{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:H3U6OS3QLCK72UNFPSYAISLMOF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c2422fd0e9636b0ad898bd9db1c14fa89d4c6cc90a3debcdb65adfe19f0f80fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-06-03T16:04:37Z","title_canon_sha256":"d832aa4d3907572ee69336f59cb05567dc047e996d0154b3a60c9ec5646df03c"},"schema_version":"1.0","source":{"id":"2509.06958","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.06958","created_at":"2026-07-05T12:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"2509.06958v1","created_at":"2026-07-05T12:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.06958","created_at":"2026-07-05T12:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"H3U6OS3QLCK7","created_at":"2026-07-05T12:07:12Z"},{"alias_kind":"pith_short_16","alias_value":"H3U6OS3QLCK72UNF","created_at":"2026-07-05T12:07:12Z"},{"alias_kind":"pith_short_8","alias_value":"H3U6OS3Q","created_at":"2026-07-05T12:07:12Z"}],"graph_snapshots":[{"event_id":"sha256:5e1a3e74888414a3237db63076097f0f5f94c3e906fb3e0e00cdb928e277454e","target":"graph","created_at":"2026-07-05T12:07:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.06958/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"William Boone Samuels","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-06-03T16:04:37Z","title":"Stratified Cohomological Quantum Codes via Colimits in Ch(R)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.06958","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5a6a4e9e0e6dfd673abc4165f9c558864488a25ac945d3737f8850acd241e925","target":"record","created_at":"2026-07-05T12:07:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c2422fd0e9636b0ad898bd9db1c14fa89d4c6cc90a3debcdb65adfe19f0f80fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-06-03T16:04:37Z","title_canon_sha256":"d832aa4d3907572ee69336f59cb05567dc047e996d0154b3a60c9ec5646df03c"},"schema_version":"1.0","source":{"id":"2509.06958","kind":"arxiv","version":1}},"canonical_sha256":"3ee9e74b705895fd51a57cb004496c715ee2b848a17f24b6d68450afba7d8ff4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ee9e74b705895fd51a57cb004496c715ee2b848a17f24b6d68450afba7d8ff4","first_computed_at":"2026-07-05T12:07:12.852908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:07:12.852908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cGBRIDMs6+w6YAQQ58Tc8Q0SKwqMYKrQEXGQ7dLIZ4eSOmC+pS1Ngxx8OqsTPt3eaSmnjkjvRgdu7uo+ovNBBA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:07:12.853402Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.06958","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a6a4e9e0e6dfd673abc4165f9c558864488a25ac945d3737f8850acd241e925","sha256:5e1a3e74888414a3237db63076097f0f5f94c3e906fb3e0e00cdb928e277454e"],"state_sha256":"880c1f259e8a35d4eee719f86dafd70450b467786cc32674581396f70b418836"}