OpenAI · 237-08 · 2026-09-26 · Probability and statistical mechanics
Disk transfer representations and confined bridge mass
preprints/Disk-transfer-representations-and-confined-bridge-mass-September-26-2026
Family 237. The three-quarter diameter exponent for honeycomb walks.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves the diameter form of Nienhuis's predicted three-quarter exponent: a uniformly chosen -step self-avoiding walk on the honeycomb lattice has diameter . Its local mass and covering numbers have exponent . These estimates hold at every sufficiently large fixed length, simultaneously across scales, with arbitrarily high polynomial probability.
We prove that critical honeycomb bridges crossing a strip of width R have mean length , with the same exponent after confinement to a fixed multiple of the strip width. The initial boundary port is fixed, the terminal port is summed, and all finite lengths receive their critical weights. The bridge mass is comparable to R−1/4; the half-plane arch kernel at endpoint separation m is comparable to m−5/4.
Preprint source and Lean scope
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A Lean scope note is stored for family 237, but it does not name this preprint. It names 237-09, 237-10, 237-11, 237-02. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.