{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UB3FANV7CU65K4AQZM4FA3RS4L","short_pith_number":"pith:UB3FANV7","canonical_record":{"source":{"id":"1502.03052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-10T19:53:28Z","cross_cats_sorted":[],"title_canon_sha256":"7625932cc46cac1b4e29377d316822e23ddf1c3227bbd5277d24526b7837f3e1","abstract_canon_sha256":"122bf20f0eec2493187defe3ba5dc7e43588d6196cfd91e546d94af3ef12b528"},"schema_version":"1.0"},"canonical_sha256":"a0765036bf153dd57010cb38506e32e2cc4ecda556bf5097a11485fecaa1a5d5","source":{"kind":"arxiv","id":"1502.03052","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.03052","created_at":"2026-05-18T02:27:29Z"},{"alias_kind":"arxiv_version","alias_value":"1502.03052v1","created_at":"2026-05-18T02:27:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03052","created_at":"2026-05-18T02:27:29Z"},{"alias_kind":"pith_short_12","alias_value":"UB3FANV7CU65","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UB3FANV7CU65K4AQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UB3FANV7","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UB3FANV7CU65K4AQZM4FA3RS4L","target":"record","payload":{"canonical_record":{"source":{"id":"1502.03052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-10T19:53:28Z","cross_cats_sorted":[],"title_canon_sha256":"7625932cc46cac1b4e29377d316822e23ddf1c3227bbd5277d24526b7837f3e1","abstract_canon_sha256":"122bf20f0eec2493187defe3ba5dc7e43588d6196cfd91e546d94af3ef12b528"},"schema_version":"1.0"},"canonical_sha256":"a0765036bf153dd57010cb38506e32e2cc4ecda556bf5097a11485fecaa1a5d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:29.960026Z","signature_b64":"KGzOFC+lB9lPQYf4r/ox9IPB+cvj7BYy0c72GjApHL4Qt42A+aFzXSwEmYOJAijFXq9qwLAwePUxP644eENYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0765036bf153dd57010cb38506e32e2cc4ecda556bf5097a11485fecaa1a5d5","last_reissued_at":"2026-05-18T02:27:29.959266Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:29.959266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.03052","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":"2026-05-18T02:27:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"36FloV7cXjU2pHq+9qCz/JHM+uciDgoO+hh895Kcqg8ZpagTKsfoyU+BNJ9JGrmKVgrGThQiRtPq5935byhHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T10:24:33.130176Z"},"content_sha256":"49f1ff0c720fa9a41cc8507d8dae094bde13792e72f5e9924d36344b5190e8cb","schema_version":"1.0","event_id":"sha256:49f1ff0c720fa9a41cc8507d8dae094bde13792e72f5e9924d36344b5190e8cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UB3FANV7CU65K4AQZM4FA3RS4L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponents of Diophantine approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yann Bugeaud","submitted_at":"2015-02-10T19:53:28Z","abstract_excerpt":"We survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03052","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":"2026-05-18T02:27:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dIcLaJDfMkRbCI2FyypE9bm+VRdFHhbhTe7+0tJLhodFjiQcEV3IzTgunhe1ghlusFJKGkC3T2ZOrNWiqyCvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T10:24:33.130876Z"},"content_sha256":"f4b4f51b05424b25bedb5eca84f5ddbcb86e0da60958959a7e5e1618ea01f92a","schema_version":"1.0","event_id":"sha256:f4b4f51b05424b25bedb5eca84f5ddbcb86e0da60958959a7e5e1618ea01f92a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UB3FANV7CU65K4AQZM4FA3RS4L/bundle.json","state_url":"https://pith.science/pith/UB3FANV7CU65K4AQZM4FA3RS4L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UB3FANV7CU65K4AQZM4FA3RS4L/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":"2026-05-24T10:24:33Z","links":{"resolver":"https://pith.science/pith/UB3FANV7CU65K4AQZM4FA3RS4L","bundle":"https://pith.science/pith/UB3FANV7CU65K4AQZM4FA3RS4L/bundle.json","state":"https://pith.science/pith/UB3FANV7CU65K4AQZM4FA3RS4L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UB3FANV7CU65K4AQZM4FA3RS4L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UB3FANV7CU65K4AQZM4FA3RS4L","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":"122bf20f0eec2493187defe3ba5dc7e43588d6196cfd91e546d94af3ef12b528","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-10T19:53:28Z","title_canon_sha256":"7625932cc46cac1b4e29377d316822e23ddf1c3227bbd5277d24526b7837f3e1"},"schema_version":"1.0","source":{"id":"1502.03052","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.03052","created_at":"2026-05-18T02:27:29Z"},{"alias_kind":"arxiv_version","alias_value":"1502.03052v1","created_at":"2026-05-18T02:27:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03052","created_at":"2026-05-18T02:27:29Z"},{"alias_kind":"pith_short_12","alias_value":"UB3FANV7CU65","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UB3FANV7CU65K4AQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UB3FANV7","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:f4b4f51b05424b25bedb5eca84f5ddbcb86e0da60958959a7e5e1618ea01f92a","target":"graph","created_at":"2026-05-18T02:27:29Z","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 survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.","authors_text":"Yann Bugeaud","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-10T19:53:28Z","title":"Exponents of Diophantine approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03052","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":"sha256:49f1ff0c720fa9a41cc8507d8dae094bde13792e72f5e9924d36344b5190e8cb","target":"record","created_at":"2026-05-18T02:27:29Z","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":"122bf20f0eec2493187defe3ba5dc7e43588d6196cfd91e546d94af3ef12b528","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-10T19:53:28Z","title_canon_sha256":"7625932cc46cac1b4e29377d316822e23ddf1c3227bbd5277d24526b7837f3e1"},"schema_version":"1.0","source":{"id":"1502.03052","kind":"arxiv","version":1}},"canonical_sha256":"a0765036bf153dd57010cb38506e32e2cc4ecda556bf5097a11485fecaa1a5d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0765036bf153dd57010cb38506e32e2cc4ecda556bf5097a11485fecaa1a5d5","first_computed_at":"2026-05-18T02:27:29.959266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:29.959266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KGzOFC+lB9lPQYf4r/ox9IPB+cvj7BYy0c72GjApHL4Qt42A+aFzXSwEmYOJAijFXq9qwLAwePUxP644eENYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:29.960026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.03052","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49f1ff0c720fa9a41cc8507d8dae094bde13792e72f5e9924d36344b5190e8cb","sha256:f4b4f51b05424b25bedb5eca84f5ddbcb86e0da60958959a7e5e1618ea01f92a"],"state_sha256":"e2c358fc5e13ec59dde6a6bd4483fc3161cc2e4882e7ba128324964a5e3cfa1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gXvzBOt3dHvzNf4XdEL8zLVT7nqO5C+56cGU01jfhdxkV0WxH5TY9rEQpF6DPOvPazfGeJa1g5oKlqPuQNImAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T10:24:33.134284Z","bundle_sha256":"f10ffcd98438d7a5fc5c9dec92a0eed7c1c8ad0ad44923cdcfbac81f19330403"}}