{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TTCMAXGZMAWFDGQTOPCFUMHSGS","short_pith_number":"pith:TTCMAXGZ","canonical_record":{"source":{"id":"1004.2797","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-16T09:23:05Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"ef50558707806e2ddebdec8d5ff9315b15a2817dc2d34b3f1267a8d3cf944bdd","abstract_canon_sha256":"fe1a7059c0df012031d5cb583ccaeec7d36207d6ecdbc398fa57a82d89fc3dc7"},"schema_version":"1.0"},"canonical_sha256":"9cc4c05cd9602c519a1373c45a30f23491212f5f94d862af4ee7c0e6f3c126e5","source":{"kind":"arxiv","id":"1004.2797","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2797","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2797v2","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2797","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"pith_short_12","alias_value":"TTCMAXGZMAWF","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TTCMAXGZMAWFDGQT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TTCMAXGZ","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TTCMAXGZMAWFDGQTOPCFUMHSGS","target":"record","payload":{"canonical_record":{"source":{"id":"1004.2797","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-16T09:23:05Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"ef50558707806e2ddebdec8d5ff9315b15a2817dc2d34b3f1267a8d3cf944bdd","abstract_canon_sha256":"fe1a7059c0df012031d5cb583ccaeec7d36207d6ecdbc398fa57a82d89fc3dc7"},"schema_version":"1.0"},"canonical_sha256":"9cc4c05cd9602c519a1373c45a30f23491212f5f94d862af4ee7c0e6f3c126e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:18.341196Z","signature_b64":"x0ZskMk9ajxnnX56bnxjF7HMNb1eeqIdnDOBQOUZIiZZAurSXZ5GqTbtQ+k+iyUIzuDXEpuuiE9PevJrX86DDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cc4c05cd9602c519a1373c45a30f23491212f5f94d862af4ee7c0e6f3c126e5","last_reissued_at":"2026-05-18T04:34:18.340652Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:18.340652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.2797","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pbYdbAC7GJOKy9U+/ah+TbgZ3MdqEI0JVFdWaYOr6GyuYpPnyIFlhkzNTjSYMVs+SqwjIErow8WHemjQVTg/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:47:58.100088Z"},"content_sha256":"cad3e5ca012524b722b0c7dfad49fb5f10a7f720819f02f53e9284218e06b7e5","schema_version":"1.0","event_id":"sha256:cad3e5ca012524b722b0c7dfad49fb5f10a7f720819f02f53e9284218e06b7e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TTCMAXGZMAWFDGQTOPCFUMHSGS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zero-cycles and rational points on some surfaces over a global function field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Jean-Louis Colliot-Th\\'el\\`ene, Sir Peter Swinnerton-Dyer","submitted_at":"2010-04-16T09:23:05Z","abstract_excerpt":"Let F be a finite field of characteristic p. We consider smooth surfaces over F(t) defined by an equation f+tg=0, where f and g are forms of degree d in 4 variables with coefficients in F, with d prime to p. We prove : For such surfaces over F(t), the Brauer-Manin obstruction to the existence of a zero-cycle of degree one is the only obstruction. For d=3 (cubic surfaces), this leads to the same result for rational points.\n  --\n  Soit F un corps fini de caract\\'eristique p. Pour une surface lisse sur F(t) d\\'efinie par une \\'equation f+tg=0, o\\`u f et g sont deux formes de degr\\'e d sur F en 4 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2797","kind":"arxiv","version":2},"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":"2026-05-18T04:34:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xNB+h2xh/l5gciNAzMPEbGNStKfq93lnihrCs3mhEEwHlsH1PZyeSGIv5XPYwxq7ZRx33PjIkR+Pxoofc0cQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:47:58.100671Z"},"content_sha256":"90de47fc408dc476ccb46581b6177984484c6694e36dd690ad5db2332a63aae3","schema_version":"1.0","event_id":"sha256:90de47fc408dc476ccb46581b6177984484c6694e36dd690ad5db2332a63aae3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TTCMAXGZMAWFDGQTOPCFUMHSGS/bundle.json","state_url":"https://pith.science/pith/TTCMAXGZMAWFDGQTOPCFUMHSGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TTCMAXGZMAWFDGQTOPCFUMHSGS/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":"2026-05-31T23:47:58Z","links":{"resolver":"https://pith.science/pith/TTCMAXGZMAWFDGQTOPCFUMHSGS","bundle":"https://pith.science/pith/TTCMAXGZMAWFDGQTOPCFUMHSGS/bundle.json","state":"https://pith.science/pith/TTCMAXGZMAWFDGQTOPCFUMHSGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TTCMAXGZMAWFDGQTOPCFUMHSGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TTCMAXGZMAWFDGQTOPCFUMHSGS","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":"fe1a7059c0df012031d5cb583ccaeec7d36207d6ecdbc398fa57a82d89fc3dc7","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-16T09:23:05Z","title_canon_sha256":"ef50558707806e2ddebdec8d5ff9315b15a2817dc2d34b3f1267a8d3cf944bdd"},"schema_version":"1.0","source":{"id":"1004.2797","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2797","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2797v2","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2797","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"pith_short_12","alias_value":"TTCMAXGZMAWF","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TTCMAXGZMAWFDGQT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TTCMAXGZ","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:90de47fc408dc476ccb46581b6177984484c6694e36dd690ad5db2332a63aae3","target":"graph","created_at":"2026-05-18T04:34:18Z","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 F be a finite field of characteristic p. We consider smooth surfaces over F(t) defined by an equation f+tg=0, where f and g are forms of degree d in 4 variables with coefficients in F, with d prime to p. We prove : For such surfaces over F(t), the Brauer-Manin obstruction to the existence of a zero-cycle of degree one is the only obstruction. For d=3 (cubic surfaces), this leads to the same result for rational points.\n  --\n  Soit F un corps fini de caract\\'eristique p. Pour une surface lisse sur F(t) d\\'efinie par une \\'equation f+tg=0, o\\`u f et g sont deux formes de degr\\'e d sur F en 4 ","authors_text":"Jean-Louis Colliot-Th\\'el\\`ene, Sir Peter Swinnerton-Dyer","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-16T09:23:05Z","title":"Zero-cycles and rational points on some surfaces over a global function field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2797","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:cad3e5ca012524b722b0c7dfad49fb5f10a7f720819f02f53e9284218e06b7e5","target":"record","created_at":"2026-05-18T04:34:18Z","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":"fe1a7059c0df012031d5cb583ccaeec7d36207d6ecdbc398fa57a82d89fc3dc7","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-16T09:23:05Z","title_canon_sha256":"ef50558707806e2ddebdec8d5ff9315b15a2817dc2d34b3f1267a8d3cf944bdd"},"schema_version":"1.0","source":{"id":"1004.2797","kind":"arxiv","version":2}},"canonical_sha256":"9cc4c05cd9602c519a1373c45a30f23491212f5f94d862af4ee7c0e6f3c126e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cc4c05cd9602c519a1373c45a30f23491212f5f94d862af4ee7c0e6f3c126e5","first_computed_at":"2026-05-18T04:34:18.340652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:18.340652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x0ZskMk9ajxnnX56bnxjF7HMNb1eeqIdnDOBQOUZIiZZAurSXZ5GqTbtQ+k+iyUIzuDXEpuuiE9PevJrX86DDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:18.341196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.2797","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cad3e5ca012524b722b0c7dfad49fb5f10a7f720819f02f53e9284218e06b7e5","sha256:90de47fc408dc476ccb46581b6177984484c6694e36dd690ad5db2332a63aae3"],"state_sha256":"04d66d88e4040ead7ef0cc3d097b7bc61aafbf1bcb80c3916e38be867730c38f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cIuLAboyzi2ErSRifrR8IyhIUL9zFKW51RDyKHnaVfYWAG9zLCcsiGBNnVGLnFCeMFeHg3jZMAmYNLE96ejwCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:47:58.104496Z","bundle_sha256":"f63e801271d61ce028b611278e3cdf6c0fe59a435829d252636c5841bbe78e85"}}