{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:5JQSD7U7NWRT6HAJHDPEHH6FLA","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":"7ff1b4cc0fd66817570c86ccad3b93f701b814be56e3914ea2d841bc60fc8bf4","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2005-04-14T18:32:32Z","title_canon_sha256":"85656089c9f2bcdc12ce5ef8009a32ac3287eaecda16669f3822b1710f8f6eb3"},"schema_version":"1.0","source":{"id":"math/0504303","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0504303","created_at":"2026-07-04T14:50:12Z"},{"alias_kind":"arxiv_version","alias_value":"math/0504303v2","created_at":"2026-07-04T14:50:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504303","created_at":"2026-07-04T14:50:12Z"},{"alias_kind":"pith_short_12","alias_value":"5JQSD7U7NWRT","created_at":"2026-07-04T14:50:12Z"},{"alias_kind":"pith_short_16","alias_value":"5JQSD7U7NWRT6HAJ","created_at":"2026-07-04T14:50:12Z"},{"alias_kind":"pith_short_8","alias_value":"5JQSD7U7","created_at":"2026-07-04T14:50:12Z"}],"graph_snapshots":[{"event_id":"sha256:3216289b78aa33cd6e431cd7cd84edc841ed7e90385507738d4b30020154a18b","target":"graph","created_at":"2026-07-04T14:50:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0504303/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we examine how well a rational point P on an algebraic variety X can be approximated by other rational points. We conjecture that if P lies on a rational curve, then the best approximations to P on X can be chosen to lie along a rational curve. We prove this conjecture for a wide range of examples, and for a great many more examples we deduce our conjecture from Vojta's Main Conjecture.","authors_text":"David McKinnon","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2005-04-14T18:32:32Z","title":"A conjecture on rational approximations to rational points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504303","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:b337709dfec0b12b87bc96709516a4d4bab91a5a0837e6f90c0badaae35c790c","target":"record","created_at":"2026-07-04T14:50:12Z","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":"7ff1b4cc0fd66817570c86ccad3b93f701b814be56e3914ea2d841bc60fc8bf4","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2005-04-14T18:32:32Z","title_canon_sha256":"85656089c9f2bcdc12ce5ef8009a32ac3287eaecda16669f3822b1710f8f6eb3"},"schema_version":"1.0","source":{"id":"math/0504303","kind":"arxiv","version":2}},"canonical_sha256":"ea6121fe9f6da33f1c0938de439fc5580f84c391cb43eac3d2de33052db919b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea6121fe9f6da33f1c0938de439fc5580f84c391cb43eac3d2de33052db919b2","first_computed_at":"2026-07-04T14:50:12.658492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:50:12.658492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bmQ782Ljz2E2ztS/x+DccE275fznWz4crndkdRkyBqNlNaFb1nG6dsUCrp2sIewp7ABFCm2GcUnmAdINiXhODA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:50:12.658843Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0504303","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b337709dfec0b12b87bc96709516a4d4bab91a5a0837e6f90c0badaae35c790c","sha256:3216289b78aa33cd6e431cd7cd84edc841ed7e90385507738d4b30020154a18b"],"state_sha256":"fac60d124b5bddd62cfba6ca3cd975a0dbfc486be4c16869b81d74bce54304fe"}