{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TTLUUZYH3W2HPNBBSTCSAX7INT","short_pith_number":"pith:TTLUUZYH","canonical_record":{"source":{"id":"1003.4325","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-03-23T02:12:49Z","cross_cats_sorted":[],"title_canon_sha256":"520f39af788721252fbc3a1c90154220ef0a4687c434987df3a8d31597d934f5","abstract_canon_sha256":"c667c7d3e3082da8cadceab8f3f6bad65bd92660cf8612f296de1f13bfa88717"},"schema_version":"1.0"},"canonical_sha256":"9cd74a6707ddb477b42194c5205fe86cc07bcd8c84c9d069d9efdadf800fac64","source":{"kind":"arxiv","id":"1003.4325","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4325","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4325v3","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4325","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"TTLUUZYH3W2H","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TTLUUZYH3W2HPNBB","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TTLUUZYH","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TTLUUZYH3W2HPNBBSTCSAX7INT","target":"record","payload":{"canonical_record":{"source":{"id":"1003.4325","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-03-23T02:12:49Z","cross_cats_sorted":[],"title_canon_sha256":"520f39af788721252fbc3a1c90154220ef0a4687c434987df3a8d31597d934f5","abstract_canon_sha256":"c667c7d3e3082da8cadceab8f3f6bad65bd92660cf8612f296de1f13bfa88717"},"schema_version":"1.0"},"canonical_sha256":"9cd74a6707ddb477b42194c5205fe86cc07bcd8c84c9d069d9efdadf800fac64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:03.754794Z","signature_b64":"Ryzs/i38Ca+bsQNJcaxeeuVG90DV7HK4fIhlUBBDMc4PQA/mWx4qRycHrZtm0epG62o9ckwl/HNZoxYNq7RADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cd74a6707ddb477b42194c5205fe86cc07bcd8c84c9d069d9efdadf800fac64","last_reissued_at":"2026-05-18T03:40:03.754210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:03.754210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.4325","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ybe4G/dyTgbvAyI1ulA/oE/sSIsrU7HB/nL0Dqe27QIl+VMXKejoVV/i3wyCkPqrTGQdf1ogSqw6z686viA1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:54:58.844977Z"},"content_sha256":"7f341dbd965cb7b959e02f324774b5377efc851dc2c19c0dee836c2d89e6b35e","schema_version":"1.0","event_id":"sha256:7f341dbd965cb7b959e02f324774b5377efc851dc2c19c0dee836c2d89e6b35e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TTLUUZYH3W2HPNBBSTCSAX7INT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Open GW theory on symplectic manifolds and symplectic cutting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Mohammad Farajzadeh Tehrani","submitted_at":"2010-03-23T02:12:49Z","abstract_excerpt":"Let $(X,\\om)$ be a symplectic manifold and $L$ be a Lagrangian submanifold diffeomorphic to $S^n$, $\\R\\P^n$, or a Lens space of a certain type. Using the symplectic cut and symplectic sum constructions, we express the open Gromov-Witten invariants of $(X,L)$ in terms of open Gromov-Witten invariants of a pair $(X_-,L)$ determined by $L$ and the standard Gromov-Witten invariants of a symplectic manifold $X_+$ determined by $(X,L)$. We also describe other applications of this approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4325","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ZeUk69g57pWRjXbC5++fr9reaN/v84m+bEstcV1S30zxXa1/m6EoTO1/DTI6OICKhWQtWgl7fvATbVBStC9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:54:58.845339Z"},"content_sha256":"f9540bb49789fe57c8364b3a130f5845774b83d751d6942649a87fb750ced37e","schema_version":"1.0","event_id":"sha256:f9540bb49789fe57c8364b3a130f5845774b83d751d6942649a87fb750ced37e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TTLUUZYH3W2HPNBBSTCSAX7INT/bundle.json","state_url":"https://pith.science/pith/TTLUUZYH3W2HPNBBSTCSAX7INT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TTLUUZYH3W2HPNBBSTCSAX7INT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T13:54:58Z","links":{"resolver":"https://pith.science/pith/TTLUUZYH3W2HPNBBSTCSAX7INT","bundle":"https://pith.science/pith/TTLUUZYH3W2HPNBBSTCSAX7INT/bundle.json","state":"https://pith.science/pith/TTLUUZYH3W2HPNBBSTCSAX7INT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TTLUUZYH3W2HPNBBSTCSAX7INT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TTLUUZYH3W2HPNBBSTCSAX7INT","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":"c667c7d3e3082da8cadceab8f3f6bad65bd92660cf8612f296de1f13bfa88717","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-03-23T02:12:49Z","title_canon_sha256":"520f39af788721252fbc3a1c90154220ef0a4687c434987df3a8d31597d934f5"},"schema_version":"1.0","source":{"id":"1003.4325","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4325","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4325v3","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4325","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"TTLUUZYH3W2H","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TTLUUZYH3W2HPNBB","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TTLUUZYH","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:f9540bb49789fe57c8364b3a130f5845774b83d751d6942649a87fb750ced37e","target":"graph","created_at":"2026-05-18T03:40:03Z","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":"Let $(X,\\om)$ be a symplectic manifold and $L$ be a Lagrangian submanifold diffeomorphic to $S^n$, $\\R\\P^n$, or a Lens space of a certain type. Using the symplectic cut and symplectic sum constructions, we express the open Gromov-Witten invariants of $(X,L)$ in terms of open Gromov-Witten invariants of a pair $(X_-,L)$ determined by $L$ and the standard Gromov-Witten invariants of a symplectic manifold $X_+$ determined by $(X,L)$. We also describe other applications of this approach.","authors_text":"Mohammad Farajzadeh Tehrani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-03-23T02:12:49Z","title":"Open GW theory on symplectic manifolds and symplectic cutting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4325","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":"sha256:7f341dbd965cb7b959e02f324774b5377efc851dc2c19c0dee836c2d89e6b35e","target":"record","created_at":"2026-05-18T03:40:03Z","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":"c667c7d3e3082da8cadceab8f3f6bad65bd92660cf8612f296de1f13bfa88717","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-03-23T02:12:49Z","title_canon_sha256":"520f39af788721252fbc3a1c90154220ef0a4687c434987df3a8d31597d934f5"},"schema_version":"1.0","source":{"id":"1003.4325","kind":"arxiv","version":3}},"canonical_sha256":"9cd74a6707ddb477b42194c5205fe86cc07bcd8c84c9d069d9efdadf800fac64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cd74a6707ddb477b42194c5205fe86cc07bcd8c84c9d069d9efdadf800fac64","first_computed_at":"2026-05-18T03:40:03.754210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:03.754210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ryzs/i38Ca+bsQNJcaxeeuVG90DV7HK4fIhlUBBDMc4PQA/mWx4qRycHrZtm0epG62o9ckwl/HNZoxYNq7RADw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:03.754794Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.4325","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f341dbd965cb7b959e02f324774b5377efc851dc2c19c0dee836c2d89e6b35e","sha256:f9540bb49789fe57c8364b3a130f5845774b83d751d6942649a87fb750ced37e"],"state_sha256":"ba3a9fc931d460425d941bebebe0a9cc051ab00c88c37055298de223120b98e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4O7AyiyjvXwc1n9W+FBbKGZYRsknPde6gmx6kTNRkcjZ2ptsRXlvkEkdtu51L1kA/BkLaQVRnLGDzl8mUsC0Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:54:58.848040Z","bundle_sha256":"b96b86775a2176036e8346235de5ea9cd6ff34f14a8813bea25a58b622f43e92"}}