mathematical-proofs
Latest stories covering mathematical-proofs, with summaries and links to related coverage.
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A new ceiling for Λ: the de Bruijn–Newman constant
research
23 min read
Jude Gomila reports a computer-assisted, unconditional upper bound of Λ ≤ 0.1787854 for the de Bruijn–Newman constant, improving the previous 0.2 ceiling obtained using the same general Polymath 15 framework and Platt–Trudgian’s verified Riemann-hypothesis height. The de Bruijn–Newman constant satisfies Λ ≤ 0 exactly when the Riemann hypothesis is true, while Rodgers and Tao proved in 2018 that Λ ≥ 0. The reported result therefore narrows the known interval for Λ to [0, 0.1787854] but does not prove the Riemann hypothesis. The bound instantiates Polymath 15’s criterion with exact rational parameters and relies on Platt and Trudgian’s 2020 verification that zeta zeros up to height 3,000,175,332,800 lie on the critical line. Gomila says the proof combines 3,149,013 interval-arithmetic certificates establishing final-time zero-free regions, a tail argument covering all remaining windows to infinity, and 883 time-sliced barrier certificates based on the argument principle. The audit package uses fail-closed checkers, SHA-256-pinned artifacts, replays with FLINT/Arb and Python interval implementations, and runs on two toolchains. Gomila says Dan Romik independently reviewed the analytic lemmas and that journal publication remains pending.
GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
research
1 min read
GPT-5.6 Sol Ultra has successfully produced a proof for the Cycle Double Cover Conjecture. The proof is documented in a PDF file available online.
What can you confidently guarantee about your software?
tool
14 min read
The cost and tooling of formal verification have become widely accessible, allowing for increased use in software development. AI is reducing the barriers to formal verification by eliminating the costs associated with writing proofs, enabling the creation of software that guarantees mathematically correct business rules.
Maxproof
research
2 min read
MaxProof is a framework designed for population-level test-time scaling in mathematical proof, specifically within the MiniMax-M3 series. It trains three key capabilities: proof generation, proof verification, and critique-conditioned proof repair.