{"paper":{"title":"Topological Thermodynamics of Black Holes: Revisiting the methods of winding numbers calculation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"A. A. M. Silva, C. R. Muniz, G. Alencar, M. Nilton, R. R. Landim","submitted_at":"2025-11-09T23:47:58Z","abstract_excerpt":"In this paper, the equivalence between two methods for computing winding numbers is established: the approach of $\\phi$-mapping topological current and the residue method. The methods are shown to be equivalent when the condition $M'' S' - S'' M' \\neq 0$ holds, while deviations appear when this relation fails, signaling subtle connections between mass $M(r_h)$, entropy $S(r_h)$, and topological structure, with $r_h$ being the horizon radius. We first verify this equivalence to Schwarzschild and Reissner-Nordstr\"om black holes, recovering known classifications and confirming the consistency of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.06579","kind":"arxiv","version":4},"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/2511.06579/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"}