{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:MKPONVEAEIYSSM5UBXWP46X2AT","short_pith_number":"pith:MKPONVEA","canonical_record":{"source":{"id":"1012.1709","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-08T09:17:47Z","cross_cats_sorted":[],"title_canon_sha256":"bababfc276215ae1741945cfed073281654248d0b22d7335df06ef62af30aef4","abstract_canon_sha256":"f1f259227e09201ee5bb75ccde536360d789bc20def943d365e4d9b9a41716df"},"schema_version":"1.0"},"canonical_sha256":"629ee6d48022312933b40decfe7afa04fdfcc790d2f6e4b02a3673108e0d2044","source":{"kind":"arxiv","id":"1012.1709","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1709","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1709v2","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1709","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"MKPONVEAEIYS","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MKPONVEAEIYSSM5U","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MKPONVEA","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:MKPONVEAEIYSSM5UBXWP46X2AT","target":"record","payload":{"canonical_record":{"source":{"id":"1012.1709","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-08T09:17:47Z","cross_cats_sorted":[],"title_canon_sha256":"bababfc276215ae1741945cfed073281654248d0b22d7335df06ef62af30aef4","abstract_canon_sha256":"f1f259227e09201ee5bb75ccde536360d789bc20def943d365e4d9b9a41716df"},"schema_version":"1.0"},"canonical_sha256":"629ee6d48022312933b40decfe7afa04fdfcc790d2f6e4b02a3673108e0d2044","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:14.597187Z","signature_b64":"n8YqzPwi4r2iuwVhoWJfXviToI+vDJ2k/ucLk8gNDJULvFrC9NujdtvOgTFlpAepbMUk/CMpkFN4jowVLBnMAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"629ee6d48022312933b40decfe7afa04fdfcc790d2f6e4b02a3673108e0d2044","last_reissued_at":"2026-05-18T03:40:14.596565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:14.596565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.1709","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":"2026-05-18T03:40:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wovR4stAtYqBd1f0l7gQHQBtzU4meyKhD0JQQm3SlxIrgD0gTeyZjbyOX4Gmw60AppOz+MJPxc/6hGN4cqybDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T10:13:06.639033Z"},"content_sha256":"8574163237e8154223184c4c68772f90bb4eb0c6f5748ac70a00284c0edea182","schema_version":"1.0","event_id":"sha256:8574163237e8154223184c4c68772f90bb4eb0c6f5748ac70a00284c0edea182"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:MKPONVEAEIYSSM5UBXWP46X2AT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automatic continued fractions are transcendental or quadratic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yann Bugeaud","submitted_at":"2010-12-08T09:17:47Z","abstract_excerpt":"We establish new combinatorial transcendence criteria for continued fraction expansions. Let $\\alpha = [0; a_1, a_2,...]$ be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients $(a_{\\ell})_{\\ell \\ge 1}$ of $\\alpha$ cannot be generated by a finite automaton, and that the complexity function of $(a_{\\ell})_{\\ell \\ge 1}$ cannot increase too slowly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1709","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":"2026-05-18T03:40:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l49roiAvx3l8PESgOa7iDA6SHI/sDGZvBiiWgKylu9K4tblxFwf1mCxyfp0SZDeOhtBeo+FLC7YpiQZ6Hhr9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T10:13:06.639721Z"},"content_sha256":"9b928a3f788f83af45db90382748bdaaee9918a42a378444feb2d983840ce70c","schema_version":"1.0","event_id":"sha256:9b928a3f788f83af45db90382748bdaaee9918a42a378444feb2d983840ce70c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MKPONVEAEIYSSM5UBXWP46X2AT/bundle.json","state_url":"https://pith.science/pith/MKPONVEAEIYSSM5UBXWP46X2AT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MKPONVEAEIYSSM5UBXWP46X2AT/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":"2026-05-24T10:13:06Z","links":{"resolver":"https://pith.science/pith/MKPONVEAEIYSSM5UBXWP46X2AT","bundle":"https://pith.science/pith/MKPONVEAEIYSSM5UBXWP46X2AT/bundle.json","state":"https://pith.science/pith/MKPONVEAEIYSSM5UBXWP46X2AT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MKPONVEAEIYSSM5UBXWP46X2AT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MKPONVEAEIYSSM5UBXWP46X2AT","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":"f1f259227e09201ee5bb75ccde536360d789bc20def943d365e4d9b9a41716df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-08T09:17:47Z","title_canon_sha256":"bababfc276215ae1741945cfed073281654248d0b22d7335df06ef62af30aef4"},"schema_version":"1.0","source":{"id":"1012.1709","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1709","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1709v2","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1709","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"MKPONVEAEIYS","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MKPONVEAEIYSSM5U","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MKPONVEA","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:9b928a3f788f83af45db90382748bdaaee9918a42a378444feb2d983840ce70c","target":"graph","created_at":"2026-05-18T03:40:14Z","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 establish new combinatorial transcendence criteria for continued fraction expansions. Let $\\alpha = [0; a_1, a_2,...]$ be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients $(a_{\\ell})_{\\ell \\ge 1}$ of $\\alpha$ cannot be generated by a finite automaton, and that the complexity function of $(a_{\\ell})_{\\ell \\ge 1}$ cannot increase too slowly.","authors_text":"Yann Bugeaud","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-08T09:17:47Z","title":"Automatic continued fractions are transcendental or quadratic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1709","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":"sha256:8574163237e8154223184c4c68772f90bb4eb0c6f5748ac70a00284c0edea182","target":"record","created_at":"2026-05-18T03:40:14Z","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":"f1f259227e09201ee5bb75ccde536360d789bc20def943d365e4d9b9a41716df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-08T09:17:47Z","title_canon_sha256":"bababfc276215ae1741945cfed073281654248d0b22d7335df06ef62af30aef4"},"schema_version":"1.0","source":{"id":"1012.1709","kind":"arxiv","version":2}},"canonical_sha256":"629ee6d48022312933b40decfe7afa04fdfcc790d2f6e4b02a3673108e0d2044","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"629ee6d48022312933b40decfe7afa04fdfcc790d2f6e4b02a3673108e0d2044","first_computed_at":"2026-05-18T03:40:14.596565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:14.596565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n8YqzPwi4r2iuwVhoWJfXviToI+vDJ2k/ucLk8gNDJULvFrC9NujdtvOgTFlpAepbMUk/CMpkFN4jowVLBnMAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:14.597187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.1709","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8574163237e8154223184c4c68772f90bb4eb0c6f5748ac70a00284c0edea182","sha256:9b928a3f788f83af45db90382748bdaaee9918a42a378444feb2d983840