{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WOYLPPZRDOBZR4PBCYT3D5MQAL","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":"83c90c37b59176be964a52ca5ce101d21eed867f8d1c7b60b210221b2f5a1aad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2017-10-29T09:02:38Z","title_canon_sha256":"8ce6a7a79224c11cc687a73e7074861ccfe7f124f6386a48d63e0e838fd51010"},"schema_version":"1.0","source":{"id":"1710.10581","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10581","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10581v2","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10581","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"WOYLPPZRDOBZ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WOYLPPZRDOBZR4PB","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WOYLPPZR","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:c31ed14e423837748a040f97a8053a2dc77fe4945682a98fa14a336633b772d4","target":"graph","created_at":"2026-05-18T00:14:16Z","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 use the approach of Ruan and Li-Ruan to construct virtual neighborhoods and show that the Gromov-Witten invariants can be defined as an integral over top strata of virtual neighborhood. We prove that the invariants defined in this way satisfy all the Gromov-Witten axioms of Kontsevich and Manin.","authors_text":"An-Min Li, Li Sheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2017-10-29T09:02:38Z","title":"Virtual Neighborhood Technique for Holomorphic Curve Moduli Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10581","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":"sha256:8b89b92eeb4f438b2f5713b880ce515e7bd861a00771a7faf9ded47af3e3620d","target":"record","created_at":"2026-05-18T00:14:16Z","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":"83c90c37b59176be964a52ca5ce101d21eed867f8d1c7b60b210221b2f5a1aad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2017-10-29T09:02:38Z","title_canon_sha256":"8ce6a7a79224c11cc687a73e7074861ccfe7f124f6386a48d63e0e838fd51010"},"schema_version":"1.0","source":{"id":"1710.10581","kind":"arxiv","version":2}},"canonical_sha256":"b3b0b7bf311b8398f1e11627b1f59002e30472f39f82e92897e39eb0992b1c72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3b0b7bf311b8398f1e11627b1f59002e30472f39f82e92897e39eb0992b1c72","first_computed_at":"2026-05-18T00:14:16.209412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:16.209412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DK3kZUK5DNwUuq1GNS26aXwBuklEk7ahtGV7LjtYNPYmAm5/WH/MxXg3d+4pkh2bg+rT0mp8EdLQCt6xpJieDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:16.210053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10581","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b89b92eeb4f438b2f5713b880ce515e7bd861a00771a7faf9ded47af3e3620d","sha256:c31ed14e423837748a040f97a8053a2dc77fe4945682a98fa14a336633b772d4"],"state_sha256":"9a26e6d4515b17e3a838499b8d7fe5f8a53dfbc74dd9456fae1d6706e0d77b8c"}