{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ZLV7MANIWB4PSGL2STTQX7FHWV","short_pith_number":"pith:ZLV7MANI","canonical_record":{"source":{"id":"2501.02398","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-04T22:45:00Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","quant-ph"],"title_canon_sha256":"c973fef26c7b78ca84f9a4598b9a003f926d9226ca1d5230ffd40054b5d7e10f","abstract_canon_sha256":"f15e0b41fe827f8f38942c3e6819da972373adb60994bf1e3207e58ba29db411"},"schema_version":"1.0"},"canonical_sha256":"caebf601a8b078f9197a94e70bfca7b5790090f03f41d8e5201774e7fc861af1","source":{"kind":"arxiv","id":"2501.02398","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.02398","created_at":"2026-07-05T09:57:06Z"},{"alias_kind":"arxiv_version","alias_value":"2501.02398v1","created_at":"2026-07-05T09:57:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.02398","created_at":"2026-07-05T09:57:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZLV7MANIWB4P","created_at":"2026-07-05T09:57:06Z"},{"alias_kind":"pith_short_16","alias_value":"ZLV7MANIWB4PSGL2","created_at":"2026-07-05T09:57:06Z"},{"alias_kind":"pith_short_8","alias_value":"ZLV7MANI","created_at":"2026-07-05T09:57:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ZLV7MANIWB4PSGL2STTQX7FHWV","target":"record","payload":{"canonical_record":{"source":{"id":"2501.02398","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-04T22:45:00Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","quant-ph"],"title_canon_sha256":"c973fef26c7b78ca84f9a4598b9a003f926d9226ca1d5230ffd40054b5d7e10f","abstract_canon_sha256":"f15e0b41fe827f8f38942c3e6819da972373adb60994bf1e3207e58ba29db411"},"schema_version":"1.0"},"canonical_sha256":"caebf601a8b078f9197a94e70bfca7b5790090f03f41d8e5201774e7fc861af1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:06.825452Z","signature_b64":"YQ5obYW/F0mEV9G0qWPH3RPh0ZJhHYgvJ7DcQ8rHeUlxkdVdEcO1z2dWLNfvaoxlqd6E4da9Dp+z1G6pmc2jCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caebf601a8b078f9197a94e70bfca7b5790090f03f41d8e5201774e7fc861af1","last_reissued_at":"2026-07-05T09:57:06.825063Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:06.825063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.02398","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:57:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ysPUb5iaFtOQNtM6E8GOCMQHDh4pkuDPyylVRhHJ+/wgKV3sw7qG2sh5JXnIZ5RiL7MlN5VtCZWxHFAceWMhCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T02:37:42.681727Z"},"content_sha256":"e67e32f67c4ce6771d71827552ffe28d4458cdd4a1ff544ce59012f5712b606d","schema_version":"1.0","event_id":"sha256:e67e32f67c4ce6771d71827552ffe28d4458cdd4a1ff544ce59012f5712b606d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ZLV7MANIWB4PSGL2STTQX7FHWV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixed state topological order: operator algebraic approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Yoshiko Ogata","submitted_at":"2025-01-04T22:45:00Z","abstract_excerpt":"We study the classification problem of mixed states in two-dimensional quantum spin systems in the operator algebraic framework of quantum statistical mechanics. We associate a braided $C^*$-tensor category to each state satisfying a mixed-state version of the approximate Haag duality. We study how this category behaves under decoherence: suppose the state is acted by a finite depth quantum channel. We prove that the braided $C^*$-tensor category of the final state is a braided $C^*$-tensor subcategory of the initial state."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.02398","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/2501.02398/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:57:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7aqjOl5V0uLDoNT6vsabWOqhCoxV2utHmwGaSWpBcLMnNNwyFzKo6dbOsP6TYym/4fn0Erc6Oq7g3h9mJF8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T02:37:42.682264Z"},"content_sha256":"b3974b99321281452b1f98b356d02b54d0fe1bd63972a20e9a721e8cb6bb011c","schema_version":"1.0","event_id":"sha256:b3974b99321281452b1f98b356d02b54d0fe1bd63972a20e9a721e8cb6bb011c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZLV7MANIWB4PSGL2STTQX7FHWV/bundle.json","state_url":"https://pith.science/pith/ZLV7MANIWB4PSGL2STTQX7FHWV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZLV7MANIWB4PSGL2STTQX7FHWV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-18T02:37:42Z","links":{"resolver":"https://pith.science/pith/ZLV7MANIWB4PSGL2STTQX7FHWV","bundle":"https://pith.science/pith/ZLV7MANIWB4PSGL2STTQX7FHWV/bundle.json","state":"https://pith.science/pith/ZLV7MANIWB4PSGL2STTQX7FHWV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZLV7MANIWB4PSGL2STTQX7FHWV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZLV7MANIWB4PSGL2STTQX7FHWV","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":"f15e0b41fe827f8f38942c3e6819da972373adb60994bf1e3207e58ba29db411","cross_cats_sorted":["cond-mat.stat-mech","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-04T22:45:00Z","title_canon_sha256":"c973fef26c7b78ca84f9a4598b9a003f926d9226ca1d5230ffd40054b5d7e10f"},"schema_version":"1.0","source":{"id":"2501.02398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.02398","created_at":"2026-07-05T09:57:06Z"},{"alias_kind":"arxiv_version","alias_value":"2501.02398v1","created_at":"2026-07-05T09:57:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.02398","created_at":"2026-07-05T09:57:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZLV7MANIWB4P","created_at":"2026-07-05T09:57:06Z"},{"alias_kind":"pith_short_16","alias_value":"ZLV7MANIWB4PSGL2","created_at":"2026-07-05T09:57:06Z"},{"alias_kind":"pith_short_8","alias_value":"ZLV7MANI","created_at":"2026-07-05T09:57:06Z"}],"graph_snapshots":[{"event_id":"sha256:b3974b99321281452b1f98b356d02b54d0fe1bd63972a20e9a721e8cb6bb011c","target":"graph","created_at":"2026-07-05T09:57:06Z","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/2501.02398/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the classification problem of mixed states in two-dimensional quantum spin systems in the operator algebraic framework of quantum statistical mechanics. We associate a braided $C^*$-tensor category to each state satisfying a mixed-state version of the approximate Haag duality. We study how this category behaves under decoherence: suppose the state is acted by a finite depth quantum channel. We prove that the braided $C^*$-tensor category of the final state is a braided $C^*$-tensor subcategory of the initial state.","authors_text":"Yoshiko Ogata","cross_cats":["cond-mat.stat-mech","math.MP","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-04T22:45:00Z","title":"Mixed state topological order: operator algebraic approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.02398","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:e67e32f67c4ce6771d71827552ffe28d4458cdd4a1ff544ce59012f5712b606d","target":"record","created_at":"2026-07-05T09:57:06Z","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":"f15e0b41fe827f8f38942c3e6819da972373adb60994bf1e3207e58ba29db411","cross_cats_sorted":["cond-mat.stat-mech","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-04T22:45:00Z","title_canon_sha256":"c973fef26c7b78ca84f9a4598b9a003f926d9226ca1d5230ffd40054b5d7e10f"},"schema_version":"1.0","source":{"id":"2501.02398","kind":"arxiv","version":1}},"canonical_sha256":"caebf601a8b078f9197a94e70bfca7b5790090f03f41d8e5201774e7fc861af1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"caebf601a8b078f9197a94e70bfca7b5790090f03f41d8e5201774e7fc861af1","first_computed_at":"2026-07-05T09:57:06.825063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:57:06.825063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YQ5obYW/F0mEV9G0qWPH3RPh0ZJhHYgvJ7DcQ8rHeUlxkdVdEcO1z2dWLNfvaoxlqd6E4da9Dp+z1G6pmc2jCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:57:06.825452Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.02398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e67e32f67c4ce6771d71827552ffe28d4458cdd4a1ff544ce59012f5712b606d","sha256:b3974b99321281452b1f98b356d02b54d0fe1bd63972a20e9a721e8cb6bb011c"],"state_sha256":"77adb59019b0d1bca111a374c18f3825f4591e1d34de5644305d7832d06f7b31"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EBdsTduiMlSNNk/XtGvTyJDnqVLWhJDlWZcRmdtCautcW2bEgCSGHdUWo1ElbD1WAK4SYzgN05ubyEPA1jALBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T02:37:42.686533Z","bundle_sha256":"4f6cfad222c726515f791c644e2c8c69f5be110122dd4106d3191a4b24675b22"}}