WORLD RESEARCH STATE
Who contributed to the recorded progress?
Explore human-origin and AI-involved work in the selected catalogue.
2849 matching records · 2791 scored scientific contributions
Published point share in the selected catalogue
Point shares among assessed contributions in the selected edition and scoring context. This is not a census of all human and AI science. AI-involved work includes human authors, guidance and experiments.
37 matching reported results have conditional scores in the main rankings. Those unverified points are excluded from this achieved-science share.
Provisional WRS ratings for the selected catalogue. Ratings can be revised; they do not measure all scientific progress.
All counts and point shares above describe this filtered selection. Work without a score is excluded from the point comparison, not treated as scientifically worthless.
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Source-linked records in this selection, including work awaiting assessment.
Contribution grades are displayed separately. Only published reference scores enter the numerical share chart.
Candidate claims and work outside the achieved-point comparison
52 matching records are outside achieved-science totals. Conditional grades and scores below mean “if the exact claim is verified”; they enter the reference rankings with an unverified label, while these achieved-science charts remain separate. Pending assessments and capability benchmarks remain separate.
OpenAI: Exact BSD formula under Selmer corank zero or one
Reported result · unverified
For an elliptic curve over the rational numbers, the manuscript claims the complete Birch–Swinnerton-Dyer leading-term formula whenever its full q-power Selmer group has corank zero or one at some prime q. It includes finiteness of the Tate–Shafarevich group and all prime factors of the formula. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceA+Claim scope and evidenceReported result · not independently verified.
AIf verified · reference score300,000Editorial revision range 180,000–500,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: A claimed fixed zero-free half-plane for zeta and Dirichlet L-functions
Reported result · unverified
The manuscript claims nonvanishing for the Riemann zeta function and every Dirichlet L-function in Re(s)>7/8, and for finite-order Hecke L-functions over Q(sqrt(-3)). The bound is independent of height and conductor. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
SIf verified · reference score700,000Editorial revision range 450,000–950,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: A claimed negative solution of Hilbert’s tenth problem over the rationals
Reported result · unverified
The manuscript claims that no algorithm can decide, for an integer-coefficient polynomial whose number of variables is part of the input, whether it has a rational zero. Rational numbers permit fractions, so this is a different decision problem from the classical integer result. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
If verified · reference score500,000Editorial revision range 300,000–750,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: Claimed ordinary two-point Chowla cancellation
Reported result · unverified
The manuscript claims a correlation bound O(X/(log X)^c) for Liouville values on every fixed pair of nonproportional affine forms, with an absolute positive c. It also claims a binary Elliott cancellation result under uniform nonpretentiousness. Ordinary averages count all integers equally. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceS−Claim scope and evidenceReported result · not independently verified.
If verified · reference score380,000Editorial revision range 230,000–580,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: A claimed irrationality exponent of two for pi
Reported result · unverified
The manuscript claims that for every exponent nu>2, all sufficiently large denominators q satisfy |pi-p/q|>=q^(-nu) for every integer numerator p. This specifies how exceptionally well fractions can approximate pi, beyond merely proving that pi is irrational. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceS−Claim scope and evidenceReported result · not independently verified.
