What was already known
The honeycomb connective constant was established, while the predicted three-quarter spatial exponent and corresponding critical polygon length-diameter relations had not been proved by that result.
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
Establishes the critical polygon tail laws that yield diameter n^{3/4+o(1)} under length-cutoff ensembles.
Limitations
Polygons are counted modulo translations at the critical activity; the tail statements differ from fixed-exact-length walk claims. The linked Lean scope checks finite bridge measures and other supporting honeycomb estimates, not these polygon diameter tails.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.
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 precise Lean-scope or conditional-input review for non-notifying local inclusion.
Read this published revision