{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PTGYOMS7PVTTNPLGUVTTVX3T6P","short_pith_number":"pith:PTGYOMS7","canonical_record":{"source":{"id":"1312.5905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-20T12:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"3c5baacbf46043c42f86c0a95ca4e302d9c1a1c7d726eec26f4bfbb1fda01b03","abstract_canon_sha256":"5b8a290403c24bfc59917206ed3bca57db038dce5763e17940ee3e2bf9af2c54"},"schema_version":"1.0"},"canonical_sha256":"7ccd87325f7d6736bd66a5673adf73f3e5296c9bce44bbeaa1303ae1e70b2dde","source":{"kind":"arxiv","id":"1312.5905","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5905","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5905v1","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5905","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"PTGYOMS7PVTT","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"PTGYOMS7PVTTNPLG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"PTGYOMS7","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PTGYOMS7PVTTNPLGUVTTVX3T6P","target":"record","payload":{"canonical_record":{"source":{"id":"1312.5905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-20T12:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"3c5baacbf46043c42f86c0a95ca4e302d9c1a1c7d726eec26f4bfbb1fda01b03","abstract_canon_sha256":"5b8a290403c24bfc59917206ed3bca57db038dce5763e17940ee3e2bf9af2c54"},"schema_version":"1.0"},"canonical_sha256":"7ccd87325f7d6736bd66a5673adf73f3e5296c9bce44bbeaa1303ae1e70b2dde","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:07.553676Z","signature_b64":"ERYdUkgIMz/Uogcq7RtJITBPtXrsC2WZlNhFp84TKKh6G0r77z4S2fMKZTkYirhFZS6fAMAzj2SklWJQP5qdBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ccd87325f7d6736bd66a5673adf73f3e5296c9bce44bbeaa1303ae1e70b2dde","last_reissued_at":"2026-05-18T03:04:07.552983Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:07.552983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.5905","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:04:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7GytuKvDTHnjNJ5F+FbqPfXPisdcSoYULgzfZTNiDJPonDEjWT6zasfsPJkIu5bNJYZR87zsqE37EPnKNAEpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:52:48.785582Z"},"content_sha256":"27146e21a599c339d48d54a91cda4245c21c4ac9020b745ddcd5b3e289e4cf4e","schema_version":"1.0","event_id":"sha256:27146e21a599c339d48d54a91cda4245c21c4ac9020b745ddcd5b3e289e4cf4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PTGYOMS7PVTTNPLGUVTTVX3T6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cubic surfaces with one rational line over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jenny Cooley","submitted_at":"2013-12-20T12:00:00Z","abstract_excerpt":"Let Fq be a finite field with q=8 or q at least 16. Let S be a smooth cubic surface defined over Fq containing at least one rational line. We use a pigeonhole principle to prove that all the rational points on S are generated via tangent and secant operations from a single point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5905","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:04:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ujUR02joLn8HYn3ovKxNtq6U8yhotXHUHecxhNzJAWr4qkNXj1CuKhJ8c/soz4CVCkKA1BNCv5GTQyfUMHE1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:52:48.786002Z"},"content_sha256":"4d646f23c0e7f43aa8cae914323082a267961205b8d8bfb33b4f853f1f9f89a3","schema_version":"1.0","event_id":"sha256:4d646f23c0e7f43aa8cae914323082a267961205b8d8bfb33b4f853f1f9f89a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PTGYOMS7PVTTNPLGUVTTVX3T6P/bundle.json","state_url":"https://pith.science/pith/PTGYOMS7PVTTNPLGUVTTVX3T6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PTGYOMS7PVTTNPLGUVTTVX3T6P/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T13:52:48Z","links":{"resolver":"https://pith.science/pith/PTGYOMS7PVTTNPLGUVTTVX3T6P","bundle":"https://pith.science/pith/PTGYOMS7PVTTNPLGUVTTVX3T6P/bundle.json","state":"https://pith.science/pith/PTGYOMS7PVTTNPLGUVTTVX3T6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PTGYOMS7PVTTNPLGUVTTVX3T6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PTGYOMS7PVTTNPLGUVTTVX3T6P","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":"5b8a290403c24bfc59917206ed3bca57db038dce5763e17940ee3e2bf9af2c54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-20T12:00:00Z","title_canon_sha256":"3c5baacbf46043c42f86c0a95ca4e302d9c1a1c7d726eec26f4bfbb1fda01b03"},"schema_version":"1.0","source":{"id":"1312.5905","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5905","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5905v1","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5905","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"PTGYOMS7PVTT","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"PTGYOMS7PVTTNPLG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"PTGYOMS7","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:4d646f23c0e7f43aa8cae914323082a267961205b8d8bfb33b4f853f1f9f89a3","target":"graph","created_at":"2026-05-18T03:04:07Z","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 Fq be a finite field with q=8 or q at least 16. Let S be a smooth cubic surface defined over Fq containing at least one rational line. We use a pigeonhole principle to prove that all the rational points on S are generated via tangent and secant operations from a single point.","authors_text":"Jenny Cooley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-20T12:00:00Z","title":"Cubic surfaces with one rational line over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5905","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":"sha256:27146e21a599c339d48d54a91cda4245c21c4ac9020b745ddcd5b3e289e4cf4e","target":"record","created_at":"2026-05-18T03:04:07Z","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":"5b8a290403c24bfc59917206ed3bca57db038dce5763e17940ee3e2bf9af2c54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-20T12:00:00Z","title_canon_sha256":"3c5baacbf46043c42f86c0a95ca4e302d9c1a1c7d726eec26f4bfbb1fda01b03"},"schema_version":"1.0","source":{"id":"1312.5905","kind":"arxiv","version":1}},"canonical_sha256":"7ccd87325f7d6736bd66a5673adf73f3e5296c9bce44bbeaa1303ae1e70b2dde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ccd87325f7d6736bd66a5673adf73f3e5296c9bce44bbeaa1303ae1e70b2dde","first_computed_at":"2026-05-18T03:04:07.552983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:07.552983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ERYdUkgIMz/Uogcq7RtJITBPtXrsC2WZlNhFp84TKKh6G0r77z4S2fMKZTkYirhFZS6fAMAzj2SklWJQP5qdBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:07.553676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.5905","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27146e21a599c339d48d54a91cda4245c21c4ac9020b745ddcd5b3e289e4cf4e","sha256:4d646f23c0e7f43aa8cae914323082a267961205b8d8bfb33b4f853f1f9f89a3"],"state_sha256":"3bb08ceaaca760061a8a649c75095405750030b8ff1c2f2dba89cc9348da27bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4wnEVE8m8X0SCdSeX0/vsLRLW+kYAyYBJJNq3OQICtU6z152u+fBdwh6wiNSe51BiwRyEetXpBass2nTtqq5CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T13:52:48.787994Z","bundle_sha256":"e308113c94b2af2ca6da449d29c43b2c1d911ef3c2604ffb155dd46bc31242b5"}}