{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QN2OQHPTUWNGBQRN57ETN6Q4FZ","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":"8aa9426266deb2f5492dea7d74375dd405f167f7a1193d06768f70a33fdbd295","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-14T16:20:31Z","title_canon_sha256":"cbaad2a0da696a4ff40a42be7f09b82e79147c7cdaf1a7c9c951cfebc378d97b"},"schema_version":"1.0","source":{"id":"1212.3511","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3511","created_at":"2026-05-18T00:59:35Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3511v5","created_at":"2026-05-18T00:59:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3511","created_at":"2026-05-18T00:59:35Z"},{"alias_kind":"pith_short_12","alias_value":"QN2OQHPTUWNG","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QN2OQHPTUWNGBQRN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QN2OQHPT","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:e11795ec2ec247f59bf10f490ec1be0c1c6159b5a11d91a3eaa43e53d93fb2fb","target":"graph","created_at":"2026-05-18T00:59:35Z","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":"Let k be a field of characteristic other than 2,3. We prove that there are no geometrically smooth quartic surfaces in IP^3 with more than 64 lines. As a key step, we derive the sharp bound that any line meets at most 20 other lines on a smooth quartic.","authors_text":"Matthias Schuett, Slawomir Rams","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-14T16:20:31Z","title":"64 lines on smooth quartic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3511","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":"sha256:57a898c54d26c7a6f108520f2c34f5204b8a3f30002e42ea1e6a4cc49ccc4d9d","target":"record","created_at":"2026-05-18T00:59:35Z","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":"8aa9426266deb2f5492dea7d74375dd405f167f7a1193d06768f70a33fdbd295","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-14T16:20:31Z","title_canon_sha256":"cbaad2a0da696a4ff40a42be7f09b82e79147c7cdaf1a7c9c951cfebc378d97b"},"schema_version":"1.0","source":{"id":"1212.3511","kind":"arxiv","version":5}},"canonical_sha256":"8374e81df3a59a60c22defc936fa1c2e4b66ad6f4f44e52b837fab49d383076a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8374e81df3a59a60c22defc936fa1c2e4b66ad6f4f44e52b837fab49d383076a","first_computed_at":"2026-05-18T00:59:35.041443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:35.041443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7KkHzrb+GDnsxP9JQOQT6HfSYxuRutEPHH8DflcjgCN8Wz23wwS3Bdrd8NYCAv5m6Ei/iMFCefG0zPxlUygyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:35.042129Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3511","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57a898c54d26c7a6f108520f2c34f5204b8a3f30002e42ea1e6a4cc49ccc4d9d","sha256:e11795ec2ec247f59bf10f490ec1be0c1c6159b5a11d91a3eaa43e53d93fb2fb"],"state_sha256":"02b9bfee195748358299a42c1782a37f8e5656abad3b562ef8e597ca52bc53e8"}