{
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  "scope": "Source-bound reported results with provisional significance and reference estimates for exact claims. Included in main rankings with explicit unverified status, separately from achieved-science totals.",
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      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "The hypothesis is on the full Selmer group, not merely Mordell–Weil rank. This is not BSD in every rank. The paper imports the unrestricted converse and the two-primary formula from separate manuscripts. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean."
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      "status": "CONDITIONAL_IF_VERIFIED",
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      "scientific_correctness_certified": false,
      "scope": "Principal-character poles at s=1 are allowed. The boundary Re(s)=7/8 is excluded. This does not put all nontrivial zeros on Re(s)=1/2 and is not the Riemann hypothesis. A bound on the number of zeros is a different result. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean."
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      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "It does not assert that any given equation is unsolvable, nor that restricted classes cannot have algorithms. The already known integer undecidability theorem cannot simply be relabelled as the rational result. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean."
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      "status": "CONDITIONAL_IF_VERIFIED",
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      "scientific_correctness_certified": false,
      "scope": "The constants may depend on fixed affine forms and need not be effective. No uniformity for coefficients growing with X is asserted. The result concerns two-point correlations, not the full higher-order Chowla conjecture. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean."
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      "status": "CONDITIONAL_IF_VERIFIED",
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      "scientific_correctness_certified": false,
      "scope": "The denominator threshold may depend on nu and is ineffective. The statement does not imply a uniform c/q^2 bound or bounded continued-fraction entries. The Flint–Hills convergence consequence is outside the selected formal statement in the scope note. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean."
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      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "This is not the Hodge conjecture for every smooth projective variety. Three withdrawn Weil/K3 manuscripts remain separate records of unsupported proofs; this manuscript was not named in those withdrawal notices, which does not establish its validity or independence from every affected dependency. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean."
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      "points": "500000",
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      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "The selected paper is the symmetric result. The general nonsymmetric theorem, functional variants and symplectic consequences need their own exact source targets. A single family is not automatically one credit per companion PDF. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean."
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      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "The known characteristic-zero theorem is unchanged. The available family scope note describes other characteristic-two and odd-characteristic constructions, not this selected torsion-free paper; that Lean coverage cannot be transferred to this target. The August nonsofic-group package needs explicit overlap review. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean."
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      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "The selected source proves a consecutive-rank step and states the two-to-three conclusion separately. These are operator algebras; the underlying free groups themselves are not being declared isomorphic. The fundamental-group corollary is beyond the selected formal statement. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean."
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      "status": "CONDITIONAL_IF_VERIFIED",
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      "scientific_correctness_certified": false,
      "scope": "This exact collisionless model is not every plasma system or a laboratory fusion demonstration. Compact support applies to the particle data; the fields may have Coulomb tails. Momentum support is bounded on each finite time interval, not by one time-independent constant. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean."
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      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "This is the maximal estimate, distinct from the prior three-dimensional set-dimension theorem and from the separate four-dimensional companion. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run."
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      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "The reduction does not prove P!=NP. Earlier conditional approximation results and their authors retain their contribution credit; the conjecture and direct companion reductions are not all one new theorem. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run."
    },
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      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "This is not P=BPP. Variable precision has its own time cost, and the formal scope note selects the class equality rather than every compiler or quantitative corollary. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run."
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    {
      "id": "openai-math-matrix-exponent-nine-fourths-2026",
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      "points": "600000",
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      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "The statement has exponent slack and is over C. It is not an unconditional O(n^2.25) practical running-time guarantee, an omega=2 solution or a measured GPU speedup. The family formalization note selects other companion paths. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run."
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      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "The saving is asymptotic and thresholds are extremely large. The bit model matters; this is not a present-day performance benchmark. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run."
    },
    {
      "id": "openai-math-dft-subnlogn-2026",
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      "points": "350000",
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      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Unrestricted coefficients, specified roots and unit-cost indexing are part of the model; preparation and organization are counted. This does not break every bounded-coefficient or bit-complexity lower bound. Its relationship with the integer-multiplication method needs credit deduplication. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run."
