermodynamics

Pressure profiles map Fermi-gas thermodynamics across tunable interactions

Nascimbène, Navon and colleagues used images of trapped lithium atoms to reconstruct local pressure and the equation of state of a strongly interacting Fermi gas. At unitarity, their measurements mapped temperature dependence and the change between normal and superfluid behavior. They then varied the interaction strength across the BEC–BCS crossover, measuring balanced-superfluid thermodynamics and phase boundaries in spin-imbalanced gases. The data quantitatively tested beyond-mean-field corrections and many-body calculations, while identifying where a simple gas of polarons ceased to describe the normal phase.

A+ · Atomic and molecular physics / quantum scattering

Quantum states and dipoles control ultracold molecular collisions

Ospelkaus, Ni and colleagues showed that quantum statistics and electric dipoles strongly affect collisions in an ultracold gas of potassium–rubidium molecules. Molecules in one internal state had slow, temperature-dependent loss consistent with a p-wave collision barrier; mixing internal states produced much faster loss when s-wave scattering became allowed. In a follow-up study, increasing the induced dipole moment strongly increased molecular loss and produced anisotropic heating, revealing how the long-range interaction controls access to short-range reactive processes.

A · Atomic and molecular physics / quantum motional cooling

Raman sideband cooling reduces molecular motion toward the quantum ground state

Two teams demonstrated Raman sideband cooling of individual calcium monofluoride molecules in optical tweezers. Lu and colleagues used low magnetic fields and alternating trap depths to reduce motion along all three axes, with a radial ground-state fraction reaching about 79%. Bao and colleagues used a high-field scheme and resolved sidebands along each axis, inferring a three-dimensional motional ground-state probability of 54±18% for molecules retained in the selected internal-state manifold. Both experiments extended molecular cooling beyond optical molasses.

A+ · Gravitation / quantum fields in curved spacetime

Traversable BTZ wormhole from a two-boundary interaction

Gao, Jafferis and Wall described a theoretical model in which an interaction coupling two boundaries of an eternal BTZ black hole changes the quantum stress tensor and makes the corresponding bridge traversable in that model.

A+ · General relativity and black holes

Horizon instability of extremal black holes

Aretakis established conserved horizon quantities for linear massless scalar waves on a class of smooth extremal axisymmetric black hole backgrounds and derived horizon non-decay; under additional geometric and decay conditions, higher transverse derivatives become unbounded. The extremal Kerr specialization gives explicit generic growth bounds.

A · Quantum many-body physics and gravity

Entanglement growth after a holographic quantum quench

Liu and Suh analyzed entanglement entropy after a homogeneous global quench in a strongly coupled holographic system, identifying early quadratic growth and a later linear growth regime for large regions, followed by shape-dependent saturation. They described the linear regime using a geometrical entanglement-tsunami picture.

A · Condensed matter and topological phases

Fractional anomalous Hall transport in pentalayer graphene

Lu and colleagues measured magnetotransport in rhombohedral five-layer graphene aligned with hexagonal boron nitride. In two devices they reported integer and fractional anomalous Hall signatures; selected zero-field Hall-resistance plateaus at fractional fillings on both sides of one half accompanied dips in longitudinal resistance. Field sweeps showed hysteresis, and the density–field slopes were compared with fractional Hall-state expectations. Near half filling, a continuously varying Hall response resembled a composite Fermi liquid.

B+ · Fluid dynamics and statistical physics

Large-domain shear-flow simulation and turbulence-transition scaling

Chantry, Tuckerman and Barkley simulated large domains of stress-free, sinusoidally forced Waleffe shear flow using four wall-normal modes. Near a fitted transition they found a growing turbulent fraction and gap statistics broadly consistent with directed-percolation scaling. A smaller simulated domain instead displayed long-lived transients and an apparent jump, illustrating how finite size can change the observed transition.

A+ · Multimessenger astronomy

Swope identifies the optical counterpart of GW170817

The 1M2H team used the Swope telescope to find a new optical transient in NGC 4993, SSS17a, in an exposure beginning 10.9 hours after the GW170817 trigger. Subsequent photometry showed rapid fading, and its location and timing supported association with the gravitational-wave event. Other teams independently observed the same transient.

