{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YWG3SM5VMQ6KX7GEFUJBKLV4D3","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":"7ca5e6ac7233e513f606650a269184fe85017e599bda0c2e646d40300bd68307","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-09-08T20:39:07Z","title_canon_sha256":"b32faafb00a56621c12d0a797e76dc87ca578881342af137a5fdc680145d1271"},"schema_version":"1.0","source":{"id":"1009.1648","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1648","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1648v3","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1648","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"YWG3SM5VMQ6K","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YWG3SM5VMQ6KX7GE","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YWG3SM5V","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:4982225b204fd782251d2626345eab4ac2fed7c5efac5f5b7ad2feb6220eecb3","target":"graph","created_at":"2026-05-18T01:18:23Z","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":"In this paper we study Lagrangian Floer theory on toric manifolds from the point of view of mirror symmetry. We construct a natural isomorphism between the Frobenius manifold structures of the (big) quantum cohomology of the toric manifold and of Saito's theory of singularities of the potential function constructed in \\cite{fooo09} via the Floer cohomology deformed by ambient cycles. Our proof of the isomorphism involves the open-closed Gromov-Witten theory of one-loop.","authors_text":"Hiroshi Ohta, Kaoru Ono, Kenji Fukaya, Yong-Geun Oh","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-09-08T20:39:07Z","title":"Lagrangian Floer theory and mirror symmetry on compact toric manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1648","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:c4e983ed9918142f19bdc017e6b0cd352c7a24e8d0fc2c32577358f486f7901e","target":"record","created_at":"2026-05-18T01:18:23Z","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":"7ca5e6ac7233e513f606650a269184fe85017e599bda0c2e646d40300bd68307","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-09-08T20:39:07Z","title_canon_sha256":"b32faafb00a56621c12d0a797e76dc87ca578881342af137a5fdc680145d1271"},"schema_version":"1.0","source":{"id":"1009.1648","kind":"arxiv","version":3}},"canonical_sha256":"c58db933b5643cabfcc42d12152ebc1ee747b4f98356cbb8a69e5025f2ee71a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c58db933b5643cabfcc42d12152ebc1ee747b4f98356cbb8a69e5025f2ee71a1","first_computed_at":"2026-05-18T01:18:23.811578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:23.811578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UUMP85/u9cNAlTkODahH4G4w+e/pR3szZHqiKWBbaY3GQZnkxCdorKSbj6I15poorY5KKMuEtVKVC3oAZdCvBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:23.812158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1648","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4e983ed9918142f19bdc017e6b0cd352c7a24e8d0fc2c32577358f486f7901e","sha256:4982225b204fd782251d2626345eab4ac2fed7c5efac5f5b7ad2feb6220eecb3"],"state_sha256":"570144f494747bed90fc441795fc3425c59e40397c7ee667175e09e24d7cc3a3"}