    },
    {
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      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Constants depend on fixed progression length. The selected formal scope covers the reciprocal-sum consequence, not the quantitative bound. It does not relabel Szemeredi or the three-term predecessor as this new proof. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run."
    },
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      "id": "openai-math-area-law-two-dimensional-2026",
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      "points": "550000",
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      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "The constant depends on local dimension, interaction range and strength and the gap. Unique ground state and graph-locality assumptions matter; no claim is made for every gapless or degenerate quantum system. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run."
    },
    {
      "id": "openai-math-quantum-parity-qac0-2026",
      "target": {
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      "modifier": "-",
      "points": "350000",
      "range": {
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      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "There is no primitive unbounded fanout, postselection or intermediate measurement in the selected model. Arbitrary final garbage is permitted. The theorem is not a lower bound for every quantum circuit class. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run."
    },
    {
      "id": "openai-math-unitary-synthesis-oracle-2026",
      "target": {
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      "modifier": "-",
      "points": "350000",
      "range": {
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      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "The oracle is allowed to depend on the unitary and is not supplied by an efficient classical construction. This is the constant-error formulation, not an arbitrary-precision or practical universal synthesis algorithm. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run."
    },
    {
      "id": "gu-et-al-ai-quantum-circuit-discovery-2026",
      "target": {
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      "modifier": "+",
      "points": "30000",
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        "upper": "70000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "The evaluator checks phase, preserved inputs and clean ancillas, but samples large input domains. Some designs permit distribution-specific failures, and Toffoli–qubit product is a logical-resource proxy rather than measured hardware runtime. Results do not establish arbitrary-circuit optimality or worst-case exactness."
    },
    {
      "id": "anthropic-claude-ecdsa-parameter-origins-2026",
      "target": {
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        "version": 1,
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      "modifier": "+",
      "points": "28000",
      "range": {
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        "upper": "65000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "This concerns public parameter provenance, not recovery of secret signing keys or a break of ECDSA. One binary-curve seed, several base points and reasons for skipped candidates remain unexplained. Reproducible parameter matches do not establish the complete historical selection process or prove absence of a backdoor."
    },
    {
      "id": "menard-claude-science-ultraviolet-map-2026",
      "target": {
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        "version": 1,
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      "band": "B",
      "modifier": null,
      "points": "20000",
      "range": {
        "lower": "7000",
        "upper": "50000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Full sky does not mean fully observed: filled regions are predictions, not discoveries of new objects or an independent dust tracer. The author project page reports held-out checks but no human peer review. Claude Science orchestrated the workflow; the gap-filling model is statistical regression, not an image generator."
    },
    {
      "id": "lange-et-al-robust-kernel-discovery-2025",
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        "version": 1,
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      "band": "B",
      "modifier": "+",
      "points": "35000",
      "range": {
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        "upper": "80000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Model-based soft verification is a fallible filter, not formal proof; hardware comparisons still test finite inputs and tolerances. Speedups depend on baseline, shape and GPU, and backward kernels remain harder. Removing contaminated tasks substantially reduces headline gains."
    },
    {
      "id": "chen-wen-kirchner-automated-alignment-research-2026",
      "target": {
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        "version": 1,
        "content_hash": "sha256:cc36a60884087c114dd713083545cea1890f82e90c2e1643c78377ac9e3d49d8"
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      "band": "B",
      "modifier": "+",
      "points": "30000",
      "range": {
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        "upper": "80000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Public benchmarks and automated audits are proxies, not overall alignment certification. Capability checks cover selected tasks, the human baseline cannot iterate, and post-hoc cheating detection is imperfect. Persistence after extensive subsequent training and effects on unmeasured capabilities remain untested."
    },
    {
      "id": "wen-et-al-claude-weak-to-strong-research-2026",
      "target": {
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      "points": "20000",
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        "upper": "60000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Repeated access makes the principal evaluation set effectively validation, and agents found shortcuts and evaluation exploits. Independent-domain transfer varies, and a production-scale posterior-label trial showed only a noise-floor improvement. Recovery on selected binary tasks is not a general solution to weak-to-strong alignment or superiority over unrestricted human research."