A+ · Multimessenger astronomy

Fermi-GBM detects the gamma-ray burst associated with GW170817

Fermi’s Gamma-ray Burst Monitor triggered on GRB 170817A, a weak gamma-ray transient following the GW170817 inspiral by roughly 1.7 seconds. Its time and sky position supported a joint gravitational-wave and electromagnetic association; the GBM team measured the burst duration and spectrum, finding properties more consistent with a short gamma-ray burst in their population model.

S- · Superfluidity and quantum fluids

Detection of quantized circulation in superfluid helium by a vibrating wire

W. F. Vinen used a vibrating wire in helium II to investigate quantized circulation. His 1958 original report already described direct evidence for single circulation quanta; the 1961 paper described the apparatus and measurement in more detail. A later experimental account explains how circulation changes the wire’s coupled vibrational modes and discusses selected stable readings near zero and one circulation quantum.

A- · Fundamental symmetries and neutron physics

Search for a permanent neutron electric dipole moment at PSI

Abel and colleagues searched for a permanent neutron electric dipole moment using ultracold neutrons and magnetic-field monitoring at the Paul Scherrer Institute. Two blinded analysis teams reported a result consistent with zero, dₙ = (0.0 ± 1.1 statistical ± 0.2 systematic) × 10⁻²⁶ e cm, corresponding to an upper limit of 1.8 × 10⁻²⁶ e cm at 90% confidence.

A- · Particle physics and fundamental symmetries

Super-Kamiokande searches for proton decay into charged leptons and neutral pions

The Super-Kamiokande Collaboration searched its 1996–2018 data for proton decays into a positron or antimuon and a neutral pion. Using 450 kiloton-years of exposure, the collaboration found no significant excess over atmospheric-neutrino backgrounds and reported 90% confidence lower limits on the partial lifetimes of 2.4 × 10³⁴ and 1.6 × 10³⁴ years for the respective channels. A later search of overlapping pure-water data in 2026 targeted different three-body channels containing two neutral pions and likewise found no significant excess; its reported 90% lower limits were 7.2 × 10³³ and 4.5 × 10³³ years for the positron and antimuon channels.

A · Neutrino astrophysics and stellar fusion

Borexino evidence for CNO-cycle solar neutrinos

The Borexino Collaboration reported evidence for solar neutrinos associated with the carbon–nitrogen–oxygen fusion cycle, extracting a small signal from electron-recoil spectra and radioactive backgrounds. In its multivariate fit the inferred interaction rate was 7.2⁺³·⁰₋₁·₇ counts per day per 100 tonnes, with a reported profile-likelihood significance of 5.1σ against the no-CNO hypothesis.

A+ · Neutrino astrophysics and stellar fusion

Borexino spectroscopy of solar proton–proton neutrinos

Borexino extracted a low-energy solar proton–proton neutrino signal from electron recoils. A later collaboration account reports 144 ± 13 statistical ± 10 systematic interactions per day per 100 tonnes, and a derived pp neutrino flux of (6.6 ± 0.7) × 10¹⁰ cm⁻² s⁻¹.

A+ · Neutrino astrophysics

SNO neutral-current evidence for solar neutrino flavor transformation

Using heavy water, the SNO Collaboration separated charged-current, neutral-current and elastic-scattering contributions from solar boron-8 neutrinos. Assuming the standard boron-8 spectrum, it inferred a non-electron active-neutrino flux of 3.41 × 10⁶ cm⁻² s⁻¹, reported as 5.3σ above zero, providing strong evidence for flavor transformation.

A- · Condensed matter and superconductivity

Zero-bias tunneling peaks in hybrid InSb nanowires

Mourik and colleagues measured zero-bias conductance peaks in InSb nanowires coupled to a superconductor. The reported peaks persisted across ranges of magnetic field and gate settings, with dependence on field orientation; the authors interpreted these features as consistent with Majorana bound states.

A+ · Quantum foundations and optics

Photonic Bell test with spacelike separation and high detection efficiency

Shalm and colleagues reported a Bell-inequality violation using polarization-entangled photon pairs, rapid setting choices, spacelike separation and efficient superconducting detectors. For a five-pulse aggregation the source table reports a local-realism p-value of 5.9 × 10⁻⁹, or 2.3 × 10⁻⁷ under its stated excess-predictability model.

