{
  "schema_version": 1,
  "problem_number": "AIM-TOPOLOGY-0147",
  "title": "The Entropy Cost of Infinite-Genus Weil-Petersson Local Limits",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "Let mu_g be normalized Weil-Petersson measure on the moduli space of closed hyperbolic surfaces of genus g. If surface laws nu_g, with arbitrary measurable rooting kernels, have a pointed smooth weak limit Q, then for every fixed h >= 1 we prove liminf H(nu_g | mu_g)/log g >= (2h-1) Q{genus >= h}. Positive mass on infinite-genus surfaces therefore requires superlogarithmic surface relative entropy. Conversely, a fixed one-ended infinite-genus hyperbolic surface can be obtained as a local limit under every joint entropy budget b_g log g with b_g tending to infinity, measured relative to area-rooted Weil-Petersson measure. The proof uses classical separating-curve volume estimates, binary entropy, positive-volume core neighborhoods, and a slow diagonal. Two further propositions explain known planar/cylindrical consequences of tangle-freeness and the systolic-cylinder mixture. This is a complete theorem for the stated model, not a resolution of the broad AIM agenda. The preprint is unrefereed; absolute priority and formal verification are not certified.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.PR",
    "math.GT",
    "math.DG"
  ],
  "keywords": [
    "Weil-Petersson measure",
    "relative entropy",
    "local limit",
    "hyperbolic surface",
    "infinite genus",
    "AIM-TOPOLOGY-0147"
  ],
  "manuscript_version_date": "2026-10-14",
  "publication_date": "2026-10-14",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-14",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-topology-0147/",
  "pdf_url": "https://eulersolve.org/papers/aim-topology-0147/paper.pdf?v=97dee2a9df99",
  "doi": "10.5281/zenodo.23375995",
  "zenodo_record_url": "https://zenodo.org/records/23375995",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "The entropy obstruction allows arbitrary conditional roots and measures surface relative entropy. The converse construction controls joint surface-and-root relative entropy and realizes a fixed one-ended infinite-genus target under every diverging entropy multiplier. The broad AIM agenda, a canonical infinite-genus Weil-Petersson measure, and sharp finite-core constants are not claimed resolved. Classical geometric inputs and known local-limit corollaries are credited. Self-audited, unrefereed and AI-assisted; no independent review, formal verification or absolute priority is claimed.",
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    "paper.pdf": {
      "sha256": "97dee2a9df997c1b3a79055f8773cd9bc0071866c2863818584c2814afcdc99d"
    },
    "source.zip": {
      "sha256": "9dcb1033c3364fa66dda7f1b69706f557c8c3582fa74bd983f462c727e740f21"
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    "verification_report.md": {
      "sha256": "9490777c930677a3cdac6e9d57d0cb42357604e5e0021cd882f996448afd4526"
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  },
  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}