What was already known
Gaia Carenini established the limiting-threshold existence result for every fixed k ≥ 3 in ECCC TR26-229, published October 5, 2026. OpenAI credits her with priority for that conjecture. The computational companion adds an oracle-free precision algorithm; existence alone does not give a computable rate of finite-size convergence (first OpenAI manuscript Section 1.1, pp. 1–2; companion abstract).
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Turns existence of the random 3-SAT threshold into an effective, terminating approximation procedure.
Limitations
Only the proper uniform random 3-SAT threshold is covered; no efficiency bound, explicit numerical value, behavior at the threshold, or computability for other clause sizes is asserted.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
Pinned OpenAI Lean solution module contains a proved matching headline theorem. This is source-reported code inspection; local build and imported-module audit were not performed.
- Checker
- OpenAI-reported Lean 4
- Scope
- The computable 3-SAT threshold, including a deterministic rational approximation for every precision.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and verification-scope review for non-notifying local inclusion.
Read this published revision