{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:H4XDNLRQKGB2GXYEJK7OSVWS5D","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":"d56158bce52c22832067266adb2d329d835e290a5d62c1fcc4a56efa7b6b1734","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-19T08:40:23Z","title_canon_sha256":"bb19372bd421e4ec615608883d6230a98f83170c08a479bc4fbfbb822dbb336d"},"schema_version":"1.0","source":{"id":"1007.3085","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3085","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3085v2","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3085","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"H4XDNLRQKGB2","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"H4XDNLRQKGB2GXYE","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"H4XDNLRQ","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:79d4ebf4f0483b5bb6776a2d1aeec6e3ca9c18da202baed1c270df42a7dbbeac","target":"graph","created_at":"2026-05-18T04:42:33Z","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":"We show that a cosection of the obstruction sheaf of a perfect obstruction theory localizes the virtual cycle to the non-surjective locus of the cosection. We give algebraic constructions of localized Gysin maps and localized virtual cycles. Various applications of these constructions are discussed.","authors_text":"Jun Li, Young-Hoon Kiem","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-19T08:40:23Z","title":"Localizing Virtual Cycles by Cosections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3085","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":"sha256:0e31d7e5c07fcc9cf697d3bb80fff59a272a0c98070595b018d2dffbe0d3db10","target":"record","created_at":"2026-05-18T04:42:33Z","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":"d56158bce52c22832067266adb2d329d835e290a5d62c1fcc4a56efa7b6b1734","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-19T08:40:23Z","title_canon_sha256":"bb19372bd421e4ec615608883d6230a98f83170c08a479bc4fbfbb822dbb336d"},"schema_version":"1.0","source":{"id":"1007.3085","kind":"arxiv","version":2}},"canonical_sha256":"3f2e36ae305183a35f044abee956d2e8d1d4c468b24db8e8b7c47374d5030f66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f2e36ae305183a35f044abee956d2e8d1d4c468b24db8e8b7c47374d5030f66","first_computed_at":"2026-05-18T04:42:33.490790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:33.490790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7gEw2uJl9OmZLnooiis65GVnNGaQmljWIgF2QdUisMCHoFCVEZBxsE4N6v9W6pDRhJc3SbjUs5rv+Pyff+oTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:33.491215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.3085","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e31d7e5c07fcc9cf697d3bb80fff59a272a0c98070595b018d2dffbe0d3db10","sha256:79d4ebf4f0483b5bb6776a2d1aeec6e3ca9c18da202baed1c270df42a7dbbeac"],"state_sha256":"ecc91d7c6af4c62da52c66049705673a56723b64fdc73243c7a2020139cdd77c"}