{"paper":{"title":"Probing Probability Geometry with Schwinger--Dyson Identities: Score Mismatch, Fisher Information, and Configurational Temperature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-lat"],"primary_cat":"hep-th","authors_text":"Anosh Joseph","submitted_at":"2026-06-25T17:58:10Z","abstract_excerpt":"We develop a geometric interpretation of Schwinger--Dyson identities by showing that their violations are controlled by a single score-mismatch field $\\delta s$. For an arbitrary sampled probability distribution $Q$ and equilibrium measure $P_{\\rm eq}$, every Schwinger--Dyson violation is determined by $\\delta s = \\nabla \\log (Q / P_{\\rm eq})$, which characterizes the departure from equilibrium. Each Schwinger--Dyson identity measures a projection of this field onto a probe direction in configuration space. The relative Fisher information is its squared norm. This gives a universal bound relat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27360","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/2606.27360/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"}