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      "id": "classical-euler-product",
      "title": "Classical baseline · θ = 1",
      "theta": {
        "numerator": "1",
        "denominator": "1"
      },
      "authors": [
        {
          "name": "Classical Euler-product theorem"
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      ],
      "method": "Absolute convergence of the Euler products gives nonvanishing of the Riemann zeta function and every Dirichlet L-function for Re(s) > 1. This is the classical starting bound; quasi-RH asks for a fixed boundary strictly below 1.",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/classical-euler-product.json"
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        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/verifier/standard/receipts/classical-first-20261012/solution-src/Solution.lean"
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        {
          "label": "Hardy–Littlewood, Partitio numerorum III, p. 4 (Hypothesis R); scan printed in 1922",
          "url": "https://archive.ymsc.tsinghua.edu.cn/pacm_download/117/5327-11511_2006_Article_BF02403921.pdf"
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        {
          "label": "Publisher catalogue: Acta Mathematica 44 (1923), pp. 1–70",
          "url": "https://link.springer.com/article/10.1007/BF02403921"
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        {
          "label": "Pinned Mathlib proof of all-Dirichlet nonvanishing for Re(s) > 1",
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        {
          "label": "Pinned standard submission and attribution",
          "url": "https://github.com/nielstron/QuasiRiemannTracker/tree/a04a07166729cadd3d74da634c6cfa7b2821f2c2/submissions/classical-euler-product"
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      "timeline_at": "1922-01-01T00:00:00Z",
      "date_precision": "year",
      "date_label": "Early QRH-era formulation",
      "verification_note": "Comparator verified the canonical all-Dirichlet statement at θ = 1. Lean, NanoDa and con-ron accepted the proof in the standard sandbox. The timeline uses the historical 1922 anchor; the verification date records the completed check.",
      "attribution_note": "The point uses 1922, the printing year shown in Hardy and Littlewood’s Partitio numerorum III; the publisher catalogues the volume in 1923. The paper supplies an early fixed-half-plane formulation and the timeline anchor. The Euler-product bound was already classical.",
      "certificate_url": "certificates/classical-euler-product.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/verifier/standard/receipts/classical-first-20261012/solution-src/Solution.lean"
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      "submitted_at": "",
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      "pr": null,
      "repository": "openai/math",
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      "first_verified_at": "2026-10-09T11:37:19Z",
      "entrypoint": {
        "module": "OAI.NumberTheory.DirichletL.Nonvanishing",
        "declaration": "OAI.DirichletCharacter.LFunction_ne_zero_of_seven_eighths_lt_re"
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      "license": "Apache-2.0",
      "builds_on": [],
      "id": "openai-baseline",
      "title": "OpenAI · seven eighths",
      "theta": {
        "numerator": "7",
        "denominator": "8"
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      "authors": [
        {
          "name": "OpenAI"
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      "method": "OpenAI’s quasi-Riemann framework establishes the 7/8 boundary. The original pinned proof has now been rebuilt and checked directly.",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/openai-baseline.json"
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        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/palomar-20261009/openai/src/Solution.lean"
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        {
          "label": "Original source and scope",
          "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/003.md"
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      "timeline_at": "2026-10-06T00:00:00Z",
      "date_label": "Public release",
      "verification_note": "Comparator verified the all-Dirichlet, zeta and finite-order Eisenstein Hecke statements and their definitions. Lean, NanoDa and con-ron accepted the exported proofs.",
      "certificate_url": "certificates/openai-baseline.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/palomar-20261009/openai/src/Solution.lean"
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      "pr": null,
      "repository": "Argonaut-Math/argonaut-math-quasi-riemann-boundary",
      "source_commit": "5971383edcb0b1cf863927eed3b359d2d3ba346e",
      "first_verified_at": "2026-10-10T10:09:10.743884+00:00",
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        "module": "PerturbedBoundaryMain",
        "declaration": "OAI.DirichletCharacter.LFunction_ne_zero_of_perturbed_boundary_lt_re"
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      "license": "Apache-2.0",
      "builds_on": [
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      "id": "argonaut-20261008",
      "title": "Argonaut · perturbed boundary",
      "theta": {
        "numerator": "3499999",
        "denominator": "4000000"
      },
      "authors": [
        {
          "name": "Argonaut Math"
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      ],
      "method": "Refinement of the OpenAI framework to 3499999/4000000. The pinned original proof has been independently reproduced and checked with Comparator and three kernels.",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/argonaut-20261008.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/argonaut-20261010-safe-replay/solution-src/Solution.lean"
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        {
          "label": "Reviewed original source package",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/argonaut-20261010-kernels/source-public.tar.gz"
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          "label": "Argonaut source and release",
          "url": "https://github.com/Argonaut-Math/argonaut-math-quasi-riemann-boundary"
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      "timeline_at": "2026-10-08T00:00:00Z",
      "date_label": "Public announcement",
      "verification_note": "The pinned v0.1.8 proof was rebuilt in an offline Linux sandbox. Comparator verified the all-Dirichlet, zeta and finite-order Eisenstein Hecke statements at exactly 3499999/4000000; Lean, NanoDa and con-ron accepted the proofs.",
      "certificate_url": "certificates/argonaut-20261008.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/argonaut-20261010-safe-replay/solution-src/Solution.lean"
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      "pr": null,
      "repository": "liubaiying101/Slightly-improved-zero-free-half-planes-for-the-quasi-Riemann-hypothesis",
      "source_commit": "7d10420de90efa2f082a06a342fc7accbd57ab37",
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        "module": "RHZeroFreeExtension.CombinedPaperVerification",
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      "license": "See source and notices",
      "builds_on": [
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      "id": "liu-20261008",
      "title": "Baiying Liu · optimized parameters",
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          "denominator": "1000000000000000000000000000000"
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      "authors": [
        {
          "name": "Baiying Liu"
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      "method": "Optimizes b and ℓ in the OpenAI argument. The exact boundary is algebraic. The plotted rational is a certified upper endpoint less than 10⁻³⁰ above it, used only for rendering.",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/liu-20261008.json"
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        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/liu-20261010-safe-replay/solution-src/Solution.lean"
