Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 237-05. Signed cylinder propagation and marked polygons on the honeycomb lattice
Manuscript map · lines 6975–6984
OpenAI@2026-10-07#rem:oai-p-237-05
Authors: OpenAI. Family 237.
Title: Signed cylinder propagation and marked polygons on the honeycomb lattice.
Abstract: At the critical activity and loop fugacity two, we prove a 1/6 partition exponent for disjoint honeycomb polygons separating opposite marks on a balanced infinite cylinder, and a 1/12 planar nesting exponent. For ordered first-exit chords in a regular hexagon of side R, with both boundary ports summed and diameter at least $R/10$, the finite critical partition is $R{}{3/4+o(1)}$ and the normalized mean length is $R{}{4/3+o(1)}$. A separate two-bond estimate on tilted cylinders with controlled site proportions bounds the length-square mass of planar polygons of diameter at most H, modulo translations, by $H{}{2/3+o(1)}$.
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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