{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PANIKK4PPDW2A5UHFB4HTOKQAK","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":"fbc9237c14c52d1c3a1b8b30cf2b707b2ce283061505d942ef436ec580ac05ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-02-18T17:24:01Z","title_canon_sha256":"84d706c21a051b78a6d8d3a4717934cc9a2bccb6fabd9ab964e798815fa6344e"},"schema_version":"1.0","source":{"id":"1302.4361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4361","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4361v1","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4361","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"pith_short_12","alias_value":"PANIKK4PPDW2","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PANIKK4PPDW2A5UH","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PANIKK4P","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:0914e7775c6d9b191434914d5da089456179bc8b1965374b04a1d5059555ca55","target":"graph","created_at":"2026-05-18T03:33:14Z","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":"In this paper we determine a minimal set of generators for the Cox rings of extremal rational elliptic surfaces. Moreover, we develop a technique for computing the ideal of relations between them which allows, in all but three cases, to provide a presentation of the Cox ring.","authors_text":"Alice Garbagnati, Antonio Laface, Michela Artebani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-02-18T17:24:01Z","title":"Cox rings of extremal rational elliptic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4361","kind":"arxiv","version":1},"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:c374d429fcfc331c78120fbd27b4c0f0f8c23c663fbcd3dafd89685011b6e85c","target":"record","created_at":"2026-05-18T03:33:14Z","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":"fbc9237c14c52d1c3a1b8b30cf2b707b2ce283061505d942ef436ec580ac05ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-02-18T17:24:01Z","title_canon_sha256":"84d706c21a051b78a6d8d3a4717934cc9a2bccb6fabd9ab964e798815fa6344e"},"schema_version":"1.0","source":{"id":"1302.4361","kind":"arxiv","version":1}},"canonical_sha256":"781a852b8f78eda07687287879b9500296c2206e0b6c72604a6d12b39e294e71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"781a852b8f78eda07687287879b9500296c2206e0b6c72604a6d12b39e294e71","first_computed_at":"2026-05-18T03:33:14.757788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:14.757788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kqxk5or8ugbSEabQ9hp5/+5j+fHOk30Vy7dO3pUZLuLcXZZEHfi1yjWm9vOzUQMOXFm7ujLXEgD/65+MIajYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:14.758630Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c374d429fcfc331c78120fbd27b4c0f0f8c23c663fbcd3dafd89685011b6e85c","sha256:0914e7775c6d9b191434914d5da089456179bc8b1965374b04a1d5059555ca55"],"state_sha256":"532734693142228c3af6670f39150c8c11020b3577a6dc3d7994b6578e1c85f7"}