Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 211-06. Metric-measure limits of subcritical FK and spanning-tree planar maps
Manuscript map · lines 6205–6214
OpenAI@2026-10-07#rem:oai-p-211-06
Authors: OpenAI. Family 211.
Title: Metric-measure limits of subcritical FK and spanning-tree planar maps.
Abstract: We resolve the finite spherical cases of Gwynne and Miller's graph-metric conjecture for critical Fortuin–Kasteleyn maps at each fixed $q{}in(0,4)$ and for uniform spanning-tree-decorated maps. After deterministic rescaling of graph distances, these maps, equipped with the vertex probability measure proportional to degree, converge in Gromov–Hausdorff–Prokhorov law to their ordinary unit-area Liouville quantum gravity spheres. Distances use every primal edge, and convergence holds through all positive integer edge counts.
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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