{
  "family_id": "211",
  "title": "The geometric phase diagram, diffusion, and spectra of random planar maps",
  "discipline": "Probability and statistical mechanics",
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    {
      "title": "Random Walks on Critical FK–Ising Maps and Liouville Brownian Motion",
      "path": "preprints/Random-Walks-on-Critical-FK-Ising-Maps-and-Liouville-Brownian-Motion-October-5-2026/fk-ising-walk-limit.pdf",
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    {
      "title": "Spectral convergence for critical FK–Ising planar maps",
      "path": "preprints/Spectral-convergence-for-critical-FK-Ising-planar-maps-October-5-2026/spectral-convergence-critical-fk-ising-planar-maps.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Spectral-convergence-for-critical-FK-Ising-planar-maps-October-5-2026/spectral-convergence-critical-fk-ising-planar-maps.pdf",
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    {
      "title": "A Linear Clock for Random Walk on Tree-Weighted Planar Maps",
      "path": "preprints/A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026/linear-clock-random-walk-tree-weighted-planar-maps.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026/linear-clock-random-walk-tree-weighted-planar-maps.pdf",
      "readme_path": "preprints/A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026/README.md",
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    {
      "title": "Canonical conformal limits of subcritical FK planar maps",
      "path": "preprints/Canonical-conformal-limits-of-subcritical-FK-planar-maps-September-24-2026/main.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Canonical-conformal-limits-of-subcritical-FK-planar-maps-September-24-2026/main.pdf",
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    },
    {
      "title": "The critical Liouville quantum sphere and geometric limits of FK maps at q=4",
      "path": "preprints/The-critical-Liouville-quantum-sphere-and-geometric-limits-of-FK-maps-at-q-equals-4-September-24-2026/main.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-critical-Liouville-quantum-sphere-and-geometric-limits-of-FK-maps-at-q-equals-4-September-24-2026/main.pdf",
      "readme_path": "preprints/The-critical-Liouville-quantum-sphere-and-geometric-limits-of-FK-maps-at-q-equals-4-September-24-2026/README.md",
      "tex_paths": [],
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    },
    {
      "title": "Metric-measure limits of subcritical FK and spanning-tree planar maps",
      "path": "preprints/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026/main.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026/main.pdf",
      "readme_path": "preprints/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026/README.md",
      "tex_paths": [],
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    },
    {
      "title": "Brownian continuum random tree limits of finite Fortuin–Kasteleyn maps above four",
      "path": "preprints/Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-four-September-24-2026/main.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-four-September-24-2026/main.pdf",
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  "review_status": "inventory_complete_deep_review_pending"
}