Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 237-13. Cap-selected amplitudes and triangle chords for honeycomb walks
Manuscript map · lines 7055–7064
OpenAI@2026-10-07#rem:oai-p-237-13
Authors: OpenAI. Family 237.
Title: Cap-selected amplitudes and triangle chords for honeycomb walks.
Abstract: At the critical honeycomb fugacity, self-avoiding port-to-port chords in an equilateral lattice triangle of side R, summed over both boundary endpoints and restricted to diameter at least $R/100$, have partition sum comparable to R3/4 and mean length $R{}{4/3+o(1)}$. We also determine the amplitude selected by two vacuum caps on a cylinder of circumference N and prove that it grows as $N{}{1/6+o(1)}$.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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