A+ · Quantum foundations and optics

Vienna entangled-photon Bell test with spacelike separation

Giustina and colleagues reported a violation of a Bell inequality using entangled photons, rapid setting choices and high-efficiency transition-edge detectors in a Vienna experiment. The analysis reported a local-realism p-value no greater than 3.74 × 10⁻³¹ under its stated statistical and predictability assumptions.

A · Condensed matter and neutron scattering

Neutron spectroscopy resolves acoustic and optical phonons in germanium

B. N. Brockhouse and P. K. Iyengar used neutron spectroscopy to study lattice vibrations in single-crystal germanium. A later participant lecture depicts acoustic and optical phonon branches in two crystal symmetry directions and explains that simple force-constant models did not fully reproduce the measured dispersion.

A+ · Experimental particle physics

JADE observes planar three-jet events consistent with gluon radiation

The JADE collaboration analysed 287 hadronic electron–positron events recorded at centre-of-mass energies of 27.7 and 30 GeV. The data contained an excess of planar events relative to its two-jet fragmentation model. A rest-frame analysis of the broad side of each selected event supported a three-jet structure; comparisons with simulated quark–antiquark–gluon events supported gluon bremsstrahlung as an interpretation.

A- · Gravitational-wave astrophysics

GW250114 ringdown constrains black-hole oscillation modes

The LIGO Scientific, Virgo and KAGRA collaborations analysed the post-merger signal of GW250114, detected by the two LIGO instruments in January 2025. Fits to the post-peak waveform favored a second rapidly damped component alongside the dominant ringdown, consistent within uncertainty with a Kerr black hole’s first overtone. A separate analysis of the full inspiral–merger–ringdown waveform constrained additional mode-frequency deviations and found consistency with the modeled general-relativity prediction.

A · Relativistic nuclear physics

PHENIX compares high-momentum hadrons in gold and deuteron–gold collisions

PHENIX measured high-transverse-momentum charged hadrons in gold–gold collisions at 200 GeV per nucleon pair and compared them with neutral-pion and nucleon-collision references. Central gold–gold collisions showed strong suppression, whereas the deuteron–gold control showed no comparable suppression and a modest charged-hadron enhancement. Together the measurements support a dense-medium final-state interpretation.

A · Optical and quantum physics

Chiao and Wu predict geometric polarization rotation in helical optical fibers

Chiao and Wu applied the geometric phase of adiabatically transported helicity to photons guided along a curved path. For a closed momentum-space circuit they related the helicity-dependent phase to the enclosed solid angle, and proposed optical-fiber interferometry and polarization rotation as observable manifestations.

A- · High-energy astrophysics

Fermi finds a background-light attenuation signature in blazar spectra

Fermi-LAT combined 46 months of gamma-ray observations of 150 selected BL Lac objects at redshifts 0.03–1.6. Their spectra showed an energy- and redshift-dependent suppression consistent with absorption on diffuse extragalactic background light, enabling model-based constraints on the optical–ultraviolet background.

A+ · Optical atomic clocks

A highly stable aluminium-ion optical clock with quantified systematic uncertainty

An aluminium-ion optical clock combined quantum-logic readout, a one-second interrogation enabled by a remote cavity-stabilized laser, and an improved trap and vacuum system. The authors report fractional systematic uncertainty of 5.5 × 10⁻¹⁹ and fractional instability of 3.5 × 10⁻¹⁶/√(τ/s), estimated by comparison with a strontium lattice clock.

A- · Stellar astrophysics

Gliese 229B resolved as a close brown-dwarf binary

VLT GRAVITY interferometry and CRIRES+ spectroscopy independently indicated that Gliese 229B is a close binary. A joint orbital fit gave a period of 12.134 ± 0.003 days and component masses of 38.1 ± 1.0 and 34.4 ± 1.5 Jupiter masses in the authors’ frequentist analysis.

A- · Low-temperature physics

Redesigned oscillators constrain helium supersolid-like responses in confined and bulk samples

Duk Y. Kim and Moses H. W. Chan redesigned a porous-glass torsional oscillator and reported no detectable low-temperature response attributable to nonclassical rotational inertia at a sensitivity of 2 × 10⁻⁵. In a separate bulk-helium study using rigid oscillators they reported a sample- and apparatus-dependent upper limit of 4 × 10⁻⁶ and a comparable period shift in solid helium-3 and helium-4.

