{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:M4DUQTNR5M7KURP2U6PHVVVC5F","short_pith_number":"pith:M4DUQTNR","canonical_record":{"source":{"id":"2205.06874","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2022-05-13T20:16:15Z","cross_cats_sorted":["math-ph","math.CT","math.GT","math.MP"],"title_canon_sha256":"93a4e70f81b5b8a7f7f0a78fcfb53434bd0d6ec251da62e0854468338fd6565b","abstract_canon_sha256":"1a396223f4806632293a75df66c9cb14e158860e031146d41c527a898a7a8779"},"schema_version":"1.0"},"canonical_sha256":"6707484db1eb3eaa45faa79e7ad6a2e973180b6a4c21f6f799c24cafa87b0d1b","source":{"kind":"arxiv","id":"2205.06874","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.06874","created_at":"2026-07-05T06:21:03Z"},{"alias_kind":"arxiv_version","alias_value":"2205.06874v2","created_at":"2026-07-05T06:21:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.06874","created_at":"2026-07-05T06:21:03Z"},{"alias_kind":"pith_short_12","alias_value":"M4DUQTNR5M7K","created_at":"2026-07-05T06:21:03Z"},{"alias_kind":"pith_short_16","alias_value":"M4DUQTNR5M7KURP2","created_at":"2026-07-05T06:21:03Z"},{"alias_kind":"pith_short_8","alias_value":"M4DUQTNR","created_at":"2026-07-05T06:21:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:M4DUQTNR5M7KURP2U6PHVVVC5F","target":"record","payload":{"canonical_record":{"source":{"id":"2205.06874","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2022-05-13T20:16:15Z","cross_cats_sorted":["math-ph","math.CT","math.GT","math.MP"],"title_canon_sha256":"93a4e70f81b5b8a7f7f0a78fcfb53434bd0d6ec251da62e0854468338fd6565b","abstract_canon_sha256":"1a396223f4806632293a75df66c9cb14e158860e031146d41c527a898a7a8779"},"schema_version":"1.0"},"canonical_sha256":"6707484db1eb3eaa45faa79e7ad6a2e973180b6a4c21f6f799c24cafa87b0d1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:21:03.451984Z","signature_b64":"QVnp3KG/yXYHC02oUPT+u4uAkDWXAhOKNCed5T7ay4kLjKaIjqqAAUI1AQUSPC2k011E0fi7DRnvkEyQ/t09Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6707484db1eb3eaa45faa79e7ad6a2e973180b6a4c21f6f799c24cafa87b0d1b","last_reissued_at":"2026-07-05T06:21:03.451573Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:21:03.451573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.06874","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:21:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KrzrGxe9Y0g1dWd+2ze/HhdgQO24aiopFjzY77a5oKQkKWqZyrZrKVWN3UcUWfaBl04+fFuwCUcRCPEYJH9LAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T17:51:57.093764Z"},"content_sha256":"2c30cdcf296739504f846143f0149ca2a592619da37fe43ce65dfd707a4a83f9","schema_version":"1.0","event_id":"sha256:2c30cdcf296739504f846143f0149ca2a592619da37fe43ce65dfd707a4a83f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:M4DUQTNR5M7KURP2U6PHVVVC5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"State sum models with defects based on spherical fusion categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CT","math.GT","math.MP"],"primary_cat":"math.QA","authors_text":"Catherine Meusburger","submitted_at":"2022-05-13T20:16:15Z","abstract_excerpt":"We define a Turaev-Viro-Barrett-Westbury state sum model of triangulated 3-manifolds with surface, line and point defects. Surface defects are oriented embedded 2d PL submanifolds and are labeled with bimodule categories over spherical fusion categories with bimodule traces. Line and point defects form directed graphs on these surfaces and labeled with bimodule functors and bimodule natural transformations. The state sum is based on generalised 6j symbols that encode the coherence isomorphisms of the defect data. We prove the triangulation independence of the state sum and show that it can be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.06874","kind":"arxiv","version":2},"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/2205.06874/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":"2026-07-05T06:21:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nmevu+6NxAxBPoDpSESC1p9RHjpAdmTYAYN/z99/ezcYhs/BkBhnEIqH6bTIYUXWLhyKegFetzgCA5HdJm99Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T17:51:57.094964Z"},"content_sha256":"baba898fde8348f717ea6b11d305b2489607fe5dc352c796c427fe71e384cad4","schema_version":"1.0","event_id":"sha256:baba898fde8348f717ea6b11d305b2489607fe5dc352c796c427fe71e384cad4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M4DUQTNR5M7KURP2U6PHVVVC5F/bundle.json","state_url":"https://pith.science/pith/