Rafael Pass.
Submitted 20 Oct 2026
Pass gives a constructive human proof of the same ω≤9/4 matrix-multiplication bound with an explicit Strassen-style identity. The construction starts from a separate OpenAI polynomial degeneration; the paper cites AlphaEvolve's earlier ω<2.371177 result in its baseline. This is related human progress, not a check of AlphaEvolve's optimization.
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Terence Tao, following Green and the Banks/Kerr expositions.
19 Oct 2026
Explains the direct Siegel-zero mechanism through prime bias, Frobenius congruences and competing determinant bounds. Tao explicitly separates it from the longer analytic quasi-Riemann proof.
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Michaël Cadilhac.
Submitted 19 Oct 2026
Gives a computable reduction from rational polynomial solvability to deciding stratifiability of semilinear sets. The author notes that OpenAI’s claimed undecidability result would therefore settle stratifiability; that consequence is conditional on the OpenAI claim.
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Ben Green; mathematical arguments credited to ChatGPT 6 Astra, text rewritten by Green.
Version 2; header 17 Oct, version history 18 Oct 2026
Gives a variant in the quadratic field using an explicit Gram determinant; separates parameters to improve the prime-bias constant. This supports human exposition of a model-generated variant, not a human-only replacement or a check of the 7/8 theorem.
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J. Arias de Reyna.
Submitted 17 Oct 2026
Arias de Reyna reconstructs Claude's reported 0.6725 lower bound for simple critical-line zeros in a student-oriented proof. This is a human exposition, not an independent verification of the original proof.
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Ilia Binder, Oleg Ivrii, Istvan Prause, and Stanislav Smirnov.
Submitted 16 Oct 2026
The authors say that, while validating OpenAI’s Brennan and Kraetzer preprints, they found redundant parts and obtained a much shorter proof of a stronger statement. The paper discloses a human–AI collaboration, so this is a refinement of the reported arguments rather than an independent check of every source claim.
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Minoru Hirose.
Submitted 16 Oct 2026
Expresses admissible words through Hoffman words and explicit confluence relations, then gives an alternative proof of the Deligne–Drinfeld conjecture. The paper identifies the OpenAI Math Release proof as prior work.
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Thomas Willwacher.
Submitted 11 Oct 2026; revised 16 Oct 2026
Presents a shorter, more human-friendly version of OpenAI’s proof of the Deligne–Drinfeld conjecture. The author revised the paper to simplify and shorten the exposition further.
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Guozheng Cheng, Xiang Fang, Menghan Li, Hongdou Qu, and Chengbo Xiao.
Submitted 15 Oct 2026
Proves a quantitative planar distance-set bound using a multiscale method from OpenAI’s September manuscript, and says later higher-dimensional versions will build on the October 6 release. It gives a planar result and makes no endpoint or sharpness claim.
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Bryce Kerr; ChatGPT assisted mathematical development and preparation.
15 Oct 2026
Simplifies the direct Siegel-zero proof using the pigeonhole principle and Masser’s polynomial bound. It retains OpenAI’s underlying strategy, with replacement steps, rather than checking the full 7/8 argument.
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Yuanda Xu and Hejian Sang.
Submitted 11 Oct 2026; revised 15 Oct 2026
Assuming the analytic inputs of OpenAI’s 7/8 zero-free result, improves the boundary to 0.8748867 for the stated Hecke and Dirichlet families. The improvement uses an amplified first moment; its conclusion remains conditional on those inputs.
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Iwao Kimura.
Submitted 15 Oct 2026
Uses an explicit version of OpenAI’s zero-free argument to claim an unconditional list of all imaginary quadratic fields with class number at most 2000. The paper says the zero-free and discriminant bounds are proved in Lean and checked by two kernels; because it adopts the unreferred OpenAI argument, it does not independently validate that analytic input.
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Antti J. Niemi.
Submitted 15 Oct 2026
Uses resistive magnetohydrodynamics to simulate flux-ring splitting and merging near a regularized flow shaped to match the geometry and scaling of OpenAI’s reported forced Navier–Stokes singularity. This studies a possible physical consequence; it does not verify the claimed singularity.
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Madhuparna Das and Soumya Banerjee.
Submitted 15 Oct 2026
Das and Banerjee propose a probabilistic benchmark for the novelty of machine-generated proofs and apply it to Claude's Zeta23 proof to assess non-trivial steps. This evaluates proof novelty, not the correctness of the 0.6725 bound.
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Dean Cureton and Jesse Thorner.
Version 2 dated 14 Oct 2026
Proves a uniform zero-free region for Dedekind zeta functions of every number field, broadening the family covered. This is a separate human result and is catalogued as its own AIProofWatch record.
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D. Shlyakhtenko.
Submitted 14 Oct 2026
Builds on OpenAI’s free group factor isomorphism result to prove the corresponding isomorphism for C*-algebras generated by free semicircular systems, and gives related reduced free product results. This is a separate operator-algebra consequence, not a check of the factor proof.
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Matt Visser.
Submitted 14 Oct 2026
Works out consequences of the claimed 7/8 quasi-Riemann hypothesis, including primes between successive eighth powers and in shorter intervals. All conclusions depend on the zero-free claim.
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Hubert Bray, Tuan Dolmen, Marcus Khuri, and David Schmidt.
Submitted 14 Oct 2026
Proves the spacetime Penrose inequality for a restricted class of maximally parameterized initial data. The authors identify a degenerate PDE system whose solvability would yield the general conjecture and say this is what the OpenAI paper claims. This is a separate restricted result, not a check of OpenAI’s proof.