If verified · reference score350,000Editorial revision range 200,000–550,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: A claimed Hodge theorem for all CM abelian varieties
Reported result · unverified
The manuscript claims algebraic representatives for every rational Hodge class on every complex abelian variety with complex multiplication, in all dimensions and codimensions. It states further implications for Tate and Hodge standard conjectures for abelian varieties. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
If verified · reference score700,000Editorial revision range 400,000–950,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: A claimed all-dimensional symmetric Mahler inequality
Reported result · unverified
The manuscript claims |K| |K-polar|>=4^n/n! for every origin-symmetric convex body in every dimension n>=1, with equality exactly for invertible linear images of Hanner polytopes. It is a sharp statement about the smallest possible volume product. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
If verified · reference score500,000Editorial revision range 300,000–750,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: A claimed torsion-free group-algebra counterexample to direct finiteness
Reported result · unverified
The manuscript claims a finitely presented torsion-free group G and elements a,b,c in F2[G] with ab=1, ac=0 and c nonzero. These identities would force ba!=1, disproving direct finiteness in this positive-characteristic setting. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
If verified · reference score450,000Editorial revision range 250,000–700,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: A claimed isomorphism of free group factors of different ranks
Reported result · unverified
The manuscript claims a normal trace-preserving isomorphism between the von Neumann algebras of the free groups on two and three generators. With the classical dichotomy, it concludes that all interpolated free group factors are isomorphic. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
If verified · reference score550,000Editorial revision range 350,000–800,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: Claimed large-data global smoothness for three-dimensional relativistic Vlasov–Maxwell
Reported result · unverified
The manuscript claims a unique global classical solution for the three-dimensional one-species relativistic Vlasov–Maxwell system, with nonnegative smooth compactly supported initial particle density and smooth finite-energy initial fields whose derivatives are bounded and whose Gauss constraints hold. No smallness or symmetry restriction is imposed. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
If verified · reference score550,000Editorial revision range 350,000–850,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: The three-dimensional Kakeya maximal conjecture
Reported result · unverified
For every positive epsilon the paper claims an L3(R3) to L3(S2) Kakeya maximal bound C_epsilon delta^(-epsilon), uniform over tube scale. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
If verified · reference score500,000Editorial revision range 300,000–750,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: The Unique Games Conjecture
Reported result · unverified
The paper claims a deterministic polynomial-time reduction from 3SAT to Unique Games for every fixed completeness and soundness error in (0,1/2), over an alphabet depending only on those errors. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
If verified · reference score650,000Editorial revision range 400,000–900,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: Derandomization of logarithmic space: L=RL=BPL
Reported result · unverified
The paper claims equality of deterministic and bounded-error polynomial-time randomized logarithmic-space language classes in its stated machine model. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
If verified · reference score500,000Editorial revision range 300,000–750,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: A matrix-multiplication exponent at most 9/4
Reported result · unverified
For every epsilon>0, the paper claims multiplication of n-by-n complex matrices in O_epsilon(n^(9/4+epsilon)) scalar arithmetic operations, hence omega(C)<=9/4. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
If verified · reference score600,000Editorial revision range 350,000–850,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: Integer multiplication below n log n
Reported result · unverified
The paper claims one exact deterministic fixed finite-tape Turing-machine algorithm with worst-case O(n(log n)^(1-kappa)) time, kappa=2^(-182), for n-bit integer products. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceS−Claim scope and evidenceReported result · not independently verified.
If verified · reference score350,000Editorial revision range 200,000–600,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: Exact discrete Fourier transforms below n log n
Reported result · unverified
The paper claims an all-length exact DFT algorithm with O(n(log n)^(1-10^(-13))) operations in its specified complex-arithmetic and indexing model. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceS−Claim scope and evidenceReported result · not independently verified.
If verified · reference score350,000Editorial revision range 200,000–600,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: Arithmetic progressions from divergent reciprocal sums
Reported result · unverified
The paper claims every set of positive integers with divergent reciprocal sum contains progressions of every finite length, via quantitative bounds r_k(N)<=C_k N exp(-c_k(log N)^epsilon_k) for each fixed k>=3. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
If verified · reference score500,000Editorial revision range 300,000–750,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: A two-dimensional gapped area law
Reported result · unverified
The paper claims an entanglement entropy bound C|boundary(A)| for unique ground states of finite-range Hamiltonians on finite induced square-lattice domains, uniformly under fixed local bounds and a global spectral gap. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceSClaim scope and evidenceReported result · not independently verified.
If verified · reference score550,000Editorial revision range 300,000–800,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: A measured-output quantum parity lower bound
Reported result · unverified
The paper claims constant-depth circuits with arbitrary one-qubit and unbounded-arity Toffoli gates, polynomially many zero-initialized qubits, cannot compute parity with any fixed positive worst-case advantage. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceS−Claim scope and evidenceReported result · not independently verified.
If verified · reference score350,000Editorial revision range 200,000–550,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.
OpenAI: Constant-error unitary synthesis from a Boolean oracle
Reported result · unverified
The paper claims a polynomial-size quantum oracle circuit generated from n alone that approximates every n-qubit unitary channel to full diamond-norm error at most 1/2 after a suitable target-dependent Boolean oracle is chosen. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
If verified · conditional significanceS−Claim scope and evidenceReported result · not independently verified.
If verified · reference score350,000Editorial revision range 200,000–600,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.