{"paper":{"title":"From Koszul-Complex Stabilizer Models to Superselection Profiles: Topological Rigidity and Nonsplit Extensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Hao Song","submitted_at":"2026-08-10T17:54:31Z","abstract_excerpt":"Koszul-complex stabilizer models unify the toric-code hierarchy and bivariate-bicycle codes in one homological framework. To study translation-symmetry-enriched topological (SET) phases in these models and, more generally, in translation-invariant Calderbank-Shor-Steane (CSS) codes with stabilizer maps $(\\varphi_X,\\varphi_Z)$, we introduce the associated topological superselection profile $\\mathscr S_\\sigma:=\\tau_{\\geq1}\\mathbf R\\!\\operatorname{Hom}_R(\\overline{\\operatorname{coker}\\varphi_\\sigma},R),\\ \\sigma=X,Z$. Its cohomology layers $E_\\sigma^\\ell:=H^\\ell(\\mathscr S_\\sigma)\\cong_R\\operatorn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09913","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/2608.09913/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"}