        },
        {
          "label": "Paper · arXiv:2610.12234",
          "url": "https://arxiv.org/abs/2610.12234"
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        {
          "label": "Reported Lean formalization",
          "url": "https://github.com/liubaiying101/Slightly-improved-zero-free-half-planes-for-the-quasi-Riemann-hypothesis"
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      ],
      "status": "framework-verified",
      "timeline_at": "2026-10-08T16:18:53Z",
      "date_label": "arXiv submission",
      "verification_note": "The pinned proof was rebuilt in an offline Linux sandbox. Comparator verified the all-Dirichlet, zeta and finite-order Eisenstein Hecke statements at (1507 − 2√921) / 1653; Lean, NanoDa and con-ron accepted the proofs. The rational enclosure determines its chart position.",
      "certificate_url": "certificates/liu-20261008.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/liu-20261010-safe-replay/solution-src/Solution.lean"
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      "pr": null,
      "repository": "",
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      "first_verified_at": "2026-10-09T11:37:19Z",
      "entrypoint": {
        "module": "QRH.Nonvanishing",
        "declaration": "QRH.DirichletCharacter.LFunction_ne_zero_of_theta_lt_re"
      },
      "license": "Apache-2.0 (Lean development; retained upstream notices)",
      "builds_on": [
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      "id": "proofcouncil-20261009",
      "title": "ProofCouncil · certified uniform descent",
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      "authors": [
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          "name": "Tim Gehrunger · ProofCouncil"
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      "method": "Extends the actual masked moment and detector range, proves optimized low/high probe estimates, and applies Mellin continuation and all-character transfer. All three targets compile at the exact rational threshold.",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/proofcouncil-20261009.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/palomar-20261009/qrh/src/Solution.lean"
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          "label": "Lean proof source",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/qrh-20261009/Nonvanishing.lean"
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          "label": "Complete proof source, inputs and logs",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/qrh-20261009/source-public.tar.gz"
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          "label": "Accepted manuscript (TeX)",
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      ],
      "status": "framework-verified",
      "timeline_at": "2026-10-09T11:37:19Z",
      "date_label": "Lean verification",
      "verification_note": "Comparator verified the all-Dirichlet, zeta and finite-order Eisenstein Hecke statements and their definitions. Lean, NanoDa and con-ron accepted the exported proofs.",
      "attribution_note": "Tim Gehrunger is the maintainer; ProofCouncil is the project credit. AI-assisted research and formalization, reusing the Apache-2.0 OpenAI/math and Mathlib developments. This display credit does not amend the supplied manuscript’s blank author field.",
      "certificate_url": "certificates/proofcouncil-20261009.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/palomar-20261009/qrh/src/Solution.lean"
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    {
      "submitted_at": "",
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      "pr": null,
      "repository": "nielstron/QuasiRiemannTracker",
      "source_commit": "2fc2b0b7f2b9510df4618936e1b2ccd58f7d9171",
      "first_verified_at": "2026-10-09T19:51:12.662856+00:00",
      "entrypoint": {
        "module": "QRH.TighterNonvanishing",
        "declaration": "QRH.DirichletCharacter.LFunction_ne_zero_of_tightTheta_lt_re"
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      "license": "Apache-2.0 (retained upstream notices)",
      "builds_on": [
        "proofcouncil-20261009",
        "openai-baseline"
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      "id": "nielstron-20261009-tightening",
      "title": "nielstron · exact algebraic endpoint",
      "theta": {
        "numerator": "874957019420098946128603850561452983",
        "denominator": "1000000000000000000000000000000000000"
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      "authors": [
        {
          "name": "nielstron",
          "url": "https://github.com/nielstron"
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      ],
      "method": "Revision of the same compressed Lean contribution to the exact cubic endpoint: 11/12-e/4, where e is the unique real root in [1/6,1/5] of 657e³−954e²+21e+20=0. The plotted rational is a rigorously proved upper bound. The final QRH package uses 259,073 source tokens under the pinned LeanLeanBench metric. The earlier N24 proof and its evidence remain available as historical snapshots.",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/nielstron-algebraic-20261009.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/nielstron-algebraic-20261009-kernels/src/Solution.lean"
        },
        {
          "label": "Frozen source and native evidence",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/nielstron-algebraic-20261009/source-public.tar.gz"
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      ],
      "status": "framework-verified",
      "timeline_at": "2026-10-09T19:51:12.662856+00:00",
      "date_label": "Independent kernel verification",
      "verification_note": "Comparator verified seven targets: three rational bounds, three exact algebraic bounds and unique root existence. Lean, NanoDa and con-ron accepted the proofs. Positive, statement-mismatch and ill-typed-proof controls passed.",
      "attribution_note": "Human contributor: nielstron. AI-assisted research and formalization; inherited ProofCouncil and OpenAI notices retained.",
      "proof_revision": "nielstron-algebraic-20261009",
      "certificate_url": "certificates/nielstron-algebraic-20261009.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/nielstron-algebraic-20261009-kernels/src/Solution.lean"
    },
    {
      "submitted_at": "2026-10-10T03:22:55Z",
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      "pr": 6,
      "repository": "akashlevy/QuasiRiemannTracker",
      "source_commit": "ec626ec9c0e7ab7b29f6c916314932caeb4df39a",
      "first_verified_at": "2026-10-10T13:35:18.422104+00:00",
      "entrypoint": {
        "module": "WeightedQRH.Statements",
        "declaration": "OAI.DirichletCharacter.LFunction_ne_zero_of_10499_12000_lt_re"
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      "license": "Apache-2.0 (retained upstream notices)",
      "builds_on": [
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      "id": "akashlevy-20261009-weighted-numerator",
      "title": "Akash Levy · weighted numerator",
      "theta": {
        "numerator": "10499",
        "denominator": "12000"
      },
      "authors": [
        {
          "name": "Akash Levy",
          "url": "https://github.com/akashlevy"
        }
      ],
      "method": "Replaces the pointwise numerator bound in the cubic-theta probe of OpenAI's argument by a weighted fourth moment of the reflected physical numerator: Mellin inversion and the Hecke functional equation reduce the actual smoothed numerator sum to a plain polynomial of length at most U/Y, and the unused length carries selected prime factors in the original fourth moment, while a coefficient-norm argument controls the original Euler correction and its ramified error terms. The moment parameter stays at the original kappa = 3/4; with ell = 167/1000, theta = 11/12 - ell/4 = 10499/12000, and the finite exponent comparisons are exact rational certificates. Lean 4.34.1 development of 228 modules on the akashlevy/math fork (c388e88e6) of OpenAI/math fd4aeeb, with Mathlib d13f23b7; it proves zeta, all-Dirichlet and finite-order Hecke nonvanishing for Re s > 10499/12000.",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/akashlevy-20261009-weighted-numerator.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/akashlevy-20261009-weighted-numerator/Solution.lean"
