{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:NZMEAAUTR5GHCOC34GHTRS7CNE","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":"88c7ddab0873d03b47e0ddf90ced84cd18bc80b1240cdac347fc673725d4a1f2","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"2000-10-29T18:56:11Z","title_canon_sha256":"71033e7fd06e905668291d272fd8c0eee6ba83a05a265b800f207b6220459393"},"schema_version":"1.0","source":{"id":"hep-th/0010269","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0010269","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0010269v2","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0010269","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"NZMEAAUTR5GH","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"NZMEAAUTR5GHCOC3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"NZMEAAUT","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:0cfa5441933ee47f3038e3d127062090e127ca3b9973c7cb43b15076fbb17fff","target":"graph","created_at":"2026-05-18T00:12:36Z","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":"I discuss the general formalism of two-dimensional topological field theories defined on open-closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for the identification of the algebraic structure governing such systems. I give a careful treatment of bulk-boundary and boundary-bulk correspondences, which are responsible for the relation between the closed and open sectors. The fact that these correspondences need not be injective nor surjective has interesting implications for the problem of classifying `","authors_text":"C. I. Lazaroiu","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2000-10-29T18:56:11Z","title":"On the structure of open-closed topological field theory in two dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0010269","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:e4bde2dae46f1be7e87cf30f0a2043cf410f6cf664be1908f690ccc3c1b7c124","target":"record","created_at":"2026-05-18T00:12:36Z","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":"88c7ddab0873d03b47e0ddf90ced84cd18bc80b1240cdac347fc673725d4a1f2","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"2000-10-29T18:56:11Z","title_canon_sha256":"71033e7fd06e905668291d272fd8c0eee6ba83a05a265b800f207b6220459393"},"schema_version":"1.0","source":{"id":"hep-th/0010269","kind":"arxiv","version":2}},"canonical_sha256":"6e584002938f4c71385be18f38cbe26929eb9b99a998d4974a8cbdced5e633e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e584002938f4c71385be18f38cbe26929eb9b99a998d4974a8cbdced5e633e5","first_computed_at":"2026-05-18T00:12:36.128066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:36.128066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rM5HhbLPZ8gF9kO8G2UMrUpc5MwzhpzY1BCrIyZ/pdMLfwZNqfZ0Nt20dLOkQRNLd5nw+mfz0XBD10/J1/+ABg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:36.128747Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0010269","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4bde2dae46f1be7e87cf30f0a2043cf410f6cf664be1908f690ccc3c1b7c124","sha256:0cfa5441933ee47f3038e3d127062090e127ca3b9973c7cb43b15076fbb17fff"],"state_sha256":"cc1a6099355791999f90c9181275a7a5745464979fc2b4027a6ed29fc016783e"}