The $N^{-1/4}$ law for the critical strip-crossing mass of honeycomb self-avoiding walk

What the AI did

The release README says the results were produced by an unreleased internal OpenAI model with a fixed procedure, on average about three hours of ChatGPT Pro thinking compute per result, and that some outputs build on earlier model results. This result is not among the README's exceptions (the Hodge conjecture for CM abelian varieties, and the Re(s) > 11/12 zero-free region whose write-up was human-edited). The manuscripts are authored 'OpenAI' and name no human author. The principal manuscript, 'Critical strip-crossing mass on the honeycomb lattice' (September 26, 2026), belongs to a thirteen-manuscript family on honeycomb walks; several companions re-derive the same bridge-mass law in other conventions and use it as input for fixed-length size exponents.

Verification

No independent mathematician has checked this yet. Checked here: Theorem 1.1 of 'Critical strip-crossing mass on the honeycomb lattice' was read against the prediction as Duminil-Copin and Smirnov state it; it gives $B_N\asymp N^{-1/4}$ with constants independent of $N$, in the manuscript's port convention. Lean: lean/ComparatorChallenges/CriticalStripMass.json exists and its solution module OAI.Combinatorics.StripMass.Main is present at the pinned commit; the challenge is not in the formalization catalogue (formalization.yaml). The statement file CriticalStripMass.lean was read here: theorem critical_strip_mass asserts finiteness of the strip sums, $c\,A_N+B_N=1$, $m_N$ comparable to $N^{3/4}$, bridge mass comparable to $N^{-1/4}$ for all $N\ge1$, and monotonicity, with paths encoded as duplicate-free chains of adjacent triangles of the dual triangular lattice. That states the headline. Not rebuilt here, and the match between the triangle encoding and the paper's port convention was read but not audited line by line.

Sources

• PaperCompanion manuscript: Polynomial vacuum representations and bridge mass for honeycomb walks · Companion manuscript: Disk transfer representations and confined bridge mass · Companion manuscript: Uniform marked-polygon estimates and sharp finite bridge moments · Companion manuscript: Mass and covering exponents for fixed-length honeycomb walks
• Lean proofLean solution module: OAI/Combinatorics/StripMass/Main.lean · Lean statement: ComparatorChallenges/CriticalStripMass.lean
• CodeOpenAI math release: Critical strip-crossing mass on the honeycomb lattice
• Problem recordDuminil-Copin and Smirnov, The connective constant of the honeycomb lattice equals sqrt(2+sqrt 2) (2012)