{"paper":{"title":"Closed-form thermal threshold functions for the proper-time renormalisation group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Daniele Rizzo","submitted_at":"2026-08-10T16:27:32Z","abstract_excerpt":"We derive closed-form expressions for the thermal threshold functions of the finite-temperature proper-time renormalisation group (PTRG): until now these have been evaluated numerically, Matsubara mode by Matsubara mode. For the standard one-parameter regulator family, Poisson resummation of the Matsubara sum yields a rapidly convergent winding-number series of modified Bessel functions, and a single algebraic identity reduces every higher threshold function to this same closed form at a shifted kernel parameter. The sharp proper-time regulator, recovered as the exact $m\\to\\infty$ endpoint of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09803","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/2608.09803/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"}