M4DUQTNR5M7KURP2U6PHVVVC5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M4DUQTNR5M7KURP2U6PHVVVC5F/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":"2026-08-10T17:51:57Z","links":{"resolver":"https://pith.science/pith/M4DUQTNR5M7KURP2U6PHVVVC5F","bundle":"https://pith.science/pith/M4DUQTNR5M7KURP2U6PHVVVC5F/bundle.json","state":"https://pith.science/pith/M4DUQTNR5M7KURP2U6PHVVVC5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M4DUQTNR5M7KURP2U6PHVVVC5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:M4DUQTNR5M7KURP2U6PHVVVC5F","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":"1a396223f4806632293a75df66c9cb14e158860e031146d41c527a898a7a8779","cross_cats_sorted":["math-ph","math.CT","math.GT","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2022-05-13T20:16:15Z","title_canon_sha256":"93a4e70f81b5b8a7f7f0a78fcfb53434bd0d6ec251da62e0854468338fd6565b"},"schema_version":"1.0","source":{"id":"2205.06874","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.06874","created_at":"2026-07-05T06:21:03Z"},{"alias_kind":"arxiv_version","alias_value":"2205.06874v2","created_at":"2026-07-05T06:21:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.06874","created_at":"2026-07-05T06:21:03Z"},{"alias_kind":"pith_short_12","alias_value":"M4DUQTNR5M7K","created_at":"2026-07-05T06:21:03Z"},{"alias_kind":"pith_short_16","alias_value":"M4DUQTNR5M7KURP2","created_at":"2026-07-05T06:21:03Z"},{"alias_kind":"pith_short_8","alias_value":"M4DUQTNR","created_at":"2026-07-05T06:21:03Z"}],"graph_snapshots":[{"event_id":"sha256:baba898fde8348f717ea6b11d305b2489607fe5dc352c796c427fe71e384cad4","target":"graph","created_at":"2026-07-05T06:21:03Z","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/2205.06874/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define a Turaev-Viro-Barrett-Westbury state sum model of triangulated 3-manifolds with surface, line and point defects. Surface defects are oriented embedded 2d PL submanifolds and are labeled with bimodule categories over spherical fusion categories with bimodule traces. Line and point defects form directed graphs on these surfaces and labeled with bimodule functors and bimodule natural transformations. The state sum is based on generalised 6j symbols that encode the coherence isomorphisms of the defect data. We prove the triangulation independence of the state sum and show that it can be ","authors_text":"Catherine Meusburger","cross_cats":["math-ph","math.CT","math.GT","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2022-05-13T20:16:15Z","title":"State sum models with defects based on spherical fusion categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.06874","kind":"arxiv","version":2},"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":"sha256:2c30cdcf296739504f846143f0149ca2a592619da37fe43ce65dfd707a4a83f9","target":"record","created_at":"2026-07-05T06:21:03Z","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":"1a396223f4806632293a75df66c9cb14e158860e031146d41c527a898a7a8779","cross_cats_sorted":["math-ph","math.CT","math.GT","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2022-05-13T20:16:15Z","title_canon_sha256":"93a4e70f81b5b8a7f7f0a78fcfb53434bd0d6ec251da62e0854468338fd6565b"},"schema_version":"1.0","source":{"id":"2205.06874","kind":"arxiv","version":2}},"canonical_sha256":"6707484db1eb3eaa45faa79e7ad6a2e973180b6a4c21f6f799c24cafa87b0d1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6707484db1eb3eaa45faa79e7ad6a2e973180b6a4c21f6f799c24cafa87b0d1b","first_computed_at":"2026-07-05T06:21:03.451573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:21:03.451573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QVnp3KG/yXYHC02oUPT+u4uAkDWXAhOKNCed5T7ay4kLjKaIjqqAAUI1AQUSPC2k011E0fi7DRnvkEyQ/t09Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:21:03.451984Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.06874","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c30cdcf296739504f846143f0149ca2a592619da37fe43ce65dfd707a4a83f9","sha256:baba898fde8348f717ea6b11d305b2489607fe5dc352c796c427fe71e384cad4"],"state_sha256":"76fded0a3dc328a4c4f0a4c3949f78537d26037492ca248fa9e17fd23ee57feb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E2qHLqfkcv3SEGQ/2a7zzgKrG2SU/GFFEFZScUHHS9cpoYsaXQXS+TuuLYNs52og9R7MI2jZcWFu56q539vgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T17:51:57.101989Z","bundle_sha256":"1dff72765d1b042e870e3617bae388b6e4eadff24524f8c9ab84b73db643f4cf"}}