    },
    {
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      "points": "180000",
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        "upper": "350000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Source-claimed proof, not independently verified by WRS. The coefficient is not the conjectured sharp value 1. The complete analytic argument and any formal coverage have not been independently reconstructed by WRS."
    },
    {
      "id": "lin-hyra-claimed-near-quadratic-hadamard-count-2026",
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      "points": "220000",
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        "lower": "120000",
        "upper": "400000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Source-claimed proof, not independently verified by WRS. The result covers each fixed power-law regime m/n^(2+η)→∞ with η>0, not the endpoint m/n²→∞. The supplied Lean counting assembly assumes the unformalized analytic row estimate hstep; the exponent module proves a sufficient-regime bridge, not impossibility of the counting formula at smaller exponents."
    },
    {
      "id": "hyra-claimed-cubic-log-commutator-bound-2026",
      "target": {
        "record_id": "urn:uuid:13e6694e-a270-4833-a366-a580d61054a1",
        "version": 1,
        "content_hash": "sha256:cddc853e0611c0caeaa625860256c91356b397b717db34101979d5a829fe65fd"
      },
      "band": "A",
      "modifier": "-",
      "points": "110000",
      "range": {
        "lower": "50000",
        "upper": "220000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Source-claimed proof, not independently verified by WRS. Arbitrary infinite dimension includes nonseparable spaces; finite dimensions have an obstruction at error below 1. The logarithmic lower bound remains separated from this cubic upper bound. Lean scope excludes the surrounding B(H) right inverse and Banach fixed-point existence argument; no compilation was run."
    },
    {
      "id": "hyra-claimed-constant-width-volume-lower-bound-2026",
      "target": {
        "record_id": "urn:uuid:2381202f-8e04-41c9-a760-eef806d4bccb",
        "version": 1,
        "content_hash": "sha256:e1bc4072eae70bdb38d457812d763dcf9139c31566e1cf47706ef46bebbd31c6"
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      "band": "A",
      "modifier": "+",
      "points": "240000",
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        "lower": "120000",
        "upper": "420000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Source-claimed computer-assisted proof, not independently verified by WRS. Rational certificate scripts have not been replayed by WRS. The analytic-only bound is about 0.4041207788w^3; neither result proves the Meissner minimizer conjecture. A subsequent preprint by Yunjiang Jiang reports 0.41275w^3 using part of this mechanism, so the original bound is a historical advance rather than the current strongest reported bound."
    },
    {
      "id": "qwen-team-omni-agent-dialect-adaptation-2026",
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        "record_id": "urn:uuid:1eb9143a-1c01-431b-a5ca-6f91253005e7",
        "version": 1,
        "content_hash": "sha256:a6b02cfe9835093f25ec71f041beb925ba1339f8579f5a96fea743072b79032e"
      },
      "band": "C",
      "modifier": "+",
      "points": "4000",
      "range": {
        "lower": "1500",
        "upper": "10000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Single source-reported four-round experiment; no WRS replay. The agent selected the evaluation set and reused its feedback, so the reported same-set improvement is not an untouched held-out generalization estimate. No general autonomous-scientist capability or new finetuning algorithm follows."
    },
    {
      "id": "lin-li-hyra-claimed-sharp-sum-difference-exponent-2026",
      "target": {
        "record_id": "urn:uuid:a11b1fc7-b8c3-47c7-ad02-10af6979c4bd",
        "version": 1,
        "content_hash": "sha256:2f129a64d32833b56f8bffaaf34506992bc1bbe077c1b5fd2be2e5267cf8c852"
      },
      "band": "S",
      "modifier": "-",
      "points": "350000",
      "range": {
        "lower": "180000",
        "upper": "600000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Source-claimed proof, not independently verified by WRS. Strict C(A)<2 for each finite integer set with |A|≥2 is inherited; the new claim is a family approaching the unattained supremum. The formal companion uses a base-39 variant rather than the paper's base-12 construction and depends on native_decide finite certificates; no Lean build or full proof audit was run."