A · Neutrino physics

KamLAND investigates antineutrinos produced inside Earth

KamLAND analyzed low-energy antineutrino candidates to investigate uranium- and thorium-chain radioactivity inside Earth. With an assumed thorium-to-uranium mass ratio of 3.9, its spectral fit gave a 90% confidence interval of 4.5–54.2 geoneutrino events and an Earth-model-dependent upper limit on uranium- and thorium-decay heat.

A- · Particle physics

ADMX low-noise cavity searches for axion dark matter

ADMX searched microwave spectra for conversion of hypothetical Galactic axions and found no statistically significant axion signal. The 2018 report reached benchmark DFSZ sensitivity near 2.66–2.81 microelectronvolts, and the later 2019 preprint reported an extended 2.81–3.31 microelectronvolt search using a Josephson parametric amplifier and alternative cavity configurations.

A · Observational astrophysics

A galaxy cluster magnifies a distant individual star

Hubble monitoring of the field containing supernova Refsdal revealed a brightening point source, LS1, in a background galaxy at redshift 1.49. Its color and light curve were interpreted as a strongly magnified individual star, with the authors estimating a peak magnification of at least about 2,000 under their lens model. The observation illustrates how cluster lensing combined with microlensing can reveal individual stars at cosmological distances.

A- · Observational astrophysics

Earendel: a highly magnified early-universe source and its contested nature

Hubble imaging revealed an unresolved persistent source named Earendel in the strongly lensed Sunrise Arc. The discovery team interpreted its size and brightness using several lens models as a highly magnified individual star or stellar system. A later JWST NIRSpec study measured the Sunrise Arc emission-line redshift at about 5.926 and found that Earendel’s continuum can also be fit by stellar-population models for a compact star cluster.

A- · Observational astrophysics

A well-observed ultraviolet and optical tidal-disruption candidate

Pan-STARRS and GALEX observed the rise and decay of PS1-10jh, a luminous ultraviolet and optical transient near the nucleus of a galaxy at redshift 0.1696. Follow-up spectroscopy showed broad ionized-helium emission without detected Balmer lines. The discovery team interpreted the light curve and line spectrum as a stellar tidal disruption; a later simulation-based analysis showed how a near-solar-composition star could also be consistent with the same observed data under a different emission model.

A · Nonlinear optics

A theory of photorefractive spatial optical solitons

Segev, Crosignani, Yariv and Fischer described a spatial optical soliton in a photorefractive medium, where diffraction is balanced by a refractive-index pattern induced by interference among the beam’s spatial-frequency components. In their model a suitable beam profile can propagate without changing transverse shape, and the predicted shape is independent of absolute intensity under the stated idealized response.

A · Condensed-matter physics

Optical four-wave mixing reveals Bloch-period modulation in a semiconductor superlattice

Feldmann and colleagues studied a biased GaAs/AlGaAs superlattice with time-resolved degenerate four-wave mixing at about 5 K. They observed oscillations in the emitted optical signal whose period changed with the electric field and agreed with the Bloch period inferred from the Wannier–Stark ladder spacing. A two-band calculation with a fitted dephasing time reproduced the signal, supporting their interpretation as coherent Bloch oscillations.

A · Atomic physics

Bloch oscillations and effective masses of cold atoms in an optical lattice

Ben Dahan and colleagues prepared ultracold cesium atoms in the lowest band of a standing-wave optical potential and applied an inertial force by accelerating the lattice. After different evolution times they switched off the potential and measured atomic momentum distributions. The distributions recurred with the predicted Bloch period, while their inferred mean velocities yielded positive and negative band effective masses at different quasimomenta.

A- · Atomic physics

Driven optical lattices control condensate tunneling and a superfluid–Mott transition

In 2007 Lignier and colleagues periodically shook a one-dimensional optical lattice containing a rubidium condensate and inferred suppressed interwell tunneling from its expansion, finding agreement with a Bessel-function dependence over the tested range. In a subsequent 2008 preprint Zenesini and colleagues ramped the drive in a three-dimensional lattice: interference visibility decreased and returned when the drive was removed. Their excitation spectra and comparison with changes in static lattice depth supported a reversible drive-induced superfluid–Mott transition.

