{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:MXFI67OC53W2OD3DRWAQDZLVRS","short_pith_number":"pith:MXFI67OC","canonical_record":{"source":{"id":"2004.05212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-10T19:45:53Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"fcaa2cf7196e08413a2b4ba7c96582de326c95887eceb0bf26a84ec105856606","abstract_canon_sha256":"be4baa653bf8178046441968c7d885a393cac387b02ad335dc7d7defd6be93b1"},"schema_version":"1.0"},"canonical_sha256":"65ca8f7dc2eeeda70f638d8101e5758c8d1dfa47e16177301b0ea60818ebdb4d","source":{"kind":"arxiv","id":"2004.05212","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.05212","created_at":"2026-07-05T00:54:34Z"},{"alias_kind":"arxiv_version","alias_value":"2004.05212v1","created_at":"2026-07-05T00:54:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.05212","created_at":"2026-07-05T00:54:34Z"},{"alias_kind":"pith_short_12","alias_value":"MXFI67OC53W2","created_at":"2026-07-05T00:54:34Z"},{"alias_kind":"pith_short_16","alias_value":"MXFI67OC53W2OD3D","created_at":"2026-07-05T00:54:34Z"},{"alias_kind":"pith_short_8","alias_value":"MXFI67OC","created_at":"2026-07-05T00:54:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:MXFI67OC53W2OD3DRWAQDZLVRS","target":"record","payload":{"canonical_record":{"source":{"id":"2004.05212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-10T19:45:53Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"fcaa2cf7196e08413a2b4ba7c96582de326c95887eceb0bf26a84ec105856606","abstract_canon_sha256":"be4baa653bf8178046441968c7d885a393cac387b02ad335dc7d7defd6be93b1"},"schema_version":"1.0"},"canonical_sha256":"65ca8f7dc2eeeda70f638d8101e5758c8d1dfa47e16177301b0ea60818ebdb4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:54:34.902169Z","signature_b64":"ssIBshgrsY5TIg8ljuBsxPhoBsszBxmPmXF7UWNT0CbxlMf1ltzo8hZDlG3z7LtioYApM2ld3dqjvSzxCfYiAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65ca8f7dc2eeeda70f638d8101e5758c8d1dfa47e16177301b0ea60818ebdb4d","last_reissued_at":"2026-07-05T00:54:34.901640Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:54:34.901640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.05212","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":"2026-07-05T00:54:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"keIcJqNsuiTF8Nao2bdrP7CB8J7OV6hpq1RHuat9MSEB+EM50sNIWIUQ1W3LPHpGdjv7V5gogOu5wgALxwSCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:06:20.952601Z"},"content_sha256":"2a37f90fe521a533c7d87eff090c939cc894345555035b10f94dd0a50295c6e6","schema_version":"1.0","event_id":"sha256:2a37f90fe521a533c7d87eff090c939cc894345555035b10f94dd0a50295c6e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:MXFI67OC53W2OD3DRWAQDZLVRS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximating rational points on toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"David McKinnon, Matthew Satriano","submitted_at":"2020-04-10T19:45:53Z","abstract_excerpt":"Given a smooth projective variety $X$ over a number field $k$ and $P\\in X(k)$, the first author conjectured that in a precise sense, any sequence that approximates $P$ sufficiently well must lie on a rational curve. We prove this conjecture for smooth split toric surfaces conditional on Vojta's conjecture. More generally, we show that if $X$ is a $\\mathbb{Q}$-factorial terminal split toric variety of arbitrary dimension, then $P$ is better approximated by points on a rational curve than by any Zariski dense sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.05212","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.05212/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:54:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/sfTJ3cBFYGa9r58LnzXFEXVB8TYf5K1bkcAtR/35PdKwUhjM2lMdob7PCPJo5Opm7X7QeTgL/aEHnfaAVMbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:06:20.953180Z"},"content_sha256":"6d0166b2e947bebd6a5cefe071c8dead18d53793327cd7ad0b1526c08e173c26","schema_version":"1.0","event_id":"sha256:6d0166b2e947bebd6a5cefe071c8dead18d53793327cd7ad0b1526c08e173c26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXFI67OC53W2OD3DRWAQDZLVRS/bundle.json","state_url":"https://pith.science/pith/MXFI67OC53W2OD3DRWAQDZLVRS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXFI67OC53W2OD3DRWAQDZLVRS/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":"2026-08-03T16:06:20Z","links":{"resolver":"https://pith.science/pith/MXFI67OC53W2OD3DRWAQDZLVRS","bundle":"https://pith.science/pith/MXFI67OC53W2OD3DRWAQDZLVRS/bundle.json","state":"https://pith.science/pith/MXFI67OC53W2OD3DRWAQDZLVRS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXFI67OC53W2OD3DRWAQDZLVRS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:MXFI67OC53W2OD3DRWAQDZLVRS","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":"be4baa653bf8178046441968c7d885a393cac387b02ad335dc7d7defd6be93b1","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-10T19:45:53Z","title_canon_sha256":"fcaa2cf7196e08413a2b4ba7c96582de326c95887eceb0bf26a84ec105856606"},"schema_version":"1.0","source":{"id":"2004.05212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.05212","created_at":"2026-07-05T00:54:34Z"},{"alias_kind":"arxiv_version","alias_value":"2004.05212v1","created_at":"2026-07-05T00:54:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.05212","created_at":"2026-07-05T00:54:34Z"},{"alias_kind":"pith_short_12","alias_value":"MXFI67OC53W2","created_at":"2026-07-05T00:54:34Z"},{"alias_kind":"pith_short_16","alias_value":"MXFI67OC53W2OD3D","created_at":"2026-07-05T00:54:34Z"},{"alias_kind":"pith_short_8","alias_value":"MXFI67OC","created_at":"2026-07-05T00:54:34Z"}],"graph_snapshots":[{"event_id":"sha256:6d0166b2e947bebd6a5cefe071c8dead18d53793327cd7ad0b1526c08e173c26","target":"graph","created_at":"2026-07-05T00:54:34Z","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/2004.05212/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a smooth projective variety $X$ over a number field $k$ and $P\\in X(k)$, the first author conjectured that in a precise sense, any sequence that approximates $P$ sufficiently well must lie on a rational curve. We prove this conjecture for smooth split toric surfaces conditional on Vojta's conjecture. More generally, we show that if $X$ is a $\\mathbb{Q}$-factorial terminal split toric variety of arbitrary dimension, then $P$ is better approximated by points on a rational curve than by any Zariski dense sequence.","authors_text":"David McKinnon, Matthew Satriano","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-10T19:45:53Z","title":"Approximating rational points on toric varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.05212","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":"sha256:2a37f90fe521a533c7d87eff090c939cc894345555035b10f94dd0a50295c6e6","target":"record","created_at":"2026-07-05T00:54:34Z","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":"be4baa653bf8178046441968c7d885a393cac387b02ad335dc7d7defd6be93b1","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-10T19:45:53Z","title_canon_sha256":"fcaa2cf7196e08413a2b4ba7c96582de326c95887eceb0bf26a84ec105856606"},"schema_version":"1.0","source":{"id":"2004.05212","kind":"arxiv","version":1}},"canonical_sha256":"65ca8f7dc2eeeda70f638d8101e5758c8d1dfa47e16177301b0ea60818ebdb4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65ca8f7dc2eeeda70f638d8101e5758c8d1dfa47e16177301b0ea60818ebdb4d","first_computed_at":"2026-07-05T00:54:34.901640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:54:34.901640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ssIBshgrsY5TIg8ljuBsxPhoBsszBxmPmXF7UWNT0CbxlMf1ltzo8hZDlG3z7LtioYApM2ld3dqjvSzxCfYiAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:54:34.902169Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.05212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a37f90fe521a533c7d87eff090c939cc894345555035b10f94dd0a50295c6e6","sha256:6d0166b2e947bebd6a5cefe071c8dead18d53793327cd7ad0b1526c08e173c26"],"state_sha256":"271f105824b5edefef6656e9d3fb843e1d5db6b655575f5654c1740ef60899f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/osp5PwlZXSKSPZ0N3iwFBeK78IIT2dGcu1PRxbbGs1aW59sE5rp5g7YkCtaMd3vLdngO4UVgvXGSJWNKyj1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:06:20.959063Z","bundle_sha256":"61519942588a00d40039f1ed818219affe62cb687857c1a676b73be5d0d9c7e2"}}