        },
        {
          "label": "Manuscript (PDF)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/akashlevy-20261009-weighted-numerator/manuscript.pdf"
        },
        {
          "label": "Manuscript (TeX)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/akashlevy-20261009-weighted-numerator/weighted_numerator_proof.tex"
        },
        {
          "label": "Manuscript lemma (TeX, input by the manuscript)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/akashlevy-20261009-weighted-numerator/weighted_numerator_lemma.tex"
        },
        {
          "label": "Complete Lean source, manuscript source and evidence",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/akashlevy-20261009-weighted-numerator/source-public.tar.gz"
        },
        {
          "label": "Lean base: akashlevy/math fork of OpenAI/math",
          "url": "https://github.com/akashlevy/math/tree/c388e88e6519d139ad2ca5571ef0c7fbf0e245b5"
        }
      ],
      "status": "framework-verified",
      "timeline_at": "2026-10-10T03:22:55Z",
      "date_label": "PR submitted",
      "verification_note": "The 228 submitted modules and 2,670 dependency modules were rebuilt in an offline Linux sandbox. Comparator verified the all-Dirichlet, zeta and Eisenstein Hecke statements at 10499/12000; Lean, NanoDa and con-ron accepted the proofs. The timeline records this first independent acceptance.",
      "attribution_note": "Akash Levy (akashlevy) is the human contributor. GPT-6 Astra (Ultra) was used to discover the proof and perform partial formalization; Opus 5.5 Ultracode was used to complete the formalization and submit the result. Builds on the Apache-2.0 OpenAI/math and Mathlib developments; upstream notices are retained.",
      "certificate_url": "certificates/akashlevy-20261009-weighted-numerator.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/akashlevy-20261009-weighted-numerator/Solution.lean"
    },
    {
      "submitted_at": "",
      "published_at": "",
      "merged_at": "",
      "pr": 8,
      "repository": "HaileyStorm/QuasiRiemannTracker",
      "source_commit": "eecd4131f1cac4f31f71e84b301a4e4619aa18d9",
      "first_verified_at": "2026-10-12T18:44:41.093487+00:00",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "license": "Apache-2.0 for the OpenAI-derived Lean sources; manuscript licensing is separate, see NOTICE.md",
      "builds_on": [
        "openai-baseline"
      ],
      "id": "single-prime-29-33-20261010",
      "title": "Single compensating prime · 29/33",
      "theta": {
        "numerator": "29",
        "denominator": "33"
      },
      "authors": [
        {
          "name": "Hailey Collet"
        }
      ],
      "method": "A single compensating-prime construction and finite descent give all-Dirichlet nonvanishing to the right of 29/33. The development includes an unconditional moving-radical mixed moment and uses pinned OpenAI foundations.",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/single-prime-29-33-20261010.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/verifier/standard/receipts/single-prime-first-20261012/solution-src/Solution.lean"
        },
        {
          "label": "Rendered manuscript (PDF)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/single-prime-29-33-20261010/zeta_zero_free_4_33_self_contained.pdf"
        },
        {
          "label": "Source and reproduction",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/tree/d716ecaae80f7823a5b8314916364fdfa0d133fb/proofs/single-prime-29-33-20261010"
        },
        {
          "label": "Pinned standard submission",
          "url": "https://github.com/HaileyStorm/QuasiRiemannTracker/tree/eecd4131f1cac4f31f71e84b301a4e4619aa18d9/submissions/single-prime-29-33-20261010"
        }
      ],
      "status": "framework-verified",
      "timeline_at": "2026-10-10T07:47:35.881822+00:00",
      "date_label": "Contributor three-kernel verification",
      "verification_note": "Comparator verified the canonical all-Dirichlet statement at 29/33. Lean, NanoDa and con-ron accepted the proof in the standard sandbox. The timeline records contributor verification; the verification date records the independent standard check.",
      "attribution_note": "Manuscript by Hailey Collet, developed with assistance from OpenAI's GPT-6 Pro. Formalization submitted as HaileyStorm with substantial OpenAI Codex assistance, adapting pinned OpenAI/math foundations. See NOTICE.md for attribution and licensing.",
      "certificate_url": "certificates/single-prime-29-33-20261010.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/verifier/standard/receipts/single-prime-first-20261012/solution-src/Solution.lean"
    },
    {
      "submitted_at": "2026-10-10T12:08:27Z",
      "published_at": "",
      "merged_at": "",
      "pr": 9,
      "repository": "HaileyStorm/QuasiRiemannTracker",
      "source_commit": "58344dfdbe756cf2f743da1908ffe0582418cf5b",
      "first_verified_at": "2026-10-10T16:09:09.733191+00:00",
      "entrypoint": {
        "module": "Cycle25.Assembly.Final.Endpoint",
        "declaration": "Cycle25.dirichlet_nonzero_catalogue"
      },
      "license": "Apache-2.0 (retained upstream notices)",
      "builds_on": [
        "openai-baseline",
        "akashlevy-20261009-weighted-numerator"
      ],
      "id": "cycle25-quartic-20261010",
      "title": "Hailey Collet · quartic boundary",
      "theta": {
        "numerator": "683505193",
        "denominator": "781250000"
      },
      "authors": [
        {
          "name": "Hailey Collet"
        }
      ],
      "method": "The exact boundary is 11/12−ℓ/4, where ℓ is the unique root in [1/6,1/5] of 927ℓ⁴−3135ℓ³+2433ℓ²+275ℓ−100=0. The plotted rational 683505193/781250000 is a proved upper bound less than 4×10⁻¹⁴ above it. The proof extends the unconditional common-mesh moving-radical moment and applies weighted low/high estimates and analytic continuation to Dirichlet, zeta and finite-order Eisenstein Hecke L-functions.",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/cycle25-quartic-20261010.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/cycle25-20261010-safe-replay/solution-src/Solution.lean"
        },
        {
          "label": "Paper (PDF)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/cycle25-quartic-20261010/paper.pdf"
        },
        {
          "label": "Paper source (TeX)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/cycle25-quartic-20261010/paper.tex"
        },
        {
          "label": "Finished proof source and evidence",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/cycle25-quartic-20261010/source-public.tar.gz"
        }
      ],
      "status": "framework-verified",
      "timeline_at": "2026-10-10T12:08:27Z",
      "date_label": "PR submitted",
      "verification_note": "The 3,224 Lean modules were rebuilt in an offline Linux sandbox. Comparator verified the rational and exact quartic all-Dirichlet, zeta and Eisenstein Hecke bounds, quartic root existence and uniqueness, and the reusable moment theorem. Lean, NanoDa and con-ron accepted all eight targets. The timeline records this first independent acceptance.",
      "attribution_note": "Human contributor: Hailey Collet. AI-assisted research and formalization, reusing OpenAI/math, Mathlib and Akash Levy’s weighted construction. The earlier single-compensating-prime development supplies a reused unconditional moment lemma; its terminal 29/33 bound is not an assumption. Upstream licenses and notices are retained.",
      "certificate_url": "certificates/cycle25-quartic-20261010.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/cycle25-20261010-safe-replay/solution-src/Solution.lean"
    },
    {
      "id": "local44-20261013",
      "title": "nielstron · local 22/5 moment",
      "theta": {
        "numerator": "87487",
        "denominator": "100000"
      },
      "authors": [
        {
          "name": "nielstron",
          "url": "https://github.com/nielstron"
        }
