{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ZCLTC7NAKC7XR4ZUHG6P5WBPTR","short_pith_number":"pith:ZCLTC7NA","canonical_record":{"source":{"id":"1001.2719","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-01-15T15:49:12Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"4f0f64da7e763c13fd54ef82cf7c31ad817ac9bf4dd7aa32b7a7b4c70085bd47","abstract_canon_sha256":"16a3599974084352f1d714df9eca53bafd517c59db32e559913d3c3ff58f67c9"},"schema_version":"1.0"},"canonical_sha256":"c897317da050bf78f33439bcfed82f9c51734e669ab459f0b7e3951c687cefdc","source":{"kind":"arxiv","id":"1001.2719","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2719","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2719v4","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2719","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZCLTC7NAKC7X","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZCLTC7NAKC7XR4ZU","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZCLTC7NA","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ZCLTC7NAKC7XR4ZUHG6P5WBPTR","target":"record","payload":{"canonical_record":{"source":{"id":"1001.2719","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-01-15T15:49:12Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"4f0f64da7e763c13fd54ef82cf7c31ad817ac9bf4dd7aa32b7a7b4c70085bd47","abstract_canon_sha256":"16a3599974084352f1d714df9eca53bafd517c59db32e559913d3c3ff58f67c9"},"schema_version":"1.0"},"canonical_sha256":"c897317da050bf78f33439bcfed82f9c51734e669ab459f0b7e3951c687cefdc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:49.915675Z","signature_b64":"KQ3U8BstTyhzj81oUJ1smGpdyCNGX7HRMXEUldtqr8foXnkmvDbpv4+JJhoifD1v3U057MD/Xh+28ibEzCy+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c897317da050bf78f33439bcfed82f9c51734e669ab459f0b7e3951c687cefdc","last_reissued_at":"2026-05-18T02:45:49.915160Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:49.915160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.2719","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bmbuqkJWmZOpd5V4sKke5XsL3qxvmAMxOVvKimi7T9T6wPD0yEVgh+g+cWOCWMgKMJLzt1WwOpy9jQedNxEuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:07:13.224810Z"},"content_sha256":"184048752408787e6c38d61e822647ec29b291a2d4834117251ed8835b9103c1","schema_version":"1.0","event_id":"sha256:184048752408787e6c38d61e822647ec29b291a2d4834117251ed8835b9103c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ZCLTC7NAKC7XR4ZUHG6P5WBPTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curves on K3 surfaces and modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"D. Maulik, R. Pandharipande, R. P. Thomas","submitted_at":"2010-01-15T15:49:12Z","abstract_excerpt":"We study the virtual geometry of the moduli spaces of curves and sheaves on K3 surfaces in primitive classes. Equivalences relating the reduced Gromov-Witten invariants of K3 surfaces to characteristic numbers of stable pairs moduli spaces are proven. As a consequence, we prove the Katz-Klemm-Vafa conjecture evaluating $\\lambda_g$ integrals (in all genera) in terms of explicit modular forms. Indeed, all K3 invariants in primitive classes are shown to be governed by modular forms.\n  The method of proof is by degeneration to elliptically fibered rational surfaces. New formulas relating reduced v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2719","kind":"arxiv","version":4},"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":"2026-05-18T02:45:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"18qQx5Tm84YppB6vHsU1ubWkuF7YGFsJvUncRcwKUglPM5+96NILhvX/hx2pP+5LjwOcNmRmtvfoH9lCauUdDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:07:13.225506Z"},"content_sha256":"9359abebb7bf5e342395f91cdd98f071f8ff14228e7f2cb97c9473d314e21c3e","schema_version":"1.0","event_id":"sha256:9359abebb7bf5e342395f91cdd98f071f8ff14228e7f2cb97c9473d314e21c3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZCLTC7NAKC7XR4ZUHG6P5WBPTR/bundle.json","state_url":"https://pith.science/pith/ZCLTC7NAKC7XR4ZUHG6P5WBPTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZCLTC7NAKC7XR4ZUHG6P5WBPTR/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":"2026-06-08T17:07:13Z","links":{"resolver":"https://pith.science/pith/ZCLTC7NAKC7XR4ZUHG6P5WBPTR","bundle":"https://pith.science/pith/ZCLTC7NAKC7XR4ZUHG6P5WBPTR/bundle.json","state":"https://pith.science/pith/ZCLTC7NAKC7XR4ZUHG6P5WBPTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZCLTC7NAKC7XR4ZUHG6P5WBPTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZCLTC7NAKC7XR4ZUHG6P5WBPTR","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":"16a3599974084352f1d714df9eca53bafd517c59db32e559913d3c3ff58f67c9","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-01-15T15:49:12Z","title_canon_sha256":"4f0f64da7e763c13fd54ef82cf7c31ad817ac9bf4dd7aa32b7a7b4c70085bd47"},"schema_version":"1.0","source":{"id":"1001.2719","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2719","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2719v4","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2719","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZCLTC7NAKC7X","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZCLTC7NAKC7XR4ZU","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZCLTC7NA","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:9359abebb7bf5e342395f91cdd98f071f8ff14228e7f2cb97c9473d314e21c3e","target":"graph","created_at":"2026-05-18T02:45:49Z","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 study the virtual geometry of the moduli spaces of curves and sheaves on K3 surfaces in primitive classes. Equivalences relating the reduced Gromov-Witten invariants of K3 surfaces to characteristic numbers of stable pairs moduli spaces are proven. As a consequence, we prove the Katz-Klemm-Vafa conjecture evaluating $\\lambda_g$ integrals (in all genera) in terms of explicit modular forms. Indeed, all K3 invariants in primitive classes are shown to be governed by modular forms.\n  The method of proof is by degeneration to elliptically fibered rational surfaces. New formulas relating reduced v","authors_text":"D. Maulik, R. Pandharipande, R. P. Thomas","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-01-15T15:49:12Z","title":"Curves on K3 surfaces and modular forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2719","kind":"arxiv","version":4},"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":"sha256:184048752408787e6c38d61e822647ec29b291a2d4834117251ed8835b9103c1","target":"record","created_at":"2026-05-18T02:45:49Z","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":"16a3599974084352f1d714df9eca53bafd517c59db32e559913d3c3ff58f67c9","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-01-15T15:49:12Z","title_canon_sha256":"4f0f64da7e763c13fd54ef82cf7c31ad817ac9bf4dd7aa32b7a7b4c70085bd47"},"schema_version":"1.0","source":{"id":"1001.2719","kind":"arxiv","version":4}},"canonical_sha256":"c897317da050bf78f33439bcfed82f9c51734e669ab459f0b7e3951c687cefdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c897317da050bf78f33439bcfed82f9c51734e669ab459f0b7e3951c687cefdc","first_computed_at":"2026-05-18T02:45:49.915160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:49.915160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KQ3U8BstTyhzj81oUJ1smGpdyCNGX7HRMXEUldtqr8foXnkmvDbpv4+JJhoifD1v3U057MD/Xh+28ibEzCy+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:49.915675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.2719","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:184048752408787e6c38d61e822647ec29b291a2d4834117251ed8835b9103c1","sha256:9359abebb7bf5e342395f91cdd98f071f8ff14228e7f2cb97c9473d314e21c3e"],"state_sha256":"5e8efff48d1142032613ce6aedfee2a7ed1083760e6c8c48bb4e87092f9862cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cvU2l+kkGzQQhXlcAckPK8mfxdgNCMjzntSI1AQGatRq7ZzTaNTcNoNj8LNbaZmQcwSsOUqCHqxG6DhPggnSBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:07:13.230499Z","bundle_sha256":"27888dd9f8a4be5193522811757a8b59673422c898a41f6a25f1a229097501ba"}}