{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:IJLPTQ66QLMIJLFD3ZSSEK72R3","short_pith_number":"pith:IJLPTQ66","canonical_record":{"source":{"id":"0707.2986","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-07-20T01:12:14Z","cross_cats_sorted":[],"title_canon_sha256":"c45c667d87b33ccf783954a4e48a19ce16e30cf84b8e23a3c19a55de49ff9ceb","abstract_canon_sha256":"9b7caa682a87baf25e3c4d071a9bb2ff1e8ed408d2e9d30d17523970df19ecce"},"schema_version":"1.0"},"canonical_sha256":"4256f9c3de82d884aca3de65222bfa8ec59b3f1292de3d5f032138aca36e2a3a","source":{"kind":"arxiv","id":"0707.2986","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.2986","created_at":"2026-07-04T15:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"0707.2986v1","created_at":"2026-07-04T15:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.2986","created_at":"2026-07-04T15:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"IJLPTQ66QLMI","created_at":"2026-07-04T15:03:10Z"},{"alias_kind":"pith_short_16","alias_value":"IJLPTQ66QLMIJLFD","created_at":"2026-07-04T15:03:10Z"},{"alias_kind":"pith_short_8","alias_value":"IJLPTQ66","created_at":"2026-07-04T15:03:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:IJLPTQ66QLMIJLFD3ZSSEK72R3","target":"record","payload":{"canonical_record":{"source":{"id":"0707.2986","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-07-20T01:12:14Z","cross_cats_sorted":[],"title_canon_sha256":"c45c667d87b33ccf783954a4e48a19ce16e30cf84b8e23a3c19a55de49ff9ceb","abstract_canon_sha256":"9b7caa682a87baf25e3c4d071a9bb2ff1e8ed408d2e9d30d17523970df19ecce"},"schema_version":"1.0"},"canonical_sha256":"4256f9c3de82d884aca3de65222bfa8ec59b3f1292de3d5f032138aca36e2a3a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:03:10.535930Z","signature_b64":"HC/Zhv1YR/CHOeFhU9VcfHjdKQVUWjVMwFEnqlfPxNxt+Gq8dUeI/lWUezu7rl4oDs+AnFSgXaGobkNH+fX0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4256f9c3de82d884aca3de65222bfa8ec59b3f1292de3d5f032138aca36e2a3a","last_reissued_at":"2026-07-04T15:03:10.535492Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:03:10.535492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0707.2986","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:03:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82iePw3hx+9J6TlrUIb2YPjXVgzALu6Puszt8tk9pb21oo6gcf71pTPQI9clBcp1yL1qogolRThm71gWFELKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:51:23.914846Z"},"content_sha256":"d7e733f509879fb9958c6b393dccdd067c6a2839841a013a1b8bb8e5ea852ddd","schema_version":"1.0","event_id":"sha256:d7e733f509879fb9958c6b393dccdd067c6a2839841a013a1b8bb8e5ea852ddd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:IJLPTQ66QLMIJLFD3ZSSEK72R3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gromov-Witten invariants of varieties with holomorphic 2-forms","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jun Li, Young-Hoon Kiem","submitted_at":"2007-07-20T01:12:14Z","abstract_excerpt":"We show that a holomorphic two-form $\\theta$ on a smooth algebraic variety X localizes the virtual fundamental class of the moduli of stable maps $\\mgn(X,\\beta)$ to the locus where $\\theta$ degenerates; it then enables us to define the localized GW-invariant, an algebro-geometric analogue of the local invariant of Lee and Parker in symplectic geometry, which coincides with the ordinary GW-invariant when X is proper. It is deformation invariant. Using this, we prove formulas for low degree GW-invariants of minimal general type surfaces with p_g>0 conjectured by Maulik and Pandharipande."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.2986","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0707.2986/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:03:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dSdRYgs8huyk4A0UBg09LM6WBHwyrdmluAeDl03KJ55GtFAhqkzODdtXkFexqt5P8Wb3wQkz9+5NNhXyAqc+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:51:23.915767Z"},"content_sha256":"23617ff7e95f8bb48a5227148f7d7b5188d5bf1ac10ceec32c051ba5294d2236","schema_version":"1.0","event_id":"sha256:23617ff7e95f8bb48a5227148f7d7b5188d5bf1ac10ceec32c051ba5294d2236"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IJLPTQ66QLMIJLFD3ZSSEK72R3/bundle.json","state_url":"https://pith.science/pith/IJLPTQ66QLMIJLFD3ZSSEK72R3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IJLPTQ66QLMIJLFD3ZSSEK72R3/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":"2026-08-04T16:51:23Z","links":{"resolver":"https://pith.science/pith/IJLPTQ66QLMIJLFD3ZSSEK72R3","bundle":"https://pith.science/pith/IJLPTQ66QLMIJLFD3ZSSEK72R3/bundle.json","state":"https://pith.science/pith/IJLPTQ66QLMIJLFD3ZSSEK72R3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IJLPTQ66QLMIJLFD3ZSSEK72R3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:IJLPTQ66QLMIJLFD3ZSSEK72R3","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":"9b7caa682a87baf25e3c4d071a9bb2ff1e8ed408d2e9d30d17523970df19ecce","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2007-07-20T01:12:14Z","title_canon_sha256":"c45c667d87b33ccf783954a4e48a19ce16e30cf84b8e23a3c19a55de49ff9ceb"},"schema_version":"1.0","source":{"id":"0707.2986","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.2986","created_at":"2026-07-04T15:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"0707.2986v1","created_at":"2026-07-04T15:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.2986","created_at":"2026-07-04T15:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"IJLPTQ66QLMI","created_at":"2026-07-04T15:03:10Z"},{"alias_kind":"pith_short_16","alias_value":"IJLPTQ66QLMIJLFD","created_at":"2026-07-04T15:03:10Z"},{"alias_kind":"pith_short_8","alias_value":"IJLPTQ66","created_at":"2026-07-04T15:03:10Z"}],"graph_snapshots":[{"event_id":"sha256:23617ff7e95f8bb48a5227148f7d7b5188d5bf1ac10ceec32c051ba5294d2236","target":"graph","created_at":"2026-07-04T15:03:10Z","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/0707.2986/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that a holomorphic two-form $\\theta$ on a smooth algebraic variety X localizes the virtual fundamental class of the moduli of stable maps $\\mgn(X,\\beta)$ to the locus where $\\theta$ degenerates; it then enables us to define the localized GW-invariant, an algebro-geometric analogue of the local invariant of Lee and Parker in symplectic geometry, which coincides with the ordinary GW-invariant when X is proper. It is deformation invariant. Using this, we prove formulas for low degree GW-invariants of minimal general type surfaces with p_g>0 conjectured by Maulik and Pandharipande.","authors_text":"Jun Li, Young-Hoon Kiem","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2007-07-20T01:12:14Z","title":"Gromov-Witten invariants of varieties with holomorphic 2-forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.2986","kind":"arxiv","version":1},"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:d7e733f509879fb9958c6b393dccdd067c6a2839841a013a1b8bb8e5ea852ddd","target":"record","created_at":"2026-07-04T15:03:10Z","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":"9b7caa682a87baf25e3c4d071a9bb2ff1e8ed408d2e9d30d17523970df19ecce","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2007-07-20T01:12:14Z","title_canon_sha256":"c45c667d87b33ccf783954a4e48a19ce16e30cf84b8e23a3c19a55de49ff9ceb"},"schema_version":"1.0","source":{"id":"0707.2986","kind":"arxiv","version":1}},"canonical_sha256":"4256f9c3de82d884aca3de65222bfa8ec59b3f1292de3d5f032138aca36e2a3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4256f9c3de82d884aca3de65222bfa8ec59b3f1292de3d5f032138aca36e2a3a","first_computed_at":"2026-07-04T15:03:10.535492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:03:10.535492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HC/Zhv1YR/CHOeFhU9VcfHjdKQVUWjVMwFEnqlfPxNxt+Gq8dUeI/lWUezu7rl4oDs+AnFSgXaGobkNH+fX0Cw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:03:10.535930Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.2986","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7e733f509879fb9958c6b393dccdd067c6a2839841a013a1b8bb8e5ea852ddd","sha256:23617ff7e95f8bb48a5227148f7d7b5188d5bf1ac10ceec32c051ba5294d2236"],"state_sha256":"5f20e964e3b64b6e1d3677a23031bcd163811607e8561e8a2da839dc5d34c851"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vfj+Sy6Lv0L0ymXuJrBpL/7+ujzRMJihqhw+3jDJTPLd5e81RAEQIDNM2Tu+XSEclX3cLGuMHLqO9Rqsd8h6DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T16:51:23.920894Z","bundle_sha256":"67a3fb4f896022f46b022a1cce45e34f4e34ff86b71b167a0082e507d7bff31a"}}