A- · Astrophysics

Rapid quasi-periodic X-ray oscillations in a magnetar giant-flare tail

Israel and colleagues analysed Rossi X-ray Timing Explorer measurements of the tail of the 27 December 2004 SGR 1806–20 giant flare and reported a quasi-periodic signal near 92.5 Hz, together with lower-frequency candidate peaks. Watts and Strohmayer subsequently analysed RHESSI observations of the same flare and found a corresponding phase-dependent feature near 92.5 Hz, a further feature near 626.5 Hz, and broad lower-frequency features. Both groups discussed neutron-star vibration interpretations.

A · Optical physics

A layered optical hyperlens magnifies sub-diffraction features for far-field imaging

Lee and colleagues described a curved layered optical hyperlens and imaged closely spaced test features with a conventional far-field microscope. In the reported 365-nanometre illumination experiment, the reconstructed image resolved a line-pair separation down to approximately 125 nanometres. An anisotropic effective-medium model and electromagnetic simulation explained how the structure magnifies fine spatial information before ordinary optical detection.

A+ · Optical physics

Narrow-mode random lasing in disordered semiconductor films and powders

Cao and colleagues reported narrow spectral peaks emerging above a pump threshold in disordered zinc-oxide polycrystalline films and, in a related report, strongly scattering zinc-oxide powder films. Peak frequencies varied with position and observation angle, and the number of peaks changed with excitation area. The film study included above-threshold spatial emission images; similar behavior was reported for gallium-nitride powder. The authors interpreted the results as laser modes with coherent feedback from recurrent scattering.

A+ · Atomic physics

Continuous output coupling from a Bose–Einstein condensate

Bloch, Hänsch and Esslinger used a weak radio-frequency field to transfer atoms from a magnetically trapped rubidium condensate into an untrapped state, forming a collimated falling atomic beam. They directly imaged continuous output over up to 40 milliseconds and monitored condensate depletion over up to 100 milliseconds. Varying radio frequency also provided spatially selective spectroscopy of the trapped condensate.

A+ · Astrophysics

Radio pulsations from the transient magnetar XTE J1810−197

Halpern and colleagues identified a compact 1.4 GHz radio source coincident with the transient anomalous X-ray pulsar XTE J1810−197 in 2004 VLA observations. In 2006 Camilo and colleagues detected narrow radio pulses at its approximately 5.54-second rotation period with Parkes and Green Bank, showing that a magnetar could also behave as a radio pulsar. The two measurements are distinct stages of the same object’s radio-observation history.

A- · Quantum Physics

Lateral Casimir force between corrugated surfaces

Chen and colleagues used a modified atomic-force microscope to measure an oscillating lateral force between aligned, corrugated gold-coated surfaces. Its phase dependence followed the corrugation period, and the authors compared its magnitude and distance dependence with a finite-conductivity Casimir calculation for their sphere–plate geometry. Their later detailed account reports the calibration, additional electrostatic-force data and a more comprehensive uncertainty analysis.

A- · Gravitation and Fluid Physics

Water-wave experiments on stimulated horizon analogues

In 2008 Rousseaux and colleagues reported negative comoving-frequency waves in a driven water channel with varying flow, interpreting mode conversion as a classical analogue of a Hawking process. In a separate water-channel experiment reported in 2010, Weinfurtner and colleagues measured positive- and negative-norm converted components across nine driving frequencies and compared their ratio with a thermal-like exponential law. These related but distinct experiments have different teams and conditions.

A+ · Atomic and Quantum Physics

Vortices and vortex lattices in stirred Bose-Einstein condensates

In 2000 Madison and colleagues used a rotating laser perturbation of a trapped rubidium Bose-Einstein condensate to observe one to four vortices and study their frequency-dependent appearance and lifetime. In 2001 Abo-Shaeer and colleagues stirred a sodium condensate and imaged ordered triangular arrays with up to about 130 vortices, as well as defects and their evolution. These related observations used different teams, atoms and conditions.

