{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:HGEAJC7T2PEZCUIOYZ7YK37YPT","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":"eed7b2993e71eb09cad09d5e3f56e7cde26a4c6c5df08cd74c5d2941834f6f70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-08-11T18:03:02Z","title_canon_sha256":"3187d2d073460f091eb60e2794dfa193346d49ca0d890a672834968e3177b488"},"schema_version":"1.0","source":{"id":"0808.1550","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.1550","created_at":"2026-05-17T23:53:39Z"},{"alias_kind":"arxiv_version","alias_value":"0808.1550v2","created_at":"2026-05-17T23:53:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.1550","created_at":"2026-05-17T23:53:39Z"},{"alias_kind":"pith_short_12","alias_value":"HGEAJC7T2PEZ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"HGEAJC7T2PEZCUIO","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"HGEAJC7T","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:c4f869cbc6d426c5a7de55e4eb15a29950f745fd1b8eab8cd608e966aaeae943","target":"graph","created_at":"2026-05-17T23:53:39Z","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 give a complete classification of del Pezzo surfaces with quotient singularities and Picard rank 1 which admit a Q-Gorenstein smoothing.\n  There are 14 infinite families of toric examples. The surfaces in each family correspond to solutions of a Markov-type equation. The remaining surfaces are obtained as deformations of the toric surfaces or belong to a finite list of sporadic surfaces.","authors_text":"Paul Hacking, Yuri Prokhorov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-08-11T18:03:02Z","title":"Smoothable del Pezzo surfaces with quotient singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1550","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":"sha256:70ce7424d6fd0dbdcf02838c8e40ae1b2d9d4b76a8d764c0f8211939d61057cd","target":"record","created_at":"2026-05-17T23:53:39Z","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":"eed7b2993e71eb09cad09d5e3f56e7cde26a4c6c5df08cd74c5d2941834f6f70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-08-11T18:03:02Z","title_canon_sha256":"3187d2d073460f091eb60e2794dfa193346d49ca0d890a672834968e3177b488"},"schema_version":"1.0","source":{"id":"0808.1550","kind":"arxiv","version":2}},"canonical_sha256":"3988048bf3d3c991510ec67f856ff87cd184db10e756ddfee2d8f99db27d6c72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3988048bf3d3c991510ec67f856ff87cd184db10e756ddfee2d8f99db27d6c72","first_computed_at":"2026-05-17T23:53:39.506246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:39.506246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jtrjdU0TJou0A/2rgmPPNzvyNYWyzRLPZdq+aGRy3MXZ8nUiwQ8deZeINOjFPQNFonYciQneKQXEgB7OpvuwAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:39.506967Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.1550","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70ce7424d6fd0dbdcf02838c8e40ae1b2d9d4b76a8d764c0f8211939d61057cd","sha256:c4f869cbc6d426c5a7de55e4eb15a29950f745fd1b8eab8cd608e966aaeae943"],"state_sha256":"2b111f2853faeba7a9038423c27c3cf19c31766feba363c039d951a8f74021ea"}