{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZTYA76KDGGII2LDSDEWR6RAKHP","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":"02983463d0cc1c417d8450ef8c638b2eb601a3ec8bb5e51cfc17892f042dfab8","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-02T17:31:42Z","title_canon_sha256":"bc8cefdfd10ee48bc12296649510b13c23ad45faff60cf387562462c94482cce"},"schema_version":"1.0","source":{"id":"1408.0402","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.0402","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"arxiv_version","alias_value":"1408.0402v2","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0402","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"pith_short_12","alias_value":"ZTYA76KDGGII","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZTYA76KDGGII2LDS","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZTYA76KD","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:12a1f3716cb85cc6812b045d05deaba1f669c6908794af4d9cc08324074909fa","target":"graph","created_at":"2026-05-18T01:37:05Z","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 investigate the density of rational points on the Fermat cubic surface and the Cayley cubic surface whose coordinates have few prime factors. The key tools used are the weighted sieve, the circle method and universal torsors.","authors_text":"Yuchao Wang","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-02T17:31:42Z","title":"On the saturation number for cubic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0402","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":"sha256:00eb40c591608d0849ffd653fa3022c990cf0341fa6110757c3a43035f8199eb","target":"record","created_at":"2026-05-18T01:37:05Z","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":"02983463d0cc1c417d8450ef8c638b2eb601a3ec8bb5e51cfc17892f042dfab8","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-02T17:31:42Z","title_canon_sha256":"bc8cefdfd10ee48bc12296649510b13c23ad45faff60cf387562462c94482cce"},"schema_version":"1.0","source":{"id":"1408.0402","kind":"arxiv","version":2}},"canonical_sha256":"ccf00ff94331908d2c72192d1f440a3beaba938d3d869afc4b258750d02803a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccf00ff94331908d2c72192d1f440a3beaba938d3d869afc4b258750d02803a4","first_computed_at":"2026-05-18T01:37:05.708680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:05.708680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WtCnVplhdkoHqvC57Atf0zS/XAycObyT9bfPtueMwbtd7IhotOOJ/mcqGkdLYlKqiX6ODzIeqYMeGDTXgIlICQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:05.709305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.0402","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00eb40c591608d0849ffd653fa3022c990cf0341fa6110757c3a43035f8199eb","sha256:12a1f3716cb85cc6812b045d05deaba1f669c6908794af4d9cc08324074909fa"],"state_sha256":"3432cf499ce9138d7b89417c17163a2f8bdbb116d237a1a7797c18aaac8d7902"}