{"paper":{"title":"Hawking--Page Universality, Thermodynamic Dipoles and Categorical Defects","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","gr-qc"],"primary_cat":"hep-th","authors_text":"Emilio Torrente-Lujan","submitted_at":"2026-06-09T10:36:20Z","abstract_excerpt":"We reconsider the Hawking--Page transition using the common thermodynamic vector field whose zeros include the Davies and Hawking--Page points. In the elementary AdS branch their winding numbers are $w_{\\rm D}=-1$ and $w_{\\rm HP}=+1$, so the pair has zero total charge but a non-zero signed first moment. After normalization by the Davies scales this moment gives the familiar universal ratios $C_S$ and $C_T$; in four dimensions $C_S=2$ and $C_T=2/\\sqrt{3}-1$. We check the construction for Schwarzschild--AdS, grand-canonical Reissner--Nordstr\\\"om--AdS, charged non-rotating black holes in arbitrar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10680","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10680/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}