The 108-page manuscript claims that a completed (3,4,∞) family of complex two-tori produces a compact complex threefold diffeomorphic to S⁶. Exact finite identities and a stipulated local torsion mechanism have been reproduced locally. Analytic quotient and gluing, relative meridian signs, integral homology, and the headline theorem remain unresolved.
Record state
Active examination
Source
retrieved 2026-08-24 · locked
Next open step
Trace the relative meridian signs and toric zero-section independently before reusing the passing group arithmetic
The manuscript claims five positive charges yield at least 24 nondegenerate critical points. A local exact-algebra check reproduces the displayed limiting polynomial's classification of 21 real, nondegenerate critical points, conditional on manual transcription. The polynomial's derivation from the charge potential, 24-point persistence, Morse perturbation, global finiteness, and the counterexample remain unresolved.
Record state
Active examination
Source
arXiv v1 · locked
Next open step
Independently derive the displayed limiting polynomial from the five-charge potential, including the exact Taylor coefficients and analytic remainder
This case is not one theorem and will not receive a corpus-wide pass or fail. The locked packet contains ten independent proposed solutions. Attempt 2 is the first blinded negative-control target; OpenAI's public assessment is held out until the lab's status and evidence are frozen.
Record state
Queued record
Source
revised packet · locked
Next open step
Freeze the blinded attempt-2 working bundle and version-delta record without leaking the known external comparator label
The locked v2 manuscript claims point convergence of the Nesterov iterates, not merely convergence of objective values. Four load-bearing gates are mapped from the recurrence and energy inequality through the unique-cluster-point argument. No gate has run.
Record state
Queued record
Source
arXiv v2 · locked
Next open step
Independently derive the recurrence equivalence and discrete energy inequality under the exact tₖ hypotheses
2026-07-10-openai-cycle-double-cover · Graph theory
The three-page manuscript claims the cycle double cover conjecture and ships with a public Lean artifact. Both sources are locked. The first gate is prose-to-Lean statement and definition correspondence; the repository has not been built or mathematically examined in this lab.
Record state
Queued record
Source
PDF + Lean 577e9d9 · locked
Next open step
Map the manuscript's theorem and graph conventions to the pinned Lean endpoint before drawing any inference from a build
Chapter 3 of OpenAI's updated Ten Advances manuscript claims that the binary Leavitt algebra's unit group is not sofic. The pinned Lean commit predates a substantive prose revision by four days. Paper-to-Lean and version correspondence is therefore the first gate; no build or mathematical examination has run.
Record state
Queued record
Source
updated 2026-08-06 · locked
Next open step
Reconcile the substantively revised August 6 prose with the August 2 Lean commit before any formal replay is treated as relevant
Statuses are records of evidence collected for a defined scope. They are not peer-review decisions, publication recommendations, or certificates of mathematical truth.