{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IO6HEKF3D3X4HSJUJLZT7452HJ","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":"32f6517b11468419a57a504d7f45288a0bad3045b9eb0055bac3a6dd60f1ce83","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-02-15T19:20:50Z","title_canon_sha256":"dd6838a0acd3751347a8fa896f533d13d090dc32158a28a80e0486b5aa31b2b5"},"schema_version":"1.0","source":{"id":"1102.3160","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3160","created_at":"2026-05-18T01:11:13Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3160v2","created_at":"2026-05-18T01:11:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3160","created_at":"2026-05-18T01:11:13Z"},{"alias_kind":"pith_short_12","alias_value":"IO6HEKF3D3X4","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"IO6HEKF3D3X4HSJU","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"IO6HEKF3","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:84c7b866aba0104e3f2020940760e3cf8d23105ecca5a4979004e2d18243bced","target":"graph","created_at":"2026-05-18T01:11:13Z","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":"This paper is a companion to the authors' forthcoming work extending Heegaard Floer theory from closed 3-manifolds to compact 3-manifolds with two boundary components via quilted Floer cohomology. We describe the first interesting case of this theory: the invariants of 3-manifolds bounding S^2 union T^2, regarded as modules over the Fukaya category of the punctured 2-torus. We extract a short proof of exactness of the Dehn surgery triangle in Heegaard Floer homology. We show that A-infinity structures on the graded algebra A formed by the cohomology of two basic objects in the Fukaya category ","authors_text":"Timothy Perutz, Yanki Lekili","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-02-15T19:20:50Z","title":"Fukaya categories of the torus and Dehn surgery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3160","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":"sha256:76ec902001b1b0bbca1c5526d72c4c9e0f07b8d7ba2eb94b9b2fba7f922da776","target":"record","created_at":"2026-05-18T01:11:13Z","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":"32f6517b11468419a57a504d7f45288a0bad3045b9eb0055bac3a6dd60f1ce83","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-02-15T19:20:50Z","title_canon_sha256":"dd6838a0acd3751347a8fa896f533d13d090dc32158a28a80e0486b5aa31b2b5"},"schema_version":"1.0","source":{"id":"1102.3160","kind":"arxiv","version":2}},"canonical_sha256":"43bc7228bb1eefc3c9344af33ff3ba3a7da7b9f1783c96492c2e4e2fda8f581e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43bc7228bb1eefc3c9344af33ff3ba3a7da7b9f1783c96492c2e4e2fda8f581e","first_computed_at":"2026-05-18T01:11:13.923834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:13.923834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GT8QYnwVQtJ7M8P1uFpSLLW1q5WKOGnN3nvy50QO2MAhG2ZRD23PhBGe/ReXrAh5i3Il1WEH1Paz1MSIVSJEBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:13.924241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3160","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76ec902001b1b0bbca1c5526d72c4c9e0f07b8d7ba2eb94b9b2fba7f922da776","sha256:84c7b866aba0104e3f2020940760e3cf8d23105ecca5a4979004e2d18243bced"],"state_sha256":"09980625e5a973f4d4211158907a2fd3a9dd979754446ebb67cf87b7b22bd85c"}