{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:X72QXE4KCPEYAOH3NGWWKTPWKI","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":"5f5a8671ce103d17f705cd08d0036b42d1250b53ca99eb02e58b95e4ee3826d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-27T17:34:35Z","title_canon_sha256":"454c7d000df237dcc95242bd0f68df315d99523bcf69ae9d33ee960e93c706f1"},"schema_version":"1.0","source":{"id":"1211.6367","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6367","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6367v5","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6367","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"X72QXE4KCPEY","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"X72QXE4KCPEYAOH3","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"X72QXE4K","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:9baadf83dc9e8c333bf82c47979e2093dd34d845de0034286b8b1315a397db49","target":"graph","created_at":"2026-05-17T23:53:18Z","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 prove a global Torelli theorem for pairs (Y,D), where Y is a smooth projective rational surface and D is an effective anti-canonical divisor which is a cycle of rational curves. This Torelli theorem was conjectured by Friedman in 1984. In addition, we construct natural universal families for such pairs.","authors_text":"Mark Gross, Paul Hacking, Sean Keel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-27T17:34:35Z","title":"Moduli of surfaces with an anti-canonical cycle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6367","kind":"arxiv","version":5},"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":"sha256:8422d2dbf62e117848be3a6bc5ee838ec2b18c8adfdb0686f16f026bbda780e5","target":"record","created_at":"2026-05-17T23:53:18Z","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":"5f5a8671ce103d17f705cd08d0036b42d1250b53ca99eb02e58b95e4ee3826d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-27T17:34:35Z","title_canon_sha256":"454c7d000df237dcc95242bd0f68df315d99523bcf69ae9d33ee960e93c706f1"},"schema_version":"1.0","source":{"id":"1211.6367","kind":"arxiv","version":5}},"canonical_sha256":"bff50b938a13c98038fb69ad654df65220a8a16fb57c524a22d67da511767ec4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bff50b938a13c98038fb69ad654df65220a8a16fb57c524a22d67da511767ec4","first_computed_at":"2026-05-17T23:53:18.239132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:18.239132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fTOO2u6FXDBlrEtoUwQ1Rd0/QLdSGKdoBiGcmYcjKY4rqQsvtLNLb3WwcunsnMvMJlyp+CZjx0fL1xuR3sQeDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:18.239796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.6367","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8422d2dbf62e117848be3a6bc5ee838ec2b18c8adfdb0686f16f026bbda780e5","sha256:9baadf83dc9e8c333bf82c47979e2093dd34d845de0034286b8b1315a397db49"],"state_sha256":"66ee4c03b44de755f59e21413973c8145facc9d8e091c6438762d61b0b524889"}