{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:EZ6AB24IFNYP7AMVLN5VCX3RO6","short_pith_number":"pith:EZ6AB24I","schema_version":"1.0","canonical_sha256":"267c00eb882b70ff81955b7b515f717793dc7612eec1303c8fb56956750f67ef","source":{"kind":"arxiv","id":"1408.0668","version":6},"attestation_state":"computed","paper":{"title":"Defining and classifying TQFTs via surgery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Andr\\'as Juh\\'asz","submitted_at":"2014-08-04T13:04:47Z","abstract_excerpt":"We give a presentation of the $n$-dimensional oriented cobordism category $\\text{Cob}_n$ with generators corresponding to diffeomorphisms and surgeries along framed spheres, and a complete set of relations. Hence, given a functor $F$ from the category of smooth oriented manifolds and diffeomorphisms to an arbitrary category $C$, and morphisms induced by surgeries along framed spheres, we obtain a necessary and sufficient set of relations these have to satisfy to extend to a functor from $\\text{Cob}_n$ to $C$. If $C$ is symmetric and monoidal, then we also characterize when the extension is a T"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.0668","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-04T13:04:47Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"be2e6aadb5d83a4fa20cf6ce46ec07fb40ebc62b5aa598e55c1226debe4d4f77","abstract_canon_sha256":"e6c04e545ef3f783e9f0238f977f547a8544a2284c618f74f948133c3287b651"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:53.696881Z","signature_b64":"94lCjoeB1EYRkwt+D3bTbm3yZa+trrl5IruOjfvU22gnx1M1B7ig2CkSy/2K/bs4R4dWOwzqdFIT2RzHtYhJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"267c00eb882b70ff81955b7b515f717793dc7612eec1303c8fb56956750f67ef","last_reissued_at":"2026-05-18T00:06:53.696251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:53.696251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Defining and classifying TQFTs via surgery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Andr\\'as Juh\\'asz","submitted_at":"2014-08-04T13:04:47Z","abstract_excerpt":"We give a presentation of the $n$-dimensional oriented cobordism category $\\text{Cob}_n$ with generators corresponding to diffeomorphisms and surgeries along framed spheres, and a complete set of relations. Hence, given a functor $F$ from the category of smooth oriented manifolds and diffeomorphisms to an arbitrary category $C$, and morphisms induced by surgeries along framed spheres, we obtain a necessary and sufficient set of relations these have to satisfy to extend to a functor from $\\text{Cob}_n$ to $C$. If $C$ is symmetric and monoidal, then we also characterize when the extension is a T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0668","kind":"arxiv","version":6},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.0668","created_at":"2026-05-18T00:06:53.696355+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0668v6","created_at":"2026-05-18T00:06:53.696355+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0668","created_at":"2026-05-18T00:06:53.696355+00:00"},{"alias_kind":"pith_short_12","alias_value":"EZ6AB24IFNYP","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"EZ6AB24IFNYP7AMV","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"EZ6AB24I","created_at":"2026-05-18T12:28:28.263976+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.08057","citing_title":"Non-semisimple open-closed 3d TFT","ref_index":25,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EZ6AB24IFNYP7AMVLN5VCX3RO6","json":"https://pith.science/pith/EZ6AB24IFNYP7AMVLN5VCX3RO6.json","graph_json":"https://pith.science/api/pith-number/EZ6AB24IFNYP7AMVLN5VCX3RO6/graph.json","events_json":"https://pith.science/api/pith-number/EZ6AB24IFNYP7AMVLN5VCX3RO6/events.json","paper":"https://pith.science/paper/EZ6AB24I"},"agent_actions":{"view_html":"https://pith.science/pith/EZ6AB24IFNYP7AMVLN5VCX3RO6","download_json":"https://pith.science/pith/EZ6AB24IFNYP7AMVLN5VCX3RO6.json","view_paper":"https://pith.science/paper/EZ6AB24I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0668&json=true","fetch_graph":"https://pith.science/api/pith-number/EZ6AB24IFNYP7AMVLN5VCX3RO6/graph.json","fetch_events":"https://pith.science/api/pith-number/EZ6AB24IFNYP7AMVLN5VCX3RO6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EZ6AB24IFNYP7AMVLN5VCX3RO6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EZ6AB24IFNYP7AMVLN5VCX3RO6/action/storage_attestation","attest_author":"https://pith.science/pith/EZ6AB24IFNYP7AMVLN5VCX3RO6/action/author_attestation","sign_citation":"https://pith.science/pith/EZ6AB24IFNYP7AMVLN5VCX3RO6/action/citation_signature","submit_replication":"https://pith.science/pith/EZ6AB24IFNYP7AMVLN5VCX3RO6/action/replication_record"}},"created_at":"2026-05-18T00:06:53.696355+00:00","updated_at":"2026-05-18T00:06:53.696355+00:00"}