{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:4CLTKOPTOI3ZITNEZI3O5RY77A","short_pith_number":"pith:4CLTKOPT","canonical_record":{"source":{"id":"2307.05309","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2023-07-11T14:57:06Z","cross_cats_sorted":[],"title_canon_sha256":"b99784b1101519a0b03cd9d053af883007d00a385915ced8d284c61d375a9eb0","abstract_canon_sha256":"841e8236e0c9187bc2ae5d9cb995b034989bb3bde1bf9c919d1af2b51436e993"},"schema_version":"1.0"},"canonical_sha256":"e0973539f37237944da4ca36eec71ff834b55f890df1775cd431f5f190875244","source":{"kind":"arxiv","id":"2307.05309","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.05309","created_at":"2026-07-05T08:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"2307.05309v2","created_at":"2026-07-05T08:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.05309","created_at":"2026-07-05T08:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"4CLTKOPTOI3Z","created_at":"2026-07-05T08:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"4CLTKOPTOI3ZITNE","created_at":"2026-07-05T08:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"4CLTKOPT","created_at":"2026-07-05T08:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:4CLTKOPTOI3ZITNEZI3O5RY77A","target":"record","payload":{"canonical_record":{"source":{"id":"2307.05309","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2023-07-11T14:57:06Z","cross_cats_sorted":[],"title_canon_sha256":"b99784b1101519a0b03cd9d053af883007d00a385915ced8d284c61d375a9eb0","abstract_canon_sha256":"841e8236e0c9187bc2ae5d9cb995b034989bb3bde1bf9c919d1af2b51436e993"},"schema_version":"1.0"},"canonical_sha256":"e0973539f37237944da4ca36eec71ff834b55f890df1775cd431f5f190875244","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:28:33.218200Z","signature_b64":"y610Qvb+/p3UW/zO+U8Kec0328YuEmUDj3+hgxTt6ygR/eNDJnPMo27hMfRssGCTAyEjr8xX6TB5YQfyAWtcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0973539f37237944da4ca36eec71ff834b55f890df1775cd431f5f190875244","last_reissued_at":"2026-07-05T08:28:33.217783Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:28:33.217783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.05309","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":"2026-07-05T08:28:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s0bhrqDKsxjjMz84SQh+rPjRf2gFJ7S8FwGfzbowquibrJGITCOL9AOsKoU/alhso6HxitnAIoVcWebEJ/CFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T21:12:33.872192Z"},"content_sha256":"4cfc20f3f99d6c7c7e79a2107cbb13b38e5ea7456fab6f23aa9d946f54e67fec","schema_version":"1.0","event_id":"sha256:4cfc20f3f99d6c7c7e79a2107cbb13b38e5ea7456fab6f23aa9d946f54e67fec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:4CLTKOPTOI3ZITNEZI3O5RY77A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetric monoidal equivalences of topological quantum field theories in dimension two and Frobenius algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Pablo S. Ocal","submitted_at":"2023-07-11T14:57:06Z","abstract_excerpt":"We show that the canonical equivalences of categories between 2-dimensional (unoriented) topological quantum field theories valued in a symmetric monoidal category and (extended) commutative Frobenius algebras in that symmetric monoidal category are symmetric monoidal equivalences. As an application, we recover that the invariant of 2-dimensional manifolds given by the product of (extended) commutative Frobenius algebras in a symmetric tensor category is the multiplication of the invariants given by each of the algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.05309","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/2307.05309/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":"2026-07-05T08:28:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MwJUusImoaQGAXPnWHMscQT8qDaaEy9D3kKz3opoQ+jLg4cq00NTVMf7G7jWigEx1GkVNkjeKR87fmrzlqQnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T21:12:33.872569Z"},"content_sha256":"aa5798c6e9503c534d236a051f925125296517ccd2c5d42145682f8551e05165","schema_version":"1.0","event_id":"sha256:aa5798c6e9503c534d236a051f925125296517ccd2c5d42145682f8551e05165"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4CLTKOPTOI3ZITNEZI3O5RY77A/bundle.json","state_url":"https://pith.science