{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:7SJYIP2Y6XMQ5BTHZG4X4RJTZK","short_pith_number":"pith:7SJYIP2Y","schema_version":"1.0","canonical_sha256":"fc93843f58f5d90e8667c9b97e4533cabcd81429783aea617d2700820e303112","source":{"kind":"arxiv","id":"2402.04468","version":2},"attestation_state":"computed","paper":{"title":"Combinatorial 2d higher topological quantum field theory from a local cyclic $A_\\infty$ algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.AT","math.GT","math.MP"],"primary_cat":"math-ph","authors_text":"Andrey Losev, Justin Beck, Pavel Mnev","submitted_at":"2024-02-06T23:28:01Z","abstract_excerpt":"We construct combinatorial analogs of 2d higher topological quantum field theories. We consider triangulations as vertices of a certain CW complex $\\Xi$. In the \"flip theory,\" cells of $\\Xi_\\mathrm{flip}$ correspond to polygonal decompositions obtained by erasing the edges in a triangulation. These theories assign to a cobordism $\\Sigma$ a cochain $Z$ on $\\Xi_\\mathrm{flip}$ constructed as a contraction of structure tensors of a cyclic $A_\\infty$ algebra $V$ assigned to polygons. The cyclic $A_\\infty$ equations imply the closedness equation $(\\delta+Q)Z=0$. In this context we define combinatori"},"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":"2402.04468","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-02-06T23:28:01Z","cross_cats_sorted":["hep-th","math.AT","math.GT","math.MP"],"title_canon_sha256":"f48f67743f4f241104bb777d824f515caecaf780567643d44dfc64fcd63bed1b","abstract_canon_sha256":"755979f457569d1d4ad9b2b8615d4e634ef4dbd33be74db3d6244f64d067bc8d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:00:40.948184Z","signature_b64":"SRl1lu1mhdpy1pFdvquYzeXDCnxrdT42xVWtE/h9cRdR3tUJ3s9jiTIMuLx7XT/Xu5TjE4rm5yREtFAjeGcBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc93843f58f5d90e8667c9b97e4533cabcd81429783aea617d2700820e303112","last_reissued_at":"2026-07-05T08:00:40.947709Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:00:40.947709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial 2d higher topological quantum field theory from a local cyclic $A_\\infty$ algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.AT","math.GT","math.MP"],"primary_cat":"math-ph","authors_text":"Andrey Losev, Justin Beck, Pavel Mnev","submitted_at":"2024-02-06T23:28:01Z","abstract_excerpt":"We construct combinatorial analogs of 2d higher topological quantum field theories. We consider triangulations as vertices of a certain CW complex $\\Xi$. In the \"flip theory,\" cells of $\\Xi_\\mathrm{flip}$ correspond to polygonal decompositions obtained by erasing the edges in a triangulation. These theories assign to a cobordism $\\Sigma$ a cochain $Z$ on $\\Xi_\\mathrm{flip}$ constructed as a contraction of structure tensors of a cyclic $A_\\infty$ algebra $V$ assigned to polygons. The cyclic $A_\\infty$ equations imply the closedness equation $(\\delta+Q)Z=0$. In this context we define combinatori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.04468","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/2402.04468/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2402.04468","created_at":"2026-07-05T08:00:40.947766+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.04468v2","created_at":"2026-07-05T08:00:40.947766+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.04468","created_at":"2026-07-05T08:00:40.947766+00:00"},{"alias_kind":"pith_short_12","alias_value":"7SJYIP2Y6XMQ","created_at":"2026-07-05T08:00:40.947766+00:00"},{"alias_kind":"pith_short_16","alias_value":"7SJYIP2Y6XMQ5BTH","created_at":"2026-07-05T08:00:40.947766+00:00"},{"alias_kind":"pith_short_8","alias_value":"7SJYIP2Y","created_at":"2026-07-05T08:00:40.947766+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7SJYIP2Y6XMQ5BTHZG4X4RJTZK","json":"https://pith.science/pith/7SJYIP2Y6XMQ5BTHZG4X4RJTZK.json","graph_json":"https://pith.science/api/pith-number/7SJYIP2Y6XMQ5BTHZG4X4RJTZK/graph.json","events_json":"https://pith.science/api/pith-number/7SJYIP2Y6XMQ5BTHZG4X4RJTZK/events.json","paper":"https://pith.science/paper/7SJYIP2Y"},"agent_actions":{"view_html":"https://pith.science/pith/7SJYIP2Y6XMQ5BTHZG4X4RJTZK","download_json":"https://pith.science/pith/7SJYIP2Y6XMQ5BTHZG4X4RJTZK.json","view_paper":"https://pith.science/paper/7SJYIP2Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.04468&json=true","fetch_graph":"https://pith.science/api/pith-number/7SJYIP2Y6XMQ5BTHZG4X4RJTZK/graph.json","fetch_events":"https://pith.science/api/pith-number/7SJYIP2Y6XMQ5BTHZG4X4RJTZK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7SJYIP2Y6XMQ5BTHZG4X4RJTZK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7SJYIP2Y6XMQ5BTHZG4X4RJTZK/action/storage_attestation","attest_author":"https://pith.science/pith/7SJYIP2Y6XMQ5BTHZG4X4RJTZK/action/author_attestation","sign_citation":"https://pith.science/pith/7SJYIP2Y6XMQ5BTHZG4X4RJTZK/action/citation_signature","submit_replication":"https://pith.science/pith/7SJYIP2Y6XMQ5BTHZG4X4RJTZK/action/replication_record"}},"created_at":"2026-07-05T08:00:40.947766+00:00","updated_at":"2026-07-05T08:00:40.947766+00:00"}