{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NZXP3ZKWGMZLOUE2GWIBGQC6TK","short_pith_number":"pith:NZXP3ZKW","canonical_record":{"source":{"id":"1112.1000","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-12-05T17:05:19Z","cross_cats_sorted":[],"title_canon_sha256":"1f5eab48e6b792eb637e1a52e23db0f1a19b2b6aa845352658467a5ae6970dbc","abstract_canon_sha256":"397026b797c8a8631cc4fbd277b5822bcda917192ae6da8868bec2281459151c"},"schema_version":"1.0"},"canonical_sha256":"6e6efde5563332b7509a359013405e9aa5abd51debb49d082b1dd1676164f394","source":{"kind":"arxiv","id":"1112.1000","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1000","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1000v2","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1000","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"NZXP3ZKWGMZL","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NZXP3ZKWGMZLOUE2","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NZXP3ZKW","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NZXP3ZKWGMZLOUE2GWIBGQC6TK","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1000","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-12-05T17:05:19Z","cross_cats_sorted":[],"title_canon_sha256":"1f5eab48e6b792eb637e1a52e23db0f1a19b2b6aa845352658467a5ae6970dbc","abstract_canon_sha256":"397026b797c8a8631cc4fbd277b5822bcda917192ae6da8868bec2281459151c"},"schema_version":"1.0"},"canonical_sha256":"6e6efde5563332b7509a359013405e9aa5abd51debb49d082b1dd1676164f394","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:03.418252Z","signature_b64":"UthBwrtue9L1iFYzFc2GQif9IG5Gpipshiy3lSP3mvtzE6i0hhLTeCUKKIBpGD17oAn0PKnQEXWjK93jRK6VCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e6efde5563332b7509a359013405e9aa5abd51debb49d082b1dd1676164f394","last_reissued_at":"2026-05-18T02:46:03.417729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:03.417729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1000","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":"2026-05-18T02:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SKFhDnJbgeqjVSzBfzPByUQYb5GrZX0+3jKzKU+5WW6IYXmyO0Swd3j1bEoshc/HwzACrh41ByGrBy3TFOsZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:36:40.375925Z"},"content_sha256":"d5d8ae49eb81bb4b25f7d944f3b9aa090417b92543cc9575de9f955fb69ee6ec","schema_version":"1.0","event_id":"sha256:d5d8ae49eb81bb4b25f7d944f3b9aa090417b92543cc9575de9f955fb69ee6ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NZXP3ZKWGMZLOUE2GWIBGQC6TK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Classification of Two-Dimensional Extended Topological Field Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Christopher J. Schommer-Pries","submitted_at":"2011-12-05T17:05:19Z","abstract_excerpt":"We provide a complete generators and relations presentation of the 2-dimensional extended unoriented and oriented bordism bicategories as symmetric monoidal bicategories. Thereby we classify these types of 2-dimensional extended topological field theories with arbitrary target bicategory. As an immediate corollary we obtain a concrete classification when the target is the symmetric monoidal bicategory of algebras, bimodules, and intertwiners over a fixed commutative ground ring. In the oriented case, such an extended topological field theory is equivalent to specifying a (non-commutative) sepa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1000","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":""},"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":"2026-05-18T02:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3gq9qkF9flrARODpdqQvuNe8DE/NhXkw03luFFzKIst3Sq02LNwiNbs5ZRN1QQehlUlUB+Ju1L3WG6WTdEnoBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:36:40.376555Z"},"content_sha256":"66a45de81e5dd9888efa551aa62a52972c2e31aad8c97db0a79ca7086d3aac08","schema_version":"1.0","event_id":"sha256:66a45de81e5dd9888efa551aa62a52972c2e31aad8c97db0a79ca7086d3aac08"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZXP3ZKWGMZLOUE2GWIBGQC6TK/bundle.json","state_url":"https://pith.science/pith/NZXP3ZKWGMZLOUE2GWIBGQC6TK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZXP3ZKWGMZLOUE2GWIBGQC6TK/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":"2026-05-31T11:36:40Z","links":{"resolver":"https://pith.science/pith/NZXP3ZKWGMZLOUE2GWIBGQC6TK","bundle":"https://pith.science/pith/NZXP3ZKWGMZLOUE2GWIBGQC6TK/bundle.json","state":"https://pith.science/pith/NZXP3ZKWGMZLOUE2GWIBGQC6TK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZXP3ZKWGMZLOUE2GWIBGQC6TK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NZXP3ZKWGMZLOUE2GWIBGQC6TK","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":"397026b797c8a8631cc4fbd277b5822bcda917192ae6da8868bec2281459151c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-12-05T17:05:19Z","title_canon_sha256":"1f5eab48e6b792eb637e1a52e23db0f1a19b2b6aa845352658467a5ae6970dbc"},"schema_version":"1.0","source":{"id":"1112.1000","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1000","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1000v2","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1000","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"NZXP3ZKWGMZL","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NZXP3ZKWGMZLOUE2","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NZXP3ZKW","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:66a45de81e5dd9888efa551aa62a52972c2e31aad8c97db0a79ca7086d3aac08","target":"graph","created_at":"2026-05-18T02:46:03Z","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"},"paper":{"abstract_excerpt":"We provide a complete generators and relations presentation of the 2-dimensional extended unoriented and oriented bordism bicategories as symmetric monoidal bicategories. Thereby we classify these types of 2-dimensional extended topological field theories with arbitrary target bicategory. As an immediate corollary we obtain a concrete classification when the target is the symmetric monoidal bicategory of algebras, bimodules, and intertwiners over a fixed commutative ground ring. In the oriented case, such an extended topological field theory is equivalent to specifying a (non-commutative) sepa","authors_text":"Christopher J. Schommer-Pries","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-12-05T17:05:19Z","title":"The Classification of Two-Dimensional Extended Topological Field Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1000","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:d5d8ae49eb81bb4b25f7d944f3b9aa090417b92543cc9575de9f955fb69ee6ec","target":"record","created_at":"2026-05-18T02:46:03Z","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":"397026b797c8a8631cc4fbd277b5822bcda917192ae6da8868bec2281459151c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-12-05T17:05:19Z","title_canon_sha256":"1f5eab48e6b792eb637e1a52e23db0f1a19b2b6aa845352658467a5ae6970dbc"},"schema_version":"1.0","source":{"id":"1112.1000","kind":"arxiv","version":2}},"canonical_sha256":"6e6efde5563332b7509a359013405e9aa5abd51debb49d082b1dd1676164f394","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e6efde5563332b7509a359013405e9aa5abd51debb49d082b1dd1676164f394","first_computed_at":"2026-05-18T02:46:03.417729Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:03.417729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UthBwrtue9L1iFYzFc2GQif9IG5Gpipshiy3lSP3mvtzE6i0hhLTeCUKKIBpGD17oAn0PKnQEXWjK93jRK6VCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:03.418252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1000","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5d8ae49eb81bb4b25f7d944f3b9aa090417b92543cc9575de9f955fb69ee6ec","sha256:66a45de81e5dd9888efa551aa62a52972c2e31aad8c97db0a79ca7086d3aac08"],"state_sha256":"0bd00cf2cdcf2ce6c477e343c2f3d37dc51d6a60f473fecfa0f551146256c06c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2wfUWSY/WkY7+anmiYI31QPsHw4o7UFvlzCIq3zhG2U6y5BHFsWWwblGe0FCGnOYWAW3Vy/1NlwoiTHvs42wBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:36:40.379258Z","bundle_sha256":"3b028461392336b678f2540013029b9590d2e5b63161be7c3c10e181f38d16a0"}}