A+ · Atomic and Quantum Physics

Phase-engineered vortices in a two-component Bose-Einstein condensate

Matthews and colleagues created vortices in either component of a two-state rubidium Bose-Einstein condensate through spatially controlled coherent transitions, following a proposal by Williams and Holland. They used an intercomponent interference measurement to map the relative phase around the vortex and observed different evolution for the two choices of component.

S- · Particle Physics

Independent B-factory observations of time-dependent CP asymmetry in neutral B mesons

The BABAR and Belle collaborations independently measured time-dependent differences in selected flavor-tagged neutral B and anti-B decays. BABAR reported sin(2β) = 0.59 ± 0.14 statistically ± 0.05 systematically; Belle reported sin(2φ1) = 0.99 ± 0.14 statistically ± 0.06 systematically. The angles β and φ1 use different names for the same standard-model parameter.

A- · Particle and Quantum Physics

Squeezed receiver speeds synthetic-signal and axion dark-matter searches

Malnou and colleagues demonstrated a squeezed microwave receiver on a synthetic weak signal, reporting a 2.12 ± 0.08 scan-rate enhancement in a setup designed to mimic an axion search. The subsequent HAYSTAC experiment used related methods in a dark-matter search, reporting about a 1.9-fold gain over an optimal unsqueezed comparator and no axion signal in two selected mass windows.

A · Astrophysics

X-ray polarization probes particle acceleration in the blazar Markarian 501

Liodakis and colleagues combined IXPE X-ray polarimetry with optical and radio observations of Markarian 501. Two March 2022 observations yielded X-ray polarization near 10–11%, larger than the host-corrected optical value, and polarization angles approximately aligned with the radio jet. The authors found this pattern consistent with an energy-stratified shock-acceleration scenario.

A · Astrophysics

Energy-dependent X-ray polarization from magnetar 4U 0142+61

Taverna and colleagues used IXPE to measure phase-averaged X-ray polarization from magnetar 4U 0142+61. They found about 12 ± 1% across 2–8 keV, with different polarization behavior at lower and higher energies and an approximately 90-degree angle change across the intervening band.

A+ · Gravitational Physics

Lunar laser ranging tests equivalence and relativistic orbital effects

Lunar laser-ranging analyses by Williams, Newhall and Dickey in 1996 and by Williams, Turyshev and Boggs in 2004 constrained differential Earth–Moon acceleration toward the Sun, geodetic precession and other relativistic parameters. The later work used a longer data span and updated model and reported results consistent with the stated relativistic framework within estimated uncertainties.

A+ · Astrophysics

OSO-8 measurements of Crab X-ray polarization

The OSO-8 team reported X-ray polarization of the Crab in two bands from 1976 quick-look satellite data. A later phase-selected analysis by a partly different author team combined 1976 and 1977 observations and measured approximately 19% polarization at 2.6 and 5.2 keV, supporting a synchrotron interpretation.

A · Atomic and quantum physics

Spectroscopy reveals Bose-Einstein condensation in trapped atomic hydrogen

Fried and colleagues reported Bose–Einstein condensation in magnetically trapped atomic hydrogen. Two-photon spectroscopy showed a shifted, high-density component as the gas cooled; the team used the spectral shift and a trap model to estimate condensate density and population.

A · Atomic and quantum physics

A metastable-helium gas forms a Bose-Einstein condensate

Pereira Dos Santos and colleagues observed a condensate of metastable helium-4 atoms in a magnetic trap using absorption imaging after release. Its bimodal distribution and changing expansion anisotropy supported condensation. They estimated the scattering length and reported roughly two-second condensate decay.

A- · Atomic and quantum physics

Nondestructive imaging resolves spin dynamics in an ultracold Bose gas

Higbie and colleagues used polarization-sensitive phase-contrast imaging to repeatedly measure a component of the magnetization of trapped spin-1 rubidium-87 gas. They observed spatially resolved Larmor precession and compared the coherence of a condensate with that of a thermal cloud.

