Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 211-02. Spectral convergence for critical FK–Ising planar maps
Manuscript map · lines 6165–6174
OpenAI@2026-10-07#rem:oai-p-211-02
Authors: OpenAI. Family 211.
Title: Spectral convergence for critical FK–Ising planar maps.
Abstract: Using the conformal and metric-measure companion results and the stated Brownian/Liouville quantum gravity inputs, we prove spectral convergence for critical spherical FK–Ising maps to Liouville Brownian motion on the ordinary unit-area ${}sqrt3$-quantum sphere. The discrete walk has total attempt rate one, uses every map edge including loops and multiplicities, and has the corner measure as its stationary law. Accelerating time by the number of map edges gives joint convergence of the metric-measure space, all ordered eigenvalues with multiplicities and padding, and the heat trace locally uniformly at strictly positive times. The conductivity and clock constant are one in these conventions.
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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