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Christopher Frei, Efthymios Sofos, and Martin Widmer.
Submitted 13 Oct 2026; v2 dated 14 Oct 2026
Uses the OpenAI and Cureton–Thorner quasi-RH results for effective Chebotarev estimates and applications to class-group torsion, splitting primes, and small generators. This is a human-authored application, not a check or explanation of either zero-free proof.
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Baochun Li, Zongpeng Li, and Sirui Liu; the paper discloses ChatGPT assistance.
Submitted 14 Oct 2026
Adapts the recursive field-interchange method to block transfers and combines it with other techniques for an external-memory integer-sorting bound. This is a distinct result, already listed separately in AIProofWatch, and the paper discloses ChatGPT assistance.
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Sang-hyun Kim and Yash Lodha.
Submitted 13 Oct 2026
Provides a human-written exposition of OpenAI’s recent proof that Thompson’s group F is nonamenable. The paper is an exposition of that argument, not an independent proof check.
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Biao Wang and Shaoyun Yi.
Submitted 12 Oct 2026
Proves the two-point case of a conjecture on consecutive prime Omega values and derives a dynamical generalization of the two-point Chowla conjecture. It cites OpenAI’s recent classical two-point result as context; the abstract does not say that the new proof uses OpenAI’s argument.
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Baiying Liu.
Submitted 8 Oct 2026; v2 dated 12 Oct 2026
Improves the stated 7/8 boundary by a small amount for the fixed field and Hecke-L setting, using a parameter variation of the strategy. The paper reports a Lean formalization; this is a strengthening, not an independent check of the OpenAI proof.
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Bjørn Kjos-Hanssen.
Submitted 11 Oct 2026
Adapts OpenAI’s proof of Turing-degree rigidity to truth-table and weak truth-table degrees, proving rigidity for automorphisms induced by Baire-measurable maps or by continuous maps on a comeager set.
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Shisheng Li and Yong Su.
Submitted 11 Oct 2026
Proves that the largest guaranteed unit-distance-free subset of any n planar points has size (m₁+o(1))n, where m₁ is the supremal density of a measurable unit-distance-free set. The proof uses OpenAI’s machine-checked Haar-rigidity theorem as its only nonclassical input and is itself formalized in Lean 4.
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William D. Banks; Claude assisted the initial expansion.
11 Oct 2026
Expands OpenAI’s separate direct Siegel-zero argument and explains its determinant mechanism. Banks reports checking every line of his text. His new explicit constant is 0.003 for conductors at least 10¹⁰; the all-conductor numerical value also uses Lu, Zaman and Zhao’s computation, which Banks did not independently verify. This does not check the broader 7/8 theorem.
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Mikhail Koshelev, Andrey Kupavskii, and Vsevolod Voronov.
Submitted 11 Oct 2026
Uses OpenAI’s planar character-law rigidity theorem to show that every finite proper coloring of R³ has a proper Lebesgue-measurable coloring with the same number of colors. It follows that the ordinary and measurable chromatic numbers agree and lie between 7 and 15.
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Przemyslaw Uznanski.
Submitted 7 Oct 2026; revised 11 Oct 2026
Extends OpenAI’s matrix-multiplication analysis to rectangular products, deriving bounds for ω(1,k,1) and consequences for directed all-pairs shortest paths. The paper extends the spectral analysis; it does not provide an independent check of the square-matrix claim.
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János Pintz and Ingo Althöfer.
Submitted 11 Oct 2026
Uses the uniform 7/8 zero-free result for Dirichlet L-functions to derive a conditional X^(7/12+ε) bound for the Goldbach exceptional set. It also gives a stronger conditional exponent under a stronger zero-free hypothesis.
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Volkan Dağlı, Zerrin Dağlı, and Dağhan Dağlı.
Submitted 9 Oct 2026
Optimizes carrier graphs inside the conditional integer-multiplication framework originating from OpenAI’s preprint, improving its reported second-moment coefficient and exponent. The paper supplies exact rational certificates and says Lean verifies the wire-reduction identity; the overall bound remains conditional on the framework’s assumptions.
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Farzad Aryan.
Submitted 9 Oct 2026
Aryan derives an imaginary-part formula for a smoothed logarithmic derivative of ζ and includes an expository account of Claude's real-part matrix argument. The new identity is a separate human result; the paper does not independently check Claude's proof.
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Cetin Hakimoglu-Brown.
Submitted 8 Oct 2026
Assuming the OpenAI 7/8 zero-free claim for the Riemann zeta function, proves the conditional bound Λ≤0.13963. The zero-free hypothesis remains an assumption; the paper also uses a published finite-region computation.
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Vojkan Jaksic and Yoram Last.
Submitted 8 Oct 2026
Gives a short proof of the classical weak-disorder result on the Bethe lattice and notes that the same structural argument shortens the final step of OpenAI’s separate weak-disorder result on Z^d. The paper’s main theorem is about the Bethe lattice, not a verification of the Z^d claim.
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The GitHub account Hrrsmjd; the page does not identify an individual author.
Dated 7 Oct 2026
An addendum reports improving the exponent deficit from κ = 2⁻¹⁸² to κ = 2⁻⁷⁴. Its Lean check covers parameter arithmetic, not the machine model, algorithm, or structural proof.
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Ruihan Chen.
Submitted 7 Oct 2026
Combines classical 2-Selmer calculations with the release’s low-corank BSD claim to derive rank equalities, finiteness of the Tate–Shafarevich group, and the exact BSD leading-term formula for specified twin-prime elliptic curves. These deductions are conditional on the OpenAI result.
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