{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:IOY6LATJREBKAR26RB4VV3ZPQU","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":"2643f86c13b373548fc74524ce5a4135d0601667db08f4f16df5ecbcd4bd28c3","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2007-08-21T16:12:14Z","title_canon_sha256":"22fcaff26c96daaf0aeeb4bbcf157dfea1e1a401d8164ef504308c5c9b460d8f"},"schema_version":"1.0","source":{"id":"0708.2851","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.2851","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"0708.2851v3","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.2851","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"IOY6LATJREBK","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"IOY6LATJREBKAR26","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"IOY6LATJ","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:d48586eadae230eb3c1cf2902b223faecc31dccce0cb7b6febd01bea8903a171","target":"graph","created_at":"2026-05-18T02:24:57Z","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":"Using quilted Floer cohomology and relative quilt invariants, we define a composition functor for categories of Lagrangian correspondences in monotone and exact symplectic Floer theory. We show that this functor agrees with geometric composition in the case that the composition is smooth and embedded. As a consequence we obtain 'categorification commutes with composition' for Lagrangian correspondences.","authors_text":"Chris T. Woodward, Katrin Wehrheim","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2007-08-21T16:12:14Z","title":"Functoriality for Lagrangian correspondences in Floer theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.2851","kind":"arxiv","version":3},"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":"sha256:33c99fe283cd429816f1c8fc37293b46edbb3c09a4ef07464653f4c2d2c1b0a4","target":"record","created_at":"2026-05-18T02:24:57Z","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":"2643f86c13b373548fc74524ce5a4135d0601667db08f4f16df5ecbcd4bd28c3","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2007-08-21T16:12:14Z","title_canon_sha256":"22fcaff26c96daaf0aeeb4bbcf157dfea1e1a401d8164ef504308c5c9b460d8f"},"schema_version":"1.0","source":{"id":"0708.2851","kind":"arxiv","version":3}},"canonical_sha256":"43b1e582698902a0475e88795aef2f850fd8f733967bb20a2e308718ee4c8838","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43b1e582698902a0475e88795aef2f850fd8f733967bb20a2e308718ee4c8838","first_computed_at":"2026-05-18T02:24:57.940859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:57.940859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dSKQf64nZhTaDXI5Eq79H+HR1+Yd1Ftypg7jBhLlOYA0x+otXsTkI7izZA9mUj27TiFSTCZ07dmZGZNdesMuCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:57.941498Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.2851","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33c99fe283cd429816f1c8fc37293b46edbb3c09a4ef07464653f4c2d2c1b0a4","sha256:d48586eadae230eb3c1cf2902b223faecc31dccce0cb7b6febd01bea8903a171"],"state_sha256":"1178bae9509850b177215c5b61b9873dd229924a60f6909f332403686674d0a2"}