# Self-avoiding polymer scaling reference

Family 237: The three-quarter exponent for honeycomb self-avoiding walk. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Lattice-polymer researchers can compare honeycomb self-avoiding walk diameter and covering observations to the claimed asymptotic exponents.

## Applicability and commercial boundary

The walk law, lattice and sufficiently large fixed lengths are specific; n^(3/4+o(1)) does not give a finite polymer size prediction or an efficient sampler.

## Initial business decision

Conditional research. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Quantify finite-size and sampling bias against an existing lattice benchmark.

## Evidence scope

The catalog statement was individually reviewed. This record does not imply a manuscript proof review or formal-scope comparison. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[Radial transfer estimates and polygon length laws for honeycomb walks](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Radial-transfer-estimates-and-polygon-length-laws-for-honeycomb-walks-September-26-2026/main.pdf).