    },
    {
      "id": "hyra-team-fixed-budget-ngram-induction-lm-recipe-2026",
      "target": {
        "record_id": "urn:uuid:482a5599-f16a-4f8f-a7b0-cc40dfb2ba16",
        "version": 1,
        "content_hash": "sha256:1c7a8586ffacf5dac811bbde8b61ebcc6e376a79a5732491b627ba412f6d10b2"
      },
      "band": "C",
      "modifier": "+",
      "points": "6000",
      "range": {
        "lower": "2500",
        "upper": "15000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "One source-reported 300-second single-B200 experiment, about 348 seconds including setup/evaluation and 169 GB memory. This is not a universal efficiency gain or large-model scaling result. Muon/AdamW, attention and embedding techniques are inherited. WRS has not replayed the training or independently established generalization."
    },
    {
      "id": "recursive-ai-fixed-budget-value-hash-recipes-2026",
      "target": {
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        "version": 1,
        "content_hash": "sha256:3e10548c9cb992382690c918607ac0c04f10fbc5091e397fa8888069c12d6eb7"
      },
      "band": "C",
      "modifier": "+",
      "points": "5500",
      "range": {
        "lower": "2200",
        "upper": "14000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Ten-seed five-minute single-B200 tests, not a large-model scaling guarantee or proof of independent rediscovery. Hash embeddings, Muon and baseline nanochat components are inherited. Search initially used H100; hardware transfer and repeated benchmark feedback constrain comparisons. No training or no-leakage audit was replayed."
    },
    {
      "id": "recursive-ai-fp8-noisy-optimizer-speedrun-2026",
      "target": {
        "record_id": "urn:uuid:1af0689f-6d5a-42ad-aedf-605e2d1f7e3d",
        "version": 1,
        "content_hash": "sha256:f06077dc0d30286a3ce8a4232d5ba4bce3878c2115b61db517ec2225a7c37ff4"
      },
      "band": "C",
      "modifier": "+",
      "points": "4000",
      "range": {
        "lower": "1500",
        "upper": "12000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "The pinned source reports a 13-run 77.34-second mean on Modal 8xH100 against 80.61 seconds for its matched baseline; official leaderboard-machine timing was pending. These differ from the article's 77.5 seconds and external 79.7-second reference. WRS has not replayed loss-threshold testing; universal quality-preserving speedup is not established."
    },
    {
      "id": "recursive-ai-generated-generic-gpu-kernels-2026",
      "target": {
        "record_id": "urn:uuid:d866277b-e023-4680-a1a4-59e89516da26",
        "version": 1,
        "content_hash": "sha256:c2fd808cea2a7bd852afa0f1c6ebd42c08ab6b2bf7fea3b1001aac453e4ac866"
      },
      "band": "B",
      "modifier": "-",
      "points": "9000",
      "range": {
        "lower": "3000",
        "upper": "25000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "Only 10 of 235 claimed benchmark implementations are public. Broad aggregate results depend on unreleased code and have not been independently reconstructed by WRS. Fixed-workload tolerance, shape and synchronization assumptions do not establish all-input or multi-stream correctness."
    },
    {
      "id": "hyra-team-qubit-routing-circuit-artifacts-2026",
      "target": {
        "record_id": "urn:uuid:98bd83eb-2f13-4896-aa04-0886b27e5c21",
        "version": 1,
        "content_hash": "sha256:92cd04ef26cbd69e1232769fbc477b0164fd82b24aef86c6376d6a406e4bdc51"
      },
      "band": "C",
      "modifier": "+",
      "points": "3500",
      "range": {
        "lower": "1200",
        "upper": "10000"
      },
      "status": "CONDITIONAL_IF_VERIFIED",
      "counts_as_achieved": false,
      "scientific_correctness_certified": false,
      "scope": "A fixed finite artifact comparison, not a generally optimal routing algorithm, hardware experiment or independently reproduced benchmark. Complete circuit equivalence, adjacency validity and reported CNOT totals still require an independent replay."
    }
  ]
}