/pith/4CLTKOPTOI3ZITNEZI3O5RY77A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4CLTKOPTOI3ZITNEZI3O5RY77A/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":"2026-07-06T21:12:33Z","links":{"resolver":"https://pith.science/pith/4CLTKOPTOI3ZITNEZI3O5RY77A","bundle":"https://pith.science/pith/4CLTKOPTOI3ZITNEZI3O5RY77A/bundle.json","state":"https://pith.science/pith/4CLTKOPTOI3ZITNEZI3O5RY77A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4CLTKOPTOI3ZITNEZI3O5RY77A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:4CLTKOPTOI3ZITNEZI3O5RY77A","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":"841e8236e0c9187bc2ae5d9cb995b034989bb3bde1bf9c919d1af2b51436e993","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2023-07-11T14:57:06Z","title_canon_sha256":"b99784b1101519a0b03cd9d053af883007d00a385915ced8d284c61d375a9eb0"},"schema_version":"1.0","source":{"id":"2307.05309","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.05309","created_at":"2026-07-05T08:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"2307.05309v2","created_at":"2026-07-05T08:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.05309","created_at":"2026-07-05T08:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"4CLTKOPTOI3Z","created_at":"2026-07-05T08:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"4CLTKOPTOI3ZITNE","created_at":"2026-07-05T08:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"4CLTKOPT","created_at":"2026-07-05T08:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:aa5798c6e9503c534d236a051f925125296517ccd2c5d42145682f8551e05165","target":"graph","created_at":"2026-07-05T08:28:33Z","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/2307.05309/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the canonical equivalences of categories between 2-dimensional (unoriented) topological quantum field theories valued in a symmetric monoidal category and (extended) commutative Frobenius algebras in that symmetric monoidal category are symmetric monoidal equivalences. As an application, we recover that the invariant of 2-dimensional manifolds given by the product of (extended) commutative Frobenius algebras in a symmetric tensor category is the multiplication of the invariants given by each of the algebras.","authors_text":"Pablo S. Ocal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2023-07-11T14:57:06Z","title":"Symmetric monoidal equivalences of topological quantum field theories in dimension two and Frobenius algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.05309","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":"sha256:4cfc20f3f99d6c7c7e79a2107cbb13b38e5ea7456fab6f23aa9d946f54e67fec","target":"record","created_at":"2026-07-05T08:28:33Z","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":"841e8236e0c9187bc2ae5d9cb995b034989bb3bde1bf9c919d1af2b51436e993","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2023-07-11T14:57:06Z","title_canon_sha256":"b99784b1101519a0b03cd9d053af883007d00a385915ced8d284c61d375a9eb0"},"schema_version":"1.0","source":{"id":"2307.05309","kind":"arxiv","version":2}},"canonical_sha256":"e0973539f37237944da4ca36eec71ff834b55f890df1775cd431f5f190875244","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0973539f37237944da4ca36eec71ff834b55f890df1775cd431f5f190875244","first_computed_at":"2026-07-05T08:28:33.217783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:28:33.217783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y610Qvb+/p3UW/zO+U8Kec0328YuEmUDj3+hgxTt6ygR/eNDJnPMo27hMfRssGCTAyEjr8xX6TB5YQfyAWtcBg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:28:33.218200Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.05309","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cfc20f3f99d6c7c7e79a2107cbb13b38e5ea7456fab6f23aa9d946f54e67fec","sha256:aa5798c6e9503c534d236a051f925125296517ccd2c5d42145682f8551e05165"],"state_sha256":"abb56c2f036b6ce8aa0bf2107fedb794cb0aaef49349f0fdb1d23bd88ac41b0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xxdmTV8MYfUI7QJ8ndT2nbwo6d4hvEkoNQpovQN9RIkgacEpewombTIRCHZrnPtw4HxX+O/w6hjSXjNVIK0mBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T21:12:33.874516Z","bundle_sha256":"0133dc8f9a87cdd05c99cb12e29ce8b08b0398994850840f12492cba501e368e"}}