Gaussian free field limit of the six-vertex height function throughout the regime a = b = 1, 0 < c <= 2

Theorem 1.1: for each $c\in(0,2]$ the balanced-torus plane law exists and $h(\cdot/\delta)$ converges to $\sigma(c)\Gamma$ , $\sigma(c)^2=2/\arccos(1-c^2/2)=1/\arcsin(c/2)$ , with Green kernel $-(2\pi)^{-1}\log|x-y|$ , jointly on finite-energy mass-zero test measures, in $B^\alpha_{p,q}$ and $W^{\alpha,p}$ restriction spaces for $-1<\alpha<0$ , and with Wick-type limits of increment moments. Priority: Duminil-Copin, Kozlowski, Lammers and Manolescu had proved this for $\sqrt3\le c\le2$ . Not shown: other slopes or Gibbs states, anisotropic $a\ne b$ , or the regime $c>2$ .

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Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Gaussian free field limit of the six-vertex height function throughout the regime a = b = 1, 0 < c <= 2 · Six-vertex GFF limit, balanced regime

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VibeMathed record: Gaussian free field limit of the six-vertex height function throughout the regime a = b = 1, 0 < c <= 2

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No independent mathematician has checked this yet. Checked here: Theorem 1.1 was read against the prediction. For every $c\in(0,2]$ it constructs the plane law $\mathbb P_c$ as an iterated limit of balanced tori and proves convergence of $h_\delta$ to $\sigma(c)\Gamma$ in finite-dimensional laws, in negative Holder, Besov and Sobolev restriction spaces, and in moments of increments. Scope limits the paper states: one zero-slope plane state only, no uniqueness among Gibbs states or slopes, no uniformity as $c\to0$ , and isotropic weights $a=b$ only. At $c=2$ and for the amplitude on $1\le c<2$ it uses Duminil-Copin-Kozlowski-Lammers-Manolescu (2026), whose rotational-invariance input is cited as in preparation; the manuscript supplies its own endpoint rotation argument. No Lean formalization.

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Gaussian free field limit of the six-vertex height function throughout the regime a = b = 1, 0 < c <= 2

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Di Francesco, Saleur, Zuber, Coulomb gas picture and conformal invariance (1987)

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Di Francesco, Saleur, Zuber, Coulomb gas picture and conformal invariance (1987) evidence for this event

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