OpenAI mathematics · October 6, 2026 snapshot

A flood of mathematics.
Let’s find our bearings.

Explore the original October 6 snapshot: 722 manuscript links in 372 related families. The publisher’s October 7 update reports 719 manuscripts after three withdrawals.

Explore by subject ↓See our first check plans →

This is a pinned publisher catalogue, not 722 independent breakthroughs or validated proofs. It is separate from Paper Watch and our proof dockets.

Source correction · recorded October 11, 2026

Three withdrawals. A preserved release record.

In its October 7 history, OpenAI withdrew these three manuscripts:

Algebraicity of Weil classes on split abelian eightfolds
Algebraicity of Kuga–Satake Correspondences for K3 Surfaces
The rational Hodge conjecture for products of K3 surfaces

OpenAI reports a sign error in the stabilization-trace argument for the split abelian eightfold paper, affecting the construction used by two dependent papers.

The publisher reports 14 other revised manuscripts covering proof repairs, corrected statements, clearer assumptions and dependencies, and an obsolete citation; 13 additional manuscripts received reference and version-date updates. The updated publisher catalogue reports 719 manuscripts across 372 families.

Publisher-reported corrections, recorded by State of Proof on October 11. We have not independently adjudicated the errors or verified the revisions. The original October 6 catalogue and its 722 pinned manuscript links are preserved below.

Read the pinned October 7 source history ↗

372related mathematical families

17subject areas to explore

235families with publisher Lean links
Availability ≠ independent verification

Start here

Big names. Exact boundaries.

003 · Number theory

The primes have a pattern. How tightly can we pin it down?

OpenAI claims a zero-free region beyond real part 7/8 for zeta and the stated L-functions. If it holds, it would substantially constrain where those elusive zeros can hide.

Not full RH. The Riemann hypothesis requires every nontrivial zeta zero to sit on the 1/2 line.

Explore the Riemann family →

032 · Algebraic geometry

Can hidden geometric patterns be built from algebra?

The original snapshot includes Hodge-related claims for specific classes of shapes. OpenAI withdrew three papers in this family on October 7, including its claim for products of K3 surfaces.

Publisher withdrawal recorded. The original links remain visible with withdrawal labels. This collection establishes no resolution of the unrestricted Hodge conjecture.

Read the source correction → · Explore the historical family →

002 · Number theory

Reading the arithmetic hidden inside a curve.

The BSD-related papers claim a precise link between elliptic curves’ rational solutions and their L-functions, under low-Selmer-corank conditions.

Conditions matter. Not general BSD for all ranks. This does not mean elliptic-curve encryption has been broken.

Explore the BSD family →

These are our plain-English descriptions of the publisher’s claims, not examination findings.

Our first examination batch

Two check plans. No shortcuts to a verdict.

Selected for examination planning. Neither has been independently replayed by State of Proof.

01 · Planned · not started

How much of Riemann does the proof establish?

A claim about the hidden structure of prime numbers deserves a precise boundary. This is not a claim to have proved the full Riemann hypothesis.

The first task

Match the stated 7/8 zero-free region to the supplied Lean theorem, inspect its assumptions and dependency chain, then attempt an isolated replay.

No independent Lean replay or theorem-to-paper comparison completed. The 11/12 companion is a separate argument, not a second verification of the 7/8 proof.

Supplied 7/8 Lean endpoint ↗ · Family 003

02 · Planned · not started

Can we reconstruct a finite lattice-game certificate?

A board-game strategy becomes a concrete object we can take apart and rebuild. This is a manageable first scope—not a promise that the entire proof is easy.

The first task

Independently reconstruct the supplied Snaky appendix certificate using exact integer coordinates and set operations; compare its table, placements and stated bounds.

The selected appendix concerns a 35-move certificate. Reproducing it would not validate the paper’s headline 21-move theorem. Feasibility and dependency review come before execution; no replay completed.

Publisher’s formalization map ↗ · Family 187

Browse the October 6 snapshot

Follow the mathematics.

A family groups a principal result with related papers, consequences or alternative proofs. Expand a subject, then a family, for the original pinned manuscripts. Counts in this catalogue describe that historical edition; subsequent withdrawals are labeled.

October 6 snapshot · 372 families · 722 manuscript links

Number theory31 families · 58 manuscripts

001Milne’s rationality conjecture and algebraic specialization1 manuscript