{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:SEUR2WDZRZ55EHVP4AUV6YSIWP","short_pith_number":"pith:SEUR2WDZ","canonical_record":{"source":{"id":"alg-geom/9708001","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1997-08-01T21:03:40Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"efa252f67408b963d42ef2ed8ce3c9002fcede37bc177a5d660a1aac7f2349e9","abstract_canon_sha256":"41c3c3020e4b85d9ea5ab288381aa0a53e8099914d41107161bfee092145ad95"},"schema_version":"1.0"},"canonical_sha256":"91291d58798e7bd21eafe0295f6248b3d82d07abc8575d5eba1a986f7e497229","source":{"kind":"arxiv","id":"alg-geom/9708001","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9708001","created_at":"2026-07-04T15:07:37Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9708001v2","created_at":"2026-07-04T15:07:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9708001","created_at":"2026-07-04T15:07:37Z"},{"alias_kind":"pith_short_12","alias_value":"SEUR2WDZRZ55","created_at":"2026-07-04T15:07:37Z"},{"alias_kind":"pith_short_16","alias_value":"SEUR2WDZRZ55EHVP","created_at":"2026-07-04T15:07:37Z"},{"alias_kind":"pith_short_8","alias_value":"SEUR2WDZ","created_at":"2026-07-04T15:07:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:SEUR2WDZRZ55EHVP4AUV6YSIWP","target":"record","payload":{"canonical_record":{"source":{"id":"alg-geom/9708001","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1997-08-01T21:03:40Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"efa252f67408b963d42ef2ed8ce3c9002fcede37bc177a5d660a1aac7f2349e9","abstract_canon_sha256":"41c3c3020e4b85d9ea5ab288381aa0a53e8099914d41107161bfee092145ad95"},"schema_version":"1.0"},"canonical_sha256":"91291d58798e7bd21eafe0295f6248b3d82d07abc8575d5eba1a986f7e497229","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:07:37.294097Z","signature_b64":"cVMFPv5xJFcEegyQcplxE22OLoU5HCzHnq8vPWSbbl/T1hSxN3wbu+K5G8RErd7QyBNAXY8Y7uDNC4np+d0vBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91291d58798e7bd21eafe0295f6248b3d82d07abc8575d5eba1a986f7e497229","last_reissued_at":"2026-07-04T15:07:37.293750Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:07:37.293750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"alg-geom/9708001","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":"2026-07-04T15:07:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"01r7C+SXPe2cDEolhrkcKT59eqEfzgq5heblj7Qwk/lQdljE0Mn/kB5Si5Lf2rkVKY2fJvh2axro/F6Ph0DqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:35:21.622204Z"},"content_sha256":"c01867337323ff1337e7f8b0c9c16feba5758f1a4cbb4661afc57f55bf3d8324","schema_version":"1.0","event_id":"sha256:c01867337323ff1337e7f8b0c9c16feba5758f1a4cbb4661afc57f55bf3d8324"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:SEUR2WDZRZ55EHVP4AUV6YSIWP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localization of virtual classes","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"R. Pandharipande, T. Graber","submitted_at":"1997-08-01T21:03:40Z","abstract_excerpt":"We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of projective space are expressed as graph sums of tautological integrals over moduli spaces of stable pointed curves (generalizing Kontsevich's genus 0 formulas). Also, excess integrals over spaces of higher genus multiple covers are computed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9708001","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/alg-geom/9708001/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":"2026-07-04T15:07:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AaRshIHR20+ZjYcL1sLO8NGwJxgvktBUW4xKedG0/AITRi9OE0+7QJay7jgd78YAQFJ5PMArl7Pjhj9nPtXhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:35:21.623157Z"},"content_sha256":"7ace07c9293e6dd97f53913f4e7d63a49126bb35c72b8269e15a5e7b4b1b9393","schema_version":"1.0","event_id":"sha256:7ace07c9293e6dd97f53913f4e7d63a49126bb35c72b8269e15a5e7b4b1b9393"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SEUR2WDZRZ55EHVP4AUV6YSIWP/bundle.json","state_url":"https://pith.science/pith/SEUR2WDZRZ55EHVP4AUV6YSIWP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SEUR2WDZRZ55EHVP4AUV6YSIWP/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":"2026-08-03T16:35:21Z","links":{"resolver":"https://pith.science/pith/SEUR2WDZRZ55EHVP4AUV6YSIWP","bundle":"https://pith.science/pith/SEUR2WDZRZ55EHVP4AUV6YSIWP/bundle.json","state":"https://pith.science/pith/SEUR2WDZRZ55EHVP4AUV6YSIWP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SEUR2WDZRZ55EHVP4AUV6YSIWP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:SEUR2WDZRZ55EHVP4AUV6YSIWP","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":"41c3c3020e4b85d9ea5ab288381aa0a53e8099914d41107161bfee092145ad95","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1997-08-01T21:03:40Z","title_canon_sha256":"efa252f67408b963d42ef2ed8ce3c9002fcede37bc177a5d660a1aac7f2349e9"},"schema_version":"1.0","source":{"id":"alg-geom/9708001","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9708001","created_at":"2026-07-04T15:07:37Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9708001v2","created_at":"2026-07-04T15:07:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9708001","created_at":"2026-07-04T15:07:37Z"},{"alias_kind":"pith_short_12","alias_value":"SEUR2WDZRZ55","created_at":"2026-07-04T15:07:37Z"},{"alias_kind":"pith_short_16","alias_value":"SEUR2WDZRZ55EHVP","created_at":"2026-07-04T15:07:37Z"},{"alias_kind":"pith_short_8","alias_value":"SEUR2WDZ","created_at":"2026-07-04T15:07:37Z"}],"graph_snapshots":[{"event_id":"sha256:7ace07c9293e6dd97f53913f4e7d63a49126bb35c72b8269e15a5e7b4b1b9393","target":"graph","created_at":"2026-07-04T15:07:37Z","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/alg-geom/9708001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of projective space are expressed as graph sums of tautological integrals over moduli spaces of stable pointed curves (generalizing Kontsevich's genus 0 formulas). Also, excess integrals over spaces of higher genus multiple covers are computed.","authors_text":"R. Pandharipande, T. Graber","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1997-08-01T21:03:40Z","title":"Localization of virtual classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9708001","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:c01867337323ff1337e7f8b0c9c16feba5758f1a4cbb4661afc57f55bf3d8324","target":"record","created_at":"2026-07-04T15:07:37Z","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":"41c3c3020e4b85d9ea5ab288381aa0a53e8099914d41107161bfee092145ad95","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1997-08-01T21:03:40Z","title_canon_sha256":"efa252f67408b963d42ef2ed8ce3c9002fcede37bc177a5d660a1aac7f2349e9"},"schema_version":"1.0","source":{"id":"alg-geom/9708001","kind":"arxiv","version":2}},"canonical_sha256":"91291d58798e7bd21eafe0295f6248b3d82d07abc8575d5eba1a986f7e497229","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91291d58798e7bd21eafe0295f6248b3d82d07abc8575d5eba1a986f7e497229","first_computed_at":"2026-07-04T15:07:37.293750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:07:37.293750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cVMFPv5xJFcEegyQcplxE22OLoU5HCzHnq8vPWSbbl/T1hSxN3wbu+K5G8RErd7QyBNAXY8Y7uDNC4np+d0vBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:07:37.294097Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9708001","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c01867337323ff1337e7f8b0c9c16feba5758f1a4cbb4661afc57f55bf3d8324","sha256:7ace07c9293e6dd97f53913f4e7d63a49126bb35c72b8269e15a5e7b4b1b9393"],"state_sha256":"2d8d1dd39429e0f8713e2a29b202bc3b7913867d11e85c86ee5450da9ecf53e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"121cLXjTecssPLkCHyvjmhiNdtHJ8Em1L0mnlA3SwsuPU2uFPTx1P8tT/ziIZjzcSjna6ND+b/oWj6ErQFjYCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:35:21.630252Z","bundle_sha256":"6d15c40b6aca042da1c3d5999b4167068a864f9bb7ffc26d18d842795796a62a"}}