      ],
      "method": "A local fourth-moment estimate with prime cost 22/5 gives all-Dirichlet nonvanishing for Re(s) > 87487/100000, excluding the principal pole. Coherent amplification and a joint reconstructed-row density estimate preserve cancellation through the error terms; independent heights, coefficient dilations and physical normalization feed the low/high assembly and unconditional continuation argument.",
      "status": "framework-verified",
      "submitted_at": "2026-10-13T00:29:50Z",
      "published_at": "",
      "merged_at": "2026-10-13T06:45:53Z",
      "pr": 26,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "16ce30342471344c2b2f0d383388e6f9acb9bccf",
      "first_verified_at": "2026-10-13T06:44:04.476615+00:00",
      "timeline_at": "2026-10-13T00:29:50Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "license": "Apache-2.0 (retained upstream notices)",
      "builds_on": [
        "openai-baseline",
        "akashlevy-20261009-weighted-numerator",
        "cycle25-quartic-20261010"
      ],
      "verification_note": "The hosted PR worker accepted the canonical all-Dirichlet theorem at 87487/100000 for the exact submitted commit. Comparator checked the statement, definitions and permitted axioms; Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "attribution_note": "Human contributor: nielstron. Builds on OpenAI/math, Akash Levy’s weighted numerator, Hailey Collet’s Cycle25 framework, Zhongpai Gao’s local-moment work, Mathlib and their dependencies. Upstream attribution and license notices are retained in the submitted Lean sources.",
      "certificate_url": "certificates/local44-20261013.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/16ce30342471344c2b2f0d383388e6f9acb9bccf/submissions/local44-20261013/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/local44-20261013.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/16ce30342471344c2b2f0d383388e6f9acb9bccf/submissions/local44-20261013/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/26"
        },
        {
          "label": "Independent verification run",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/actions/runs/38342781752/attempts/1"
        },
        {
          "label": "Original mathematical explanation",
          "url": "https://github.com/nielstron/QuasiRiemannTracker/blob/ef2ae62e99e2df364aaf4f4680e03a24216fdb22/submissions/local44-20261013/explanation.md"
        },
        {
          "label": "Zhongpai Gao’s local-moment work",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/15"
        }
      ]
    },
    {
      "id": "affine-local-20261013",
      "title": "Affine local-moment capacity",
      "theta": {
        "numerator": "4374347",
        "denominator": "5000000"
      },
      "authors": [
        {
          "name": "Kari Roegnvaldsson",
          "url": "https://github.com/karirogg"
        }
      ],
      "method": "Retains the local fourth-moment proof's separate volume and capacity-defect allowances through its actual-source and physical transport wrappers. This replaces the narrower 22/5 capacity slice by an affine capacity and feeds a revised exact endpoint certificate into the all-Dirichlet continuation argument. Builds on nielstron's local 22/5 moment, Zhongpai Gao's local-moment work, Hailey Collet's Cycle25 framework, Akash Levy's weighted numerator, and OpenAI/math. Prepared with AI assistance.",
      "license": "Apache-2.0 (inherited notices retained)",
      "builds_on": [
        "local44-20261013"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-13T11:42:58Z",
      "published_at": "",
      "merged_at": "2026-10-13T14:53:44Z",
      "pr": 37,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "c707738a659786b9a44a79c629bed8c801cca8f3",
      "first_verified_at": "2026-10-13T13:04:36.374379+00:00",
      "timeline_at": "2026-10-13T11:42:58Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 4374347/5000000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/affine-local-20261013.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/c707738a659786b9a44a79c629bed8c801cca8f3/submissions/affine-local-20261013/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/affine-local-20261013.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/c707738a659786b9a44a79c629bed8c801cca8f3/submissions/affine-local-20261013/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/37"
        },
        {
          "label": "Local 22/5 predecessor",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/26"
        }
      ]
    },
    {
      "id": "reserve-local-20261013",
      "title": "Reserve-balanced affine local moment",
      "theta": {
        "numerator": "87486797",
        "denominator": "100000000"
      },
      "authors": [
        {
          "name": "Kari Roegnvaldsson",
          "url": "https://github.com/karirogg"
        }
      ],
      "method": "Reallocates intermediate LOW and extracted-error reserves to enlarge the affine local-moment defect allowance to 1/250 while retaining the amplifier, volume cap, and final analytic savings. Regenerates the endpoint and transport arithmetic for the canonical all-Dirichlet statement. Builds on Kari Roegnvaldsson's affine-capacity proof, nielstron's local 22/5 moment, Zhongpai Gao's local-moment work, Hailey Collet's Cycle25 framework, Akash Levy's weighted numerator, and OpenAI/math. Prepared with AI assistance.",
      "license": "Apache-2.0 (inherited notices retained)",
      "builds_on": [
        "local44-20261013"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-13T13:23:23Z",
      "published_at": "",
      "merged_at": "2026-10-13T15:24:43Z",
      "pr": 38,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "14ab1618c5133a7d12e06aa76661bbcb34e843cd",
      "first_verified_at": "2026-10-13T14:41:11.858515+00:00",
      "timeline_at": "2026-10-13T13:23:23Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 87486797/100000000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/reserve-local-20261013.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/14ab1618c5133a7d12e06aa76661bbcb34e843cd/submissions/reserve-local-20261013/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/reserve-local-20261013.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/14ab1618c5133a7d12e06aa76661bbcb34e843cd/submissions/reserve-local-20261013/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/38"
        },
        {
          "label": "Verified affine-capacity predecessor",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/37"
        },
        {
          "label": "Local 22/5 predecessor",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/26"
        }
      ]
    },
    {
      "id": "gao-asymmetric-reserves-20261013",
      "title": "Asymmetric reserves · 0.8748673",
      "theta": {
        "numerator": "8748673",
        "denominator": "10000000"
      },
      "authors": [
        {
          "name": "Zhongpai Gao",
          "url": "https://github.com/Gaozhongpai"
        }
      ],
      "method": "Refines affine local capacity to defect 1/241 using asymmetric LOW reserves and exact endpoint geometry. Complete 128-module candidate proof of the all-moduli Dirichlet theorem. Builds on Kari Roegnvaldsson, nielstron, OpenAI, Akash Levy, Hailey Collet, and Gao's earlier adapters. AI-assisted; inherited notices retained.",
      "license": "Apache-2.0",
      "builds_on": [
        "reserve-local-20261013",
        "affine-local-20261013",
        "local44-20261013"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-13T15:53:59Z",
      "published_at": "",
      "merged_at": "2026-10-13T20:53:36Z",
      "pr": 41,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "82da425c8f8da008de063eaebe1c8d33e9c33f21",
      "first_verified_at": "2026-10-13T18:43:50.342009+00:00",
      "timeline_at": "2026-10-13T15:53:59Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 8748673/10000000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/gao-asymmetric-reserves-20261013.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/82da425c8f8da008de063eaebe1c8d33e9c33f21/submissions/gao-asymmetric-reserves-20261013/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/gao-asymmetric-reserves-20261013.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/82da425c8f8da008de063eaebe1c8d33e9c33f21/submissions/gao-asymmetric-reserves-20261013/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/41"
        },
        {
          "label": "Asymmetric reserve allocation paper",
          "url": "https://github.com/Gaozhongpai/QuasiRiemannTracker/blob/c5235c0c4b21e548a86b0c616fb295e2c3a00441/proofs/gao-asymmetric-reserves-20261013/paper.pdf"
        }
      ]
    },
    {
      "id": "cycle61-c0125139",
      "title": "A zero-free half-plane with boundary 874861/1000000",
      "theta": {
        "numerator": "874861",
        "denominator": "1000000"
      },
      "authors": [
        {
          "name": "Hailey Collet",
          "url": "https://github.com/HaileyStorm"
        }
      ],
      "method": "An unconditional all-Dirichlet zero-free half-plane at theta=874861/1000000, with strict boundary and the principal pole excluded. The proof combines earlier moment and physical-source estimates with Zhongpai Gao’s local refinement, extends the density range and local numerical region, and supplies a common probe for zero exclusion. It builds on OpenAI’s seven-eighths framework, Akash Levy’s weighted-numerator work, and the earlier AI-assisted QRH research directed by Hailey Collet. Hailey is the sole human author; research direction and source integration are distinguished from the AI-produced derivations, substantial drafting and formalization. Exact source attribution is retained in the paper and accompanying provenance.",
      "license": "Apache-2.0, with retained upstream licenses and notices",
      "builds_on": [
        "openai-baseline",
        "akashlevy-20261009-weighted-numerator",
        "single-prime-29-33-20261010",
        "cycle25-quartic-20261010"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-13T16:56:38Z",
      "published_at": "",
      "merged_at": "2026-10-13T20:55:29Z",
      "pr": 42,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "fb6d4fd11aeaff0b37dd96bad3b274ce28a5c08b",
      "first_verified_at": "2026-10-13T18:43:23.391812+00:00",
      "timeline_at": "2026-10-13T16:56:38Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 874861/1000000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/cycle61-c0125139.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/fb6d4fd11aeaff0b37dd96bad3b274ce28a5c08b/submissions/cycle61-c0125139/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/cycle61-c0125139.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/fb6d4fd11aeaff0b37dd96bad3b274ce28a5c08b/submissions/cycle61-c0125139/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/42"
        },
        {
          "label": "Paper and downloads",
          "url": "https://haileystorm.github.io/research/cycle61-qrh-boundary/"
        },
        {
          "label": "Gao local-refinement source",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/15"
        }
      ]
    },
    {
      "id": "gao-cycle61-plane-20261013",
      "title": "Refine the Cycle61 zero-free boundary to 0.8748598",
      "theta": {
        "numerator": "4374299",
        "denominator": "5000000"
      },
      "authors": [
        {
          "name": "Zhongpai Gao",
          "url": "https://github.com/Gaozhongpai"
        }
      ],
      "method": "A Cycle61 parameter refinement at the canonical all-moduli Dirichlet boundary 4374299/5000000, adapting Hailey Collet’s complete source. It couples the density split and source/amplification parameters, propagates exact reserves through the actual analytic consumers, and supplies global quadratic row certificates. The 206-module source splits the slow B167/B176 compilation units. Prepared with AI assistance; original attribution and Apache-2.0 notices retained.",
      "license": "Apache-2.0; inherited source notices and dependency licenses retained.",
      "builds_on": [
        "openai-baseline",
        "akashlevy-20261009-weighted-numerator",
        "cycle25-quartic-20261010",
        "cycle61-c0125139"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-13T21:06:27Z",
      "published_at": "",
      "merged_at": "2026-10-14T11:47:05Z",
      "pr": 43,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "9e0008692e77836a9a61cff25c808727d6d6690d",
      "first_verified_at": "2026-10-14T10:07:04.865497+00:00",
      "timeline_at": "2026-10-13T21:06:27Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 4374299/5000000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/gao-cycle61-plane-20261013.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/9e0008692e77836a9a61cff25c808727d6d6690d/submissions/gao-cycle61-plane-20261013/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/gao-cycle61-plane-20261013.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/9e0008692e77836a9a61cff25c808727d6d6690d/submissions/gao-cycle61-plane-20261013/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/43"
        },
        {
          "label": "Cycle61 source (PR #42)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/42"
        },
        {
          "label": "Exact Cycle61 source snapshot",
          "url": "https://github.com/HaileyStorm/QuasiRiemannTracker/tree/fb6d4fd11aeaff0b37dd96bad3b274ce28a5c08b/submissions/cycle61-c0125139/src/Candidate"
        },
        {
          "label": "Gao local-refinement predecessor",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/15"
        },
        {
          "label": "Three-page mathematical note",
          "url": "https://github.com/Gaozhongpai/QuasiRiemannTracker/blob/752fd1952a4dec6ef92181f6abc20e41269ff9b7/proofs/gao-cycle61-plane-20261013/paper.pdf"
        },
        {
          "label": "Complete Lean source",
          "url": "https://github.com/Gaozhongpai/QuasiRiemannTracker/blob/0a73e73348befd36061ff251e43540c1b11135bc/submissions/gao-cycle61-plane-20261013/src/Candidate/Main.lean"
        },
        {
          "label": "Independent maintainer verification and logs (14 October 2026)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/e238cab21d1ab48cfa17cff8f06ea11f0aaf3f7e/verifier/standard/receipts/pr43-9e000869-20261014/README.md"
        }
      ]
    },
    {
      "id": "marked-high-count-20261014",
      "title": "Marked high-zero counting gives the all-Dirichlet boundary 0.874858",
      "theta": {
        "numerator": "437429",
        "denominator": "500000"
      },
      "authors": [
        {
          "name": "timbalud",
          "url": "https://github.com/timbalud"
        }
      ],
      "method": "Proves the canonical all-moduli Dirichlet zero-free bound by retaining prime-slot amplitudes in high-zero counting and combining the resulting gain with common-allocation width conservation. Overlapping prime pools are handled by collision partitions. The source estimate gains 33/20000 before explicit losses. Builds on the complete Cycle61 construction and the listed predecessor proofs; inherited source attribution is preserved.",
      "license": "Apache-2.0; inherited notices and dependency licenses retained.",
      "builds_on": [
        "openai-baseline",
        "akashlevy-20261009-weighted-numerator",
        "cycle25-quartic-20261010",
        "cycle61-c0125139"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-14T16:56:17Z",
      "published_at": "",
      "merged_at": "2026-10-15T01:14:54Z",
      "pr": 48,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "57ca0662b4ddeb2a75c0e302d0350cc65cf67c12",
      "first_verified_at": "2026-10-15T01:10:53.369530+00:00",
      "timeline_at": "2026-10-14T16:56:17Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 437429/500000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/marked-high-count-20261014.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/57ca0662b4ddeb2a75c0e302d0350cc65cf67c12/submissions/marked-high-count-20261014/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/marked-high-count-20261014.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/57ca0662b4ddeb2a75c0e302d0350cc65cf67c12/submissions/marked-high-count-20261014/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/48"
        },
        {
