{"paper":{"title":"Irreversibility from Self-Reference: Gradient Flow and an H-Theorem for a Self-Referential Statistical Operator Framework","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Lucio Marassi","submitted_at":"2026-05-12T19:07:09Z","abstract_excerpt":"This paper is a direct companion to arXiv:2605.06705, where the self-referential operator Omega was introduced and the Tsallis index q = alpha + beta was derived as a fixed-point condition within the local kernel approximation (LKA). Here we address four aspects deferred from the previous work. First, we carry out the first-order perturbative expansion of Omega beyond the LKA and demonstrate structural stability of q = alpha + beta at leading order in (xi/L)^2. Second, we define the iterative dynamical scheme Psi_(n+1) = Omega[Psi_n] and analyze convergence via Frechet spectral radius. Third, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.16400","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/2605.16400/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T21:01:57.380473Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:34:36.602930Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"fb06caec01ee8a08f034b04274e6975a851349b44bee037e5d03696a6b5f867d"},"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"}