{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ECRJIZH5SZ7LCQ4QPM5IJDUPME","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":"52ad98031eb00dba2872ebba95d3629f520056fa3435b96454aa1fd11861f132","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-02T17:49:34Z","title_canon_sha256":"fb4e9427265ae48fa84eb244bb24ff9a3da57faf162ae4da9a658b31c6fb9771"},"schema_version":"1.0","source":{"id":"1606.00781","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00781","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00781v1","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00781","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"ECRJIZH5SZ7L","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"ECRJIZH5SZ7LCQ4Q","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"ECRJIZH5","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:3cc9677515586720594559781ded97388c6a216e9c787912efd3df25effb2ee4","target":"graph","created_at":"2026-05-18T01:13:00Z","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":"The purpose of this paper is to give a twisted version of the Eynard-Orantin topological recursion by a 2D Topological Quantum Field Theory. We define a kernel for a 2D TQFT and use an algebraic definition for a topological recursion to define how to twist a standard topological recursion by a 2D TQFT. The A-model side enumerative problem consists of counting cell graphs where in addition vertices are decorated by elements in a Frobenius algebra, and which are a twisted version of the generalized Catalan numbers of Dumitrescu-Mulase-Safnuk-Sorkin. We show that the function which counts these d","authors_text":"Daniel Hern\\'andez Serrano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-02T17:49:34Z","title":"Topological recursion, topological quantum field theory and Gromov-Witten invariants of BG"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00781","kind":"arxiv","version":1},"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":"sha256:9549837feb9414d9c32068b273c6d43ad7f703a57f7934b3cf53c58397bd2d71","target":"record","created_at":"2026-05-18T01:13:00Z","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":"52ad98031eb00dba2872ebba95d3629f520056fa3435b96454aa1fd11861f132","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-02T17:49:34Z","title_canon_sha256":"fb4e9427265ae48fa84eb244bb24ff9a3da57faf162ae4da9a658b31c6fb9771"},"schema_version":"1.0","source":{"id":"1606.00781","kind":"arxiv","version":1}},"canonical_sha256":"20a29464fd967eb143907b3a848e8f6124f5146dd9f8403bc7e26f7aec84876a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20a29464fd967eb143907b3a848e8f6124f5146dd9f8403bc7e26f7aec84876a","first_computed_at":"2026-05-18T01:13:00.637619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:00.637619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yfKl+QBavKyQkqeAaZ3lw0NfSSo0MypAtBmS8iYV/E/kwt7Gc6ChSGqpDkJ2wNEs7tjdLnFlllCleYI7IuxuAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:00.638158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00781","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9549837feb9414d9c32068b273c6d43ad7f703a57f7934b3cf53c58397bd2d71","sha256:3cc9677515586720594559781ded97388c6a216e9c787912efd3df25effb2ee4"],"state_sha256":"e530897d6c35df1a4b7cc3f0d400d65abb1b8d10a39dd768e2139925a55aca4d"}