          "label": "Cycle61 proof",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/42"
        },
        {
          "label": "Verified comparison bound 0.8748598",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/43"
        }
      ]
    },
    {
      "id": "radical-asymmetric-count-20261014",
      "title": "Asymmetric marked counting with coupled radical allocation",
      "theta": {
        "numerator": "8748559",
        "denominator": "10000000"
      },
      "authors": [
        {
          "name": "timbalud",
          "url": "https://github.com/timbalud"
        }
      ],
      "method": "Proves the all-moduli Dirichlet boundary 0.8748559. Separate inverse and plain prime-slot selections increase the marked count gain; retaining the common-radical penalty strengthens the allocation estimate. Their combined source saving is 37/10000 before charged errors. Builds on the marked high-zero construction, Cycle61, and the listed predecessor proofs; inherited attribution is preserved.",
      "license": "Apache-2.0; inherited notices and dependency licenses retained.",
      "builds_on": [
        "openai-baseline",
        "akashlevy-20261009-weighted-numerator",
        "cycle25-quartic-20261010",
        "cycle61-c0125139"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-14T19:38:41Z",
      "published_at": "",
      "merged_at": "2026-10-14T23:12:08Z",
      "pr": 50,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "8cb265dc34909040c6f8cb48f53b19670a217ceb",
      "first_verified_at": "2026-10-14T22:53:11.065059+00:00",
      "timeline_at": "2026-10-14T19:38:41Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 8748559/10000000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/radical-asymmetric-count-20261014.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/8cb265dc34909040c6f8cb48f53b19670a217ceb/submissions/radical-asymmetric-count-20261014/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/radical-asymmetric-count-20261014.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/8cb265dc34909040c6f8cb48f53b19670a217ceb/submissions/radical-asymmetric-count-20261014/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/50"
        },
        {
          "label": "Marked high-zero predecessor",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/48"
        },
        {
          "label": "Cycle61 construction",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/42"
        },
        {
          "label": "Verified comparison bound 0.8748598",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/43"
        }
      ]
    },
    {
      "id": "certb-local-20261013",
      "title": "CertB-pushed affine local moment and formal cubic-theta limit hierarchy (10935831/12500000 = 0.87486648)",
      "theta": {
        "numerator": "10935831",
        "denominator": "12500000"
      },
      "authors": [
        {
          "name": "Devin Watson",
          "url": "https://github.com/DevinWatson"
        }
      ],
      "method": "Tightens the reserve-balanced affine local-moment defect from g = 1/250 = 400/100000 to g = 429/100000 by utilizing the available slack in the extracted-error B026/B025 budget (leaving 19/15000000 > 0 on Face 2) and tightening final analytic/endpoint reserves to 1/50000000. Regenerates the dyadic Bernstein enclosure certificates in B028, B030, B038, and B116 at h = 397/500, ell = 1567507/9375000, ly = 4308736/9375000, and kappa = 4685831/6250000, yielding theta = 10935831/12500000 = 0.87486648. Also adds B127.lean proving the formal multi-regime hard-limit hierarchy across the cubic-theta strip architecture (fixed-plane single-cell wall 10935831/12500000, B026 four-face ceiling g <= 36/8375, variable-slope pivot domination, truncated-sieve no-go, multi-regime base-contract closure walls down to 0.874835, Regime V interior coupled variable-slope physical envelope down to 328/375 = 0.87466667, and the universal 13/15 low-side LP floor). Builds on Kari Roegnvaldsson's reserve-local-20261013 and affine-local-20261013, nielstron's local44-20261013, Zhongpai Gao's local-moment work, Hailey Collet's Cycle25 framework, Akash Levy's weighted numerator, and OpenAI/math.",
      "license": "Apache-2.0 (inherited notices retained)",
      "builds_on": [
        "reserve-local-20261013",
        "affine-local-20261013",
        "local44-20261013"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-14T20:34:45Z",
      "published_at": "",
      "merged_at": "2026-10-15T09:14:58Z",
      "pr": 53,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "df08a83bd6d336d50c9243a86d3234e29877097c",
      "first_verified_at": "2026-10-15T08:34:27.618778+00:00",
      "timeline_at": "2026-10-14T20:34:45Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 10935831/12500000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/certb-local-20261013.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/df08a83bd6d336d50c9243a86d3234e29877097c/submissions/certb-local-20261013/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/certb-local-20261013.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/df08a83bd6d336d50c9243a86d3234e29877097c/submissions/certb-local-20261013/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/53"
        },
        {
          "label": "Reserve-balanced affine local moment predecessor",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/38"
        },
        {
          "label": "Verified affine-capacity predecessor",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/37"
        },
        {
          "label": "Local 22/5 predecessor",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/26"
        }
      ]
    },
    {
      "id": "detector-affine-c0125154",
      "title": "Cycle61 with the affine moment in the detector count",
      "theta": {
        "numerator": "437423",
        "denominator": "500000"
      },
      "authors": [
        {
          "name": "DaysSky",
          "url": "https://github.com/DaysSky"
        }
      ],
      "method": "Builds on Hailey Collet's Cycle61 (874861/1000000). Cycle61's initial affine moment (Theorem 2.2), previously used only in the source row, is also applied in the detector's per-fiber count. For plain lengths m in [0.4137, 0.4235], the marked plain capacity (1-2m)/(6κ) becomes (B-2m)/Λ. On the critical region δ ∈ [0.445, 0.485], p ∈ [0.495, 0.5], this replaces Cycle25's countingR κ* by a κ-independent closed form and moves the endpoint to 437423/500000 with h = 15903/20000. The detector moment is supplied by Cycle61's generic paid main and error families at each dictionary character, with heights chosen per character. All other estimates are Cycle61's, rechecked at the new endpoint with exact rational certificates. AI disclosure: DaysSky with Claude assistance.",
      "license": "Apache-2.0",
      "builds_on": [
        "cycle61-c0125139"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-14T23:49:00Z",
      "published_at": "",
      "merged_at": "2026-10-15T03:57:21Z",
      "pr": 56,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "67edfb7a1161008b37ff32aadec35cecaa711731",
      "first_verified_at": "2026-10-15T03:53:47.992181+00:00",
      "timeline_at": "2026-10-14T23:49:00Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 437423/500000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/detector-affine-c0125154.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/67edfb7a1161008b37ff32aadec35cecaa711731/submissions/detector-affine-c0125154/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/detector-affine-c0125154.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/67edfb7a1161008b37ff32aadec35cecaa711731/submissions/detector-affine-c0125154/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/56"
        },
        {
          "label": "Original manuscript, provenance, licenses and supporting verification material",
          "url": "https://github.com/DaysSky/QuasiRiemannTracker/tree/a0efd9ee546b417de650f36bc8403f781706a94e/proofs/detector-affine-c0125154"
        }
      ]
    },
    {
      "id": "gao-affine-asymmetric-20261015",
      "title": "Affine detector counting with asymmetric marked reserves at 0.874840",
      "theta": {
        "numerator": "21871",
