{"paper":{"title":"Quantized topological invariant of symmetry-projected Gibbs states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.other","cond-mat.stat-mech","hep-th"],"primary_cat":"cond-mat.str-el","authors_text":"Haruki Watanabe, Weiguang Cao","submitted_at":"2026-08-05T01:49:48Z","abstract_excerpt":"We study Gibbs states projected onto the symmetric sector of contractible one-form symmetries. In a three-dimensional cluster-model interpolation, this projection stabilizes symmetry-protected topological and projected-paramagnetic phases, both sharply distinct from thermal disorder. A flux-twisted membrane invariant distinguishes these three phases by the values $-1,+1,0$, respectively. These values are exact on the endpoint, self-dual, zero-temperature, and infinite-temperature lines; elsewhere their quantization requires positive spatial-sheet, winding-line, and interface tensions. Quantum "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04350","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/2608.04350/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"}