{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CV5JJ2IZIH3OJ2HGZ3WZ27WWWF","short_pith_number":"pith:CV5JJ2IZ","canonical_record":{"source":{"id":"1103.4229","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-22T08:22:53Z","cross_cats_sorted":[],"title_canon_sha256":"01485ea76ddd8d62cf9366fea7dd73fb8838cb7885028366cf6f719275a80dc7","abstract_canon_sha256":"3a1ce65682db9c0f1b2caa8000021ccf80de37fb08315428c564913be6364704"},"schema_version":"1.0"},"canonical_sha256":"157a94e91941f6e4e8e6ceed9d7ed6b160f64852d8ccf90349b608fce50830ed","source":{"kind":"arxiv","id":"1103.4229","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4229","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4229v2","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4229","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"CV5JJ2IZIH3O","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CV5JJ2IZIH3OJ2HG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CV5JJ2IZ","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CV5JJ2IZIH3OJ2HGZ3WZ27WWWF","target":"record","payload":{"canonical_record":{"source":{"id":"1103.4229","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-22T08:22:53Z","cross_cats_sorted":[],"title_canon_sha256":"01485ea76ddd8d62cf9366fea7dd73fb8838cb7885028366cf6f719275a80dc7","abstract_canon_sha256":"3a1ce65682db9c0f1b2caa8000021ccf80de37fb08315428c564913be6364704"},"schema_version":"1.0"},"canonical_sha256":"157a94e91941f6e4e8e6ceed9d7ed6b160f64852d8ccf90349b608fce50830ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:25.604852Z","signature_b64":"co56WBBVeZyaoUB/ycu/gy5/kwFS53Wrm7U3IxGkgry7z84ts8qH0qBXZn8x8A+P9hCTI3sBlLOum9CJl7COBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"157a94e91941f6e4e8e6ceed9d7ed6b160f64852d8ccf90349b608fce50830ed","last_reissued_at":"2026-05-18T02:29:25.604408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:25.604408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.4229","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2kxRTzFOJ+zxH6vYEs4XTd74epxVK8BiUc02cgEG1umprnJaK3bwh7lSlY85e6FO7Q0K7nQLdzzHHRjdE/QVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:41:28.637150Z"},"content_sha256":"1be35277ce15b4d8864bc64ead5e02b1a3a82e48aa480591e18387e9a3728daa","schema_version":"1.0","event_id":"sha256:1be35277ce15b4d8864bc64ead5e02b1a3a82e48aa480591e18387e9a3728daa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CV5JJ2IZIH3OJ2HGZ3WZ27WWWF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability conditions and curve counting invariants on Calabi-Yau 3-folds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yukinobu Toda","submitted_at":"2011-03-22T08:22:53Z","abstract_excerpt":"The purpose of this paper is twofold: first we give a survey on the recent developments of curve counting invariants on Calabi-Yau 3-folds, e.g. Gromov-Witten theory, Donaldson-Thomas theory and Pandharipande-Thomas theory. Next we focus on the proof of the rationality conjecture of the generating series of PT invariants, and discuss its conjectural Gopakumar-Vafa form."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4229","kind":"arxiv","version":2},"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":"2026-05-18T02:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fSnQ0a2/tRhzfgasdhjd15i4B03ncJa+pM3A+IW6LIjCqRt7foEk1IJXQf8KoJLV5Uc6Vs6HrPjIrTgp/q/cDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:41:28.637815Z"},"content_sha256":"d4dcda4d7d6e7074ef3047225242f96bdbf10f48e9cf5ce79cf0272c43f7a814","schema_version":"1.0","event_id":"sha256:d4dcda4d7d6e7074ef3047225242f96bdbf10f48e9cf5ce79cf0272c43f7a814"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CV5JJ2IZIH3OJ2HGZ3WZ27WWWF/bundle.json","state_url":"https://pith.science/pith/CV5JJ2IZIH3OJ2HGZ3WZ27WWWF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CV5JJ2IZIH3OJ2HGZ3WZ27WWWF/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":"2026-06-06T15:41:28Z","links":{"resolver":"https://pith.science/pith/CV5JJ2IZIH3OJ2HGZ3WZ27WWWF","bundle":"https://pith.science/pith/CV5JJ2IZIH3OJ2HGZ3WZ27WWWF/bundle.json","state":"https://pith.science/pith/CV5JJ2IZIH3OJ2HGZ3WZ27WWWF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CV5JJ2IZIH3OJ2HGZ3WZ27WWWF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CV5JJ2IZIH3OJ2HGZ3WZ27WWWF","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":"3a1ce65682db9c0f1b2caa8000021ccf80de37fb08315428c564913be6364704","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-22T08:22:53Z","title_canon_sha256":"01485ea76ddd8d62cf9366fea7dd73fb8838cb7885028366cf6f719275a80dc7"},"schema_version":"1.0","source":{"id":"1103.4229","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4229","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4229v2","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4229","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"CV5JJ2IZIH3O","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CV5JJ2IZIH3OJ2HG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CV5JJ2IZ","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:d4dcda4d7d6e7074ef3047225242f96bdbf10f48e9cf5ce79cf0272c43f7a814","target":"graph","created_at":"2026-05-18T02:29:25Z","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":"The purpose of this paper is twofold: first we give a survey on the recent developments of curve counting invariants on Calabi-Yau 3-folds, e.g. Gromov-Witten theory, Donaldson-Thomas theory and Pandharipande-Thomas theory. Next we focus on the proof of the rationality conjecture of the generating series of PT invariants, and discuss its conjectural Gopakumar-Vafa form.","authors_text":"Yukinobu Toda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-22T08:22:53Z","title":"Stability conditions and curve counting invariants on Calabi-Yau 3-folds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4229","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":"sha256:1be35277ce15b4d8864bc64ead5e02b1a3a82e48aa480591e18387e9a3728daa","target":"record","created_at":"2026-05-18T02:29:25Z","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":"3a1ce65682db9c0f1b2caa8000021ccf80de37fb08315428c564913be6364704","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-22T08:22:53Z","title_canon_sha256":"01485ea76ddd8d62cf9366fea7dd73fb8838cb7885028366cf6f719275a80dc7"},"schema_version":"1.0","source":{"id":"1103.4229","kind":"arxiv","version":2}},"canonical_sha256":"157a94e91941f6e4e8e6ceed9d7ed6b160f64852d8ccf90349b608fce50830ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"157a94e91941f6e4e8e6ceed9d7ed6b160f64852d8ccf90349b608fce50830ed","first_computed_at":"2026-05-18T02:29:25.604408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:25.604408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"co56WBBVeZyaoUB/ycu/gy5/kwFS53Wrm7U3IxGkgry7z84ts8qH0qBXZn8x8A+P9hCTI3sBlLOum9CJl7COBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:25.604852Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4229","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1be35277ce15b4d8864bc64ead5e02b1a3a82e48aa480591e18387e9a3728daa","sha256:d4dcda4d7d6e7074ef3047225242f96bdbf10f48e9cf5ce79cf0272c43f7a814"],"state_sha256":"eb956af43314e7331d7cf93c07d2122d1befed82f9434e3b6814c2e025e3faa9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wBou5qlMDyfUslNiIvpimaa/o+hoBcZ8vC15nkMp+/WEa5zogZUF1xfnjqc2BM9zgchvymWX9PN+9SBx/9mMDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:41:28.641525Z","bundle_sha256":"8c95d86871a8ee7e2b16b4c138283cbfc914bcd983c9429c75f6bf0a485ac42d"}}