{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LKDCEWWJFTKHFVXZII5VIEQSHT","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":"03096c90ea4465e04a27b93bd8bdf95ab36c2c202db6e4cd0564930f44da4635","cross_cats_sorted":["hep-th","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-03-03T14:25:08Z","title_canon_sha256":"2619373ef853a8b76b25577df353a95bfcfd7051de6926904d7eee9fc976f749"},"schema_version":"1.0","source":{"id":"1103.0693","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0693","created_at":"2026-05-18T02:03:00Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0693v2","created_at":"2026-05-18T02:03:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0693","created_at":"2026-05-18T02:03:00Z"},{"alias_kind":"pith_short_12","alias_value":"LKDCEWWJFTKH","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LKDCEWWJFTKHFVXZ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LKDCEWWJ","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:cee4da561d3fb5849e479ba691560f10070577b19284d440103eaf4d36e34980","target":"graph","created_at":"2026-05-18T02:03:00Z","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":"We present a proof of the mirror conjecture of Aganagic-Vafa [arXiv:hep-th/0012041] and Aganagic-Klemm-Vafa [arXiv:hep-th/0105045] on disk enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary framing. In particular, we recover previous results on the conjecture for (i) an inner brane at zero framing in the total space of the canonical line bundle of the projective plane (Graber-Zaslow [arXiv:hep-th/0109075]), (ii) an outer brane at arbitrary framing in the resolved conifold (Zhou [arXiv:1001.0447]","authors_text":"Bohan Fang, Chiu-Chu Melissa Liu","cross_cats":["hep-th","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-03-03T14:25:08Z","title":"Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0693","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":"sha256:5559d46933af6853c666022bf951a9ae38dffd0b0785f01897de238e73cbafce","target":"record","created_at":"2026-05-18T02:03:00Z","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":"03096c90ea4465e04a27b93bd8bdf95ab36c2c202db6e4cd0564930f44da4635","cross_cats_sorted":["hep-th","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-03-03T14:25:08Z","title_canon_sha256":"2619373ef853a8b76b25577df353a95bfcfd7051de6926904d7eee9fc976f749"},"schema_version":"1.0","source":{"id":"1103.0693","kind":"arxiv","version":2}},"canonical_sha256":"5a86225ac92cd472d6f9423b5412123cc16554c7ee7e3b6103a3009e0d33f257","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a86225ac92cd472d6f9423b5412123cc16554c7ee7e3b6103a3009e0d33f257","first_computed_at":"2026-05-18T02:03:00.433985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:00.433985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hslMCeq5GGkVG933mYtgEQc+FNgrY58uv+Stb0q8AJGhOA5F2aqGIE9gP5JeNdVHdqL4zl9/f700fqXKABioAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:00.434560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0693","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5559d46933af6853c666022bf951a9ae38dffd0b0785f01897de238e73cbafce","sha256:cee4da561d3fb5849e479ba691560f10070577b19284d440103eaf4d36e34980"],"state_sha256":"2cfd67cfb894ba54006a56b34d924be4e269b8781a8f49ce3c298e8360c76c61"}