The $N^{-1/4}$ law for the critical strip-crossing mass of honeycomb self-avoiding walk

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The $N^{-1/4}$ law for the critical strip-crossing mass of honeycomb self-avoiding walk parent of this event

Theorem 1.1: for every $N\ge1$ the strip sums are finite, $c\mathcal A_N+\mathcal B_N=1$ with $c=\cos(3\pi/8)$, $m_{N+1}-m_N\asymp\mathcal B_N$, the first rightward displacement moment of arches satisfies $m_N\asymp N^{3/4}$, and the bridge mass satisfies $\mathcal B_N\asymp N^{-1/4}$, nonincreasing in $N$, with constants independent of $N$. The route computes $m_N$ through rhombic transfer matrices and a positive integral, then recovers $\mathcal B_N$ from its increments. Not shown: a limiting constant for $N^{1/4}\mathcal B_N$, statements about walks of fixed length (treated in companions), or other lattices. parent of this event

VibeMathed record: The $N^{-1/4}$ law for the critical strip-crossing mass of honeycomb self-avoiding walk evidence for this event

Companion manuscript: Critical strip-crossing mass on the honeycomb lattice evidence for this event

Companion manuscript: Polynomial vacuum representations and bridge mass for honeycomb walks evidence for this event

Companion manuscript: Disk transfer representations and confined bridge mass evidence for this event

Companion manuscript: Uniform marked-polygon estimates and sharp finite bridge moments evidence for this event

Nienhuis's 3/4 exponent for self-avoiding walk on the honeycomb lattice, in diameter form evidence for this event

Lean solution module: OAI/Combinatorics/StripMass/Main.lean evidence for this event

Lean statement (supporting): CriticalStripMass evidence for this event

Duminil-Copin and Smirnov, The connective constant of the honeycomb lattice equals sqrt(2+sqrt 2) (2012) evidence for this event

This event attributed to Unreleased internal OpenAI model