        "denominator": "25000"
      },
      "authors": [
        {
          "name": "Zhongpai Gao",
          "url": "https://github.com/Gaozhongpai"
        }
      ],
      "method": "Submission of the canonical all-moduli Dirichlet bound 21871/25000 (0.874840); official admission remains pending. Combines timbalud's asymmetric marked counting and coupled radical allocation (PR50) with DaysSky's affine detector-count source integration (PR56), using Hailey Collet's Cycle61 interior affine moment theorem for each detector character. Uses h=1989/2500 and lower height 159/200. Prepared with AI assistance; inherited mathematical attribution and source notices retained.",
      "license": "Apache-2.0; inherited source notices and dependency licenses retained.",
      "builds_on": [
        "openai-baseline",
        "akashlevy-20261009-weighted-numerator",
        "cycle25-quartic-20261010",
        "cycle61-c0125139",
        "gao-cycle61-plane-20261013",
        "radical-asymmetric-count-20261014",
        "detector-affine-c0125154"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-15T03:51:26Z",
      "published_at": "",
      "merged_at": "2026-10-15T10:56:12Z",
      "pr": 60,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "3874f3e75de18ff5806dcb9519fc260e034ef0e9",
      "first_verified_at": "2026-10-15T09:17:19.521444+00:00",
      "timeline_at": "2026-10-15T03:51:26Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 21871/25000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/gao-affine-asymmetric-20261015.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/3874f3e75de18ff5806dcb9519fc260e034ef0e9/submissions/gao-affine-asymmetric-20261015/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/gao-affine-asymmetric-20261015.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/3874f3e75de18ff5806dcb9519fc260e034ef0e9/submissions/gao-affine-asymmetric-20261015/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/60"
        },
        {
          "label": "Asymmetric marked counting and coupled radical allocation (timbalud)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/50"
        },
        {
          "label": "Affine detector count source integration (DaysSky)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/56"
        },
        {
          "label": "Cycle61 interior affine moment theorem (Hailey Collet)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/42"
        },
        {
          "label": "Earlier affine plane refinement (Zhongpai Gao)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/43"
        },
        {
          "label": "Related affine detector arithmetic proposal (liqsweep; incomplete integration)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/52"
        }
      ]
    },
    {
      "id": "gao-directional-affine-20261016",
      "title": "Directional marked affine source at 0.874836",
      "theta": {
        "numerator": "218709",
        "denominator": "250000"
      },
      "authors": [
        {
          "name": "Zhongpai Gao",
          "url": "https://github.com/Gaozhongpai"
        }
      ],
      "method": "All-moduli Dirichlet zero-free boundary 218709/250000 (0.874836), using the independently proved 0.874840 Hecke bound for LOW, moving marked HIGH width and valuation coupling, and separately paid ERROR estimates. Builds on OpenAI, Hailey Collet, Akash Levy, timbalud and DaysSky; inherited source notices retained. Zhongpai Gao, with AI assistance.",
      "license": "Apache-2.0; inherited source notices and dependency licenses retained.",
      "builds_on": [
        "openai-baseline",
        "akashlevy-20261009-weighted-numerator",
        "cycle25-quartic-20261010",
        "cycle61-c0125139",
        "gao-cycle61-plane-20261013",
        "radical-asymmetric-count-20261014",
        "detector-affine-c0125154",
        "gao-affine-asymmetric-20261015"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-16T13:08:46Z",
      "published_at": "",
      "merged_at": "2026-10-16T18:30:05Z",
      "pr": 62,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "b5e69ce575f43a72ec49ed690f1afb76d919f925",
      "first_verified_at": "2026-10-16T16:03:54.930059+00:00",
      "timeline_at": "2026-10-16T13:08:46Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 218709/250000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/gao-directional-affine-20261016.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/b5e69ce575f43a72ec49ed690f1afb76d919f925/submissions/gao-directional-affine-20261016/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/gao-directional-affine-20261016.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/b5e69ce575f43a72ec49ed690f1afb76d919f925/submissions/gao-directional-affine-20261016/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/62"
        },
        {
          "label": "Asymmetric marked counting and coupled radical allocation (timbalud)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/50"
        },
        {
          "label": "Affine detector count source integration (DaysSky)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/56"
        },
        {
          "label": "Cycle61 interior affine moment theorem (Hailey Collet)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/42"
        },
        {
          "label": "Earlier affine plane refinement (Zhongpai Gao)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/43"
        },
        {
          "label": "Related affine detector arithmetic proposal (liqsweep; incomplete integration)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/52"
        },
        {
          "label": "Accepted all-moduli affine boundary 0.874840 (Zhongpai Gao)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/60"
        },
        {
          "label": "Paper",
          "url": "https://github.com/Gaozhongpai/QuasiRiemannTracker/blob/gao-directional-affine-paper-20261016/papers/gao-directional-affine-20261016/paper.pdf"
        }
      ]
    },
    {
      "id": "gao-balanced-marked-20261017",
      "title": "Balanced common geometry and adaptive marked source at 0.874830",
      "theta": {
        "numerator": "87483",
        "denominator": "100000"
      },
      "authors": [
        {
          "name": "Zhongpai Gao",
          "url": "https://github.com/Gaozhongpai"
        }
      ],
      "method": "All-moduli Dirichlet zero-free boundary 87483/100000 (0.874830), combining balanced common-geometry normalization, density-adaptive marked caps, a finite two-plane affine source/count family, and the independently proved 0.874836 incumbent for LOW and ERROR. Builds on OpenAI, Hailey Collet, Akash Levy, timbalud and DaysSky; all inherited source notices retained. Zhongpai Gao, with AI assistance.",
      "license": "Apache-2.0; inherited source notices and dependency licenses retained.",
      "builds_on": [
        "gao-directional-affine-20261016",
        "openai-baseline",
        "akashlevy-20261009-weighted-numerator",
        "cycle25-quartic-20261010",
        "cycle61-c0125139",
        "gao-cycle61-plane-20261013",
        "radical-asymmetric-count-20261014",
        "detector-affine-c0125154",
        "gao-affine-asymmetric-20261015"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-17T02:59:24Z",
      "published_at": "",
      "merged_at": "2026-10-18T08:42:24Z",
      "pr": 63,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "52419a826d4a8465cdeb56aaa2d471c489221d1d",
      "first_verified_at": "2026-10-17T11:32:52.190604+00:00",
      "timeline_at": "2026-10-17T02:59:24Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 87483/100000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/gao-balanced-marked-20261017.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/52419a826d4a8465cdeb56aaa2d471c489221d1d/submissions/gao-balanced-marked-20261017/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/gao-balanced-marked-20261017.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/52419a826d4a8465cdeb56aaa2d471c489221d1d/submissions/gao-balanced-marked-20261017/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/63"
        },
        {
