{"paper":{"title":"Stratified Cohomological Quantum Codes via Colimits in Ch(R)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"William Boone Samuels","submitted_at":"2025-06-03T16:04:37Z","abstract_excerpt":"We introduce \\emph{stratified colimit codes}: stabiliser codes obtained by taking the degree-wise colimit $\\mathcal C_\\bullet(X):=\\operatorname*{colim}_{\\sigma\\in X}F(\\sigma)$ of a functor $F\\colon X\\to\\mathbf{Ch}(R)$ from a finite poset into the category of chain complexes over a commutative ring~$R$. Axioms requiring only transitivity and boundary-compatibility of the morphisms in $F$ ensure that $\\partial^2=0$, so the homology $H_\\bullet$ and cohomology $H^\\bullet$ furnish the usual CSS $Z$- and $X$-type logical sectors; torsion in $H_\\bullet$ classifies qudit charges via the universal coef"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.06958","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/2509.06958/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"}