A- · Atomic interferometry and gravitation

A cold-atom gravity gradiometer measures the Newtonian gravitational constant

Lamporesi and colleagues used two freely falling rubidium samples as a differential atom interferometer while moving tungsten source masses between two configurations. Comparing the observed phase shift with a numerical gravitational-field model yielded an estimate of the Newtonian constant G of 6.667 × 10⁻¹¹ m³ kg⁻¹ s⁻², with separate reported statistical and systematic uncertainties. In a later experiment using the same apparatus lineage, Rosi and colleagues reported G = 6.67191(99) × 10⁻¹¹ m³ kg⁻¹ s⁻² with a combined uncertainty of about 150 parts per million.

A- · Atomic interferometry and gravitation

An atom gravity gradiometer rejects common vibration and measures tidal signals

McGuirk and colleagues operated two light-pulse atom accelerometers as a gravity gradiometer. They characterized common-mode vibration rejection and measured a tidal acceleration signal, and presented interference fringes and tests of sensitivity to platform motion. A source archive supplies the eleven original figures missing from the generated preprint PDF.

A+ · Quantum optics

Coincidence measurements reveal entanglement in photon orbital-angular-momentum modes

Mair, Vaziri, Weihs and Zeilinger measured coincidences between pairs of photons whose spatial modes carry orbital angular momentum. Measurements in selected modes and superpositions supported entanglement in this spatial degree of freedom, extending the set of optical states available for quantum-information experiments.

A- · Ultracold atomic gases

A tunable one-dimensional cesium gas enters an excited attractive regime

Haller and colleagues used confined cesium atoms to move a one-dimensional gas from strong repulsion into an attractive regime. Collective oscillations and loss measurements supported a metastable, highly excited gas state rather than immediate collapse into the clustered ground state.

A+ · Observational astrophysics and exoplanets

A coherent Doppler signal reveals a candidate planet around Proxima Centauri

Anglada-Escudé and colleagues combined new HARPS radial-velocity observations with earlier HARPS and UVES measurements and reported a coherent approximately 11.2-day Doppler signal around Proxima Centauri. They interpreted the combined signal as a planetary companion and tested stellar-activity indicators alongside the velocity data. In 2020 a separate ESPRESSO campaign recovered the 11.2-day signal in its own radial velocities and combined it with earlier datasets to refine the model parameters.

A- · Cosmology and gravitational lensing

A lens time-delay and stellar-dynamics analysis constrains the Hubble constant

Suyu and colleagues combined earlier measured time delays in the four-image lens B1608+656 with Hubble imaging, a new lens-galaxy velocity-dispersion measurement and an environment model. Their Bayesian analysis quantified how the density profile and matter along the line of sight affect a time-delay distance and cosmological inferences.

A+ · Exoplanetary astronomy and spectroscopy

JWST transmission spectroscopy identifies carbon dioxide in WASP-39b

The JWST Transiting Exoplanet Community Early Release Science Team observed a transit of the hot gas giant WASP-39b and measured a strong approximately 4.3-micrometre absorption feature, attributed to carbon dioxide from its spectral shape. Four reductions of the same observing dataset yielded similar spectra. A separate G395H transit spectrum showed additional absorption near 4.1 micrometres, interpreted as sulfur dioxide by model comparison.

A+ · Condensed matter and topological transport

Short-edge quantum spin Hall transport in monolayer WTe₂ up to 100 K

Wu, Fatemi and colleagues measured gated monolayer WTe₂ devices and found an edge-dominated resistance approaching h/(2e²) in short channels, consistent with approximately e²/h conductance per edge. They observed magnetic-field suppression and a Zeeman-like conductance gap and reported edge-dominated behavior up to about 100 K.

A · Condensed matter and topological transport

Edge conduction in insulating monolayer WTe₂

Fei, Palomaki and colleagues measured monolayer WTe₂ devices and found edge-dominated conduction as the interior became insulating below roughly 100 K. Nonlocal measurements and grounded pincer contacts separated edge and bulk conduction, while an in-plane magnetic field suppressed the edge response. Bilayer devices offered a comparison. A later microwave impedance microscopy study mapped enhanced conductivity along physical edges and additional internal lines in separate monolayer samples.

A- · Cosmic rays and astroparticle physics

Telescope Array records an exceptionally energetic cosmic-ray air shower

On 27 May 2021 Telescope Array recorded an extensive air shower across 23 surface detectors. Its reconstructed primary energy was 244 ± 29 statistical and +51/−76 systematic exaelectronvolts on the fluorescence-calibrated energy scale. The arrival direction and backtracking under selected Galactic magnetic-field models were compared with nearby source distributions.

