{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:7A3Z6JVIZKKCRULKDLDD2LFO5M","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":"17ccf56e37a0c0eecd867015116e64eff975ee7ba6ef09e1cb92cad18fcfe6a1","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2005-04-10T08:16:01Z","title_canon_sha256":"0b9840d32ac16265d492ba77b83843bf1d0154589645ddc8f4643ffcab2b733f"},"schema_version":"1.0","source":{"id":"math/0504188","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0504188","created_at":"2026-07-04T14:50:12Z"},{"alias_kind":"arxiv_version","alias_value":"math/0504188v3","created_at":"2026-07-04T14:50:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504188","created_at":"2026-07-04T14:50:12Z"},{"alias_kind":"pith_short_12","alias_value":"7A3Z6JVIZKKC","created_at":"2026-07-04T14:50:12Z"},{"alias_kind":"pith_short_16","alias_value":"7A3Z6JVIZKKCRULK","created_at":"2026-07-04T14:50:12Z"},{"alias_kind":"pith_short_8","alias_value":"7A3Z6JVI","created_at":"2026-07-04T14:50:12Z"}],"graph_snapshots":[{"event_id":"sha256:4860d866c600ca29bed3dbd68a96bd1c58acad8b0753845ab472770d7937593c","target":"graph","created_at":"2026-07-04T14:50:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0504188/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Gopakumar-Vafa invariants are numbers defined as certain linear combinations of the Gromov-Witten invariants. We prove that the GV invariants of a toric Calabi-Yau threefold are integers and that the invariants for high genera vanish. The proof of the integrality is based on elementary number theory and that of the vanishing uses the operator formalism and the exponential formula.","authors_text":"Yukiko Konishi","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2005-04-10T08:16:01Z","title":"Integrality of Gopakumar-Vafa Invariants of Toric Calabi-Yau Threefolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504188","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":"sha256:35d3637523731dafbb69f8e4b9dc24ce649b5ccc5ab03b4dd152dd3f50288411","target":"record","created_at":"2026-07-04T14:50:12Z","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":"17ccf56e37a0c0eecd867015116e64eff975ee7ba6ef09e1cb92cad18fcfe6a1","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2005-04-10T08:16:01Z","title_canon_sha256":"0b9840d32ac16265d492ba77b83843bf1d0154589645ddc8f4643ffcab2b733f"},"schema_version":"1.0","source":{"id":"math/0504188","kind":"arxiv","version":3}},"canonical_sha256":"f8379f26a8ca9428d16a1ac63d2caeeb108dbf9b7fe2f9f891a459405c9fdd5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8379f26a8ca9428d16a1ac63d2caeeb108dbf9b7fe2f9f891a459405c9fdd5b","first_computed_at":"2026-07-04T14:50:12.417898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:50:12.417898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lb8JOqWb29Dk3lV1IceY9L/cIy0IeB71XvxLVYvW7MeQQfTV5zW2MrWAZ9Aldp54o66MkGCmpRvwcyUBqjWoCw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:50:12.418240Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0504188","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35d3637523731dafbb69f8e4b9dc24ce649b5ccc5ab03b4dd152dd3f50288411","sha256:4860d866c600ca29bed3dbd68a96bd1c58acad8b0753845ab472770d7937593c"],"state_sha256":"a2a14f112adc0194a8864d0e469ffbe72397515c075f60cc4cce0e9e87e7c22a"}