Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 237-10. Renewal and changes of law for critical honeycomb walks
Manuscript map · lines 7025–7034
OpenAI@2026-10-07#rem:oai-p-237-10
Authors: OpenAI. Family 237.
Title: Renewal and changes of law for critical honeycomb walks.
Abstract: For critical honeycomb self-avoiding walk, we prove spatial exponent 3/4 for the infinite irreducible-bridge law and for bridges of every sufficiently large compatible even length. We establish the corresponding thermal laws at every large discount scale, including all positive length and spatial moments. For unrestricted uniform walks, the endpoint lower law holds on a common set of lengths of natural density one. We also determine the near-critical exponential correlation scale and small-force free-energy exponent, and prove spatial local lower bounds that permit conditioning on a prescribed terminal vertex.
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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