A · Neutrino and astroparticle physics

LZ finds evidence for solar-neutrino coherent nuclear scattering in xenon

The LZ Collaboration searched 5.7 tonne-years of liquid-xenon data for low-energy nuclear recoils and found evidence consistent with coherent elastic scattering of solar boron-8 neutrinos. In its no-dark-matter fit the zero-neutrino-signal hypothesis was rejected at a reported 4.5 sigma, with a best-fit 12.3 +7.0/−5.4 neutrino events. The same analysis found no significant excess attributable to light dark matter.

A · Nuclear astrophysics and spectroscopy

Spectral reanalysis identifies strontium in the GW170817 kilonova

Watson and colleagues reanalyzed VLT X-shooter spectra of the GW170817 kilonova AT2017gfo and interpreted broad evolving features as signatures of singly ionized strontium. They compared thermal line calculations, a simplified expanding-atmosphere profile and radiative-transfer models, supporting neutron-capture element production in this merger event.

A+ · Neutrino and solar physics

Borexino measures the low-energy beryllium-7 solar neutrino spectrum

The Borexino Collaboration extracted a real-time spectral signal attributed to 0.862 MeV beryllium-7 solar neutrinos from electron recoils in a low-background liquid scintillator. For the first 47.4 live days in 2007 the reported interaction rate was 47 ± 7 statistical ± 12 systematic counts per day per 100 tonnes.

A- · Particle physics / dissipative muon-beam compression

Longitudinal and transverse compression of stopped positive muons in helium gas

The muCool team demonstrated separate longitudinal and transverse compression stages for positive muons stopped in helium gas. Bao and colleagues used electric fields to concentrate the stopping distribution along a magnetic field. Antognini and colleagues later used a cryogenic density gradient and crossed fields to obtain transverse convergence. Decay-positron time spectra, control conditions and collision simulations supported both demonstrations. The inferred final sizes and compression times were obtained through those models rather than direct complete beam tomography.

A- · Ultracold-gas theory / measurement methods

Inferring bulk thermodynamics from trapped-gas density profiles

Ho and Zhou proposed a way to recover bulk thermodynamic information from the density profiles of trapped atomic gases. Within a local-density description, spatially varying confinement scans the local chemical potential. Their scheme combines pressure reconstruction with comparisons between nearby equilibrated states at matched local chemical potentials to infer entropy and other thermodynamic responses. They also proposed extensions for superfluid density and staggered magnetization, connecting experimentally accessible images to quantities needed to map many-body phase diagrams.

S- · Gravitation and cosmology / inflationary spacetime boundaries

Positive averaged expansion implies past geodesic incompleteness under a kinematic condition

Borde, Guth and Vilenkin derived a kinematic bound on the past length of null and noncomoving timelike geodesics in an expanding spacetime. They express a directional expansion rate as the derivative of a function of the observer’s relative motion through a congruence of freely falling test particles. If the expansion averaged along the relevant past geodesic stays positive, the available affine length or proper time is finite. The argument does not require an energy condition, spatial homogeneity or isotropy, and constrains attempts to make inflation alone a past-complete description.

S- · Quantum gravity / gauge forces and black holes

Weak gravity conjecture and evidence from charged black holes and string theory

Arkani-Hamed, Motl, Nicolis and Vafa proposed that gravity is the weakest force in a consistent quantum-gravity theory with a U(1) gauge field. Their weaker electric conjecture requires a suitable charged state whose mass-to-charge ratio is no greater than that of an extremal black hole, with equality in supersymmetric examples. They examined black-hole stability, heterotic compactifications and other string-theory examples, and discussed a magnetic argument for a gauge-dependent effective-theory cutoff. These are conjectural consistency conditions and supporting theoretical evidence, not an observed particle or a general proof.

A+ · Quantum gravity and black holes

Black hole shock waves and sensitivity to early perturbations

Shenker and Stanford used a two-sided holographic black hole model to connect a small early perturbation to a blueshifted gravitational shock wave and the loss of leading-order local correlations. In their BTZ calculation the onset time scales logarithmically with black hole entropy for a thermal-sized perturbation.

Corrections and reassessment