          "label": "Accepted 0.874836 predecessor source and proof",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/62"
        },
        {
          "label": "Paper",
          "url": "https://github.com/Gaozhongpai/QuasiRiemannTracker/blob/ee7be4e7f4aae2835610fe3a5d620dbe3a1b6791/papers/gao-balanced-marked-20261017/paper.pdf"
        },
        {
          "label": "Asymmetric marked counting and coupled radical allocation (timbalud)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/50"
        },
        {
          "label": "Affine detector count source integration (DaysSky)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/56"
        },
        {
          "label": "Cycle61 interior affine moment theorem (Hailey Collet)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/42"
        },
        {
          "label": "Earlier affine plane refinement (Zhongpai Gao)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/43"
        },
        {
          "label": "Related affine detector arithmetic proposal (liqsweep; incomplete integration)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/52"
        },
        {
          "label": "Accepted all-moduli affine boundary 0.874840 (Zhongpai Gao)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/60"
        }
      ]
    },
    {
      "id": "no-hardcoding-20261017",
      "title": "No hardcoding: the marked ledger's constants computed from their constraints, at 0.874835173",
      "theta": {
        "numerator": "874835173",
        "denominator": "1000000000"
      },
      "authors": [
        {
          "name": "ArviFoxy",
          "url": "https://github.com/ArviFoxy"
        }
      ],
      "method": "Proves the all-moduli Dirichlet boundary 874835173/1000000000. Starting from PR 50's source tree with the affine detector count of PR 52 and PR 56, the hand-picked constants of the marked ledger are replaced by the quantities they stand for, computed in Lean. The bin split of the LOW/HIGH ledger is the root of a strictly increasing residual (the price channel and the capped live channel of the marked saving both tight in the top cell), located by interval arithmetic and proved exact; the slope is the moving slope (430q^2 - 399q + 135)/(q(24q^2 - 34q + 35)) that makes the price bound of the HIGH reserve equal in every cell; the intercept is the largest one the price channel allows; the caps of the marked count, its bin top, its root cutoff and the amplifier cap and floor are the values at which their constraints hold with equality; the row length is the optimum of the top-row certificate; the slacks with a gate are the formulas of that gate; the savings of the row certificates are fixed fractions of the claim margin. All enclosures are computed by a bracket command at elaboration time and checked by the kernel. A Lean theorem shows that no other bin split and intercept admitted by the marked ledger gives a smaller class bound. 33 hand-picked constants of the starting tree are eliminated. The valuation price and the per-cell supplied width follow PR 62. Inherited attribution is preserved in the modules.",
      "license": "Apache-2.0; inherited notices and dependency licenses retained.",
      "builds_on": [
        "openai-baseline",
        "akashlevy-20261009-weighted-numerator",
        "cycle25-quartic-20261010",
        "cycle61-c0125139",
        "radical-asymmetric-count-20261014",
        "detector-affine-c0125154",
        "gao-directional-affine-20261016"
      ],
      "status": "framework-verified",
      "submitted_at": "2026-10-17T11:06:24Z",
      "published_at": "",
      "merged_at": "2026-10-18T00:27:51Z",
      "pr": 64,
      "repository": "GTimG/QuasiRiemannTracker",
      "source_commit": "edbb22b1a080c961b19e438e9e8ce6d6b3842739",
      "first_verified_at": "2026-10-17T23:31:58.056623+00:00",
      "timeline_at": "2026-10-17T11:06:24Z",
      "date_label": "PR submitted",
      "entrypoint": {
        "module": "Candidate.Main",
        "declaration": "Candidate.bound"
      },
      "verification_note": "Comparator checked the canonical all-Dirichlet statement at 874835173/1000000000 for the submitted commit. Lean, NanoDa and con-ron accepted the proof in the standard sandbox.",
      "certificate_url": "certificates/no-hardcoding-20261017.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/edbb22b1a080c961b19e438e9e8ce6d6b3842739/submissions/no-hardcoding-20261017/src/Candidate/Main.lean",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/no-hardcoding-20261017.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/edbb22b1a080c961b19e438e9e8ce6d6b3842739/submissions/no-hardcoding-20261017/src/Candidate/Main.lean"
        },
        {
          "label": "Reviewed submission",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/64"
        },
        {
          "label": "Asymmetric marked counting and source tree (PR 50)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/50"
        },
        {
          "label": "Collet's affine moment in the detector count (PR 52)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/52"
        },
        {
          "label": "Detector affine count on Cycle61 (PR 56)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/56"
        },
        {
          "label": "Directional marked affine source (PR 62)",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/pull/62"
        }
      ]
    }
  ],
  "historical_records": [
    {
      "submitted_at": "2026-10-09T17:29:56Z",
      "published_at": "",
      "merged_at": "",
      "pr": 1,
      "repository": "nielstron/QuasiRiemannTracker",
      "source_commit": "49331e02e2c04bb2388ae9c6e9ea424c23b96ac6",
      "first_verified_at": "2026-10-09T18:25:39.673785+00:00",
      "entrypoint": {
        "module": "QRH.TighterNonvanishing",
        "declaration": "QRH.DirichletCharacter.LFunction_ne_zero_of_tightTheta_lt_re"
      },
      "license": "Apache-2.0 (retained upstream notices)",
      "builds_on": [
        "proofcouncil-20261009",
        "openai-baseline"
      ],
      "id": "nielstron-20261009-tightening",
      "title": "nielstron · compressed rational refinement",
      "theta": {
        "numerator": "874957019420098946128604623",
        "denominator": "1000000000000000000000000000"
      },
      "authors": [
        {
          "name": "nielstron",
          "url": "https://github.com/nielstron"
        }
      ],
      "method": "Compresses the ProofCouncil Lean development, then tightens its exact rational certificate and slack budgets. The all-Dirichlet, zeta and finite-order Eisenstein Hecke targets compile at the smaller rational boundary. Final QRH source tokens decrease from 294,019 to 251,464 under the pinned LeanLeanBench metric.",
      "references": [
        {
          "label": "Verification record",
          "url": "certificates/nielstron-20261009-tightening.json"
        },
        {
          "label": "Checked Lean solution",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/nielstron-20261009-kernels/src/Solution.lean"
        },
        {
          "label": "Tighter Lean proof source",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/nielstron-20261009-tightening/TighterNonvanishing.lean"
        },
        {
          "label": "Complete reproducible source and evidence",
          "url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/nielstron-20261009-tightening/source-public.tar.gz"
        }
      ],
      "status": "framework-verified",
      "timeline_at": "2026-10-09T17:29:56Z",
      "date_label": "PR submitted",
      "verification_note": "Comparator verified the all-Dirichlet, zeta and finite-order Eisenstein Hecke statements. Lean, NanoDa and con-ron accepted the proofs.",
      "attribution_note": "nielstron is the human contributor; this research and formalization were AI-assisted. The result derives from Tim Gehrunger / ProofCouncil and the Apache-2.0 OpenAI/math and Mathlib developments; upstream notices are retained.",
      "certificate_url": "certificates/nielstron-20261009-tightening.json",
      "solution_url": "https://github.com/GTimG/QuasiRiemannTracker/blob/d716ecaae80f7823a5b8314916364fdfa0d133fb/public/proofs/nielstron-20261009-kernels/src/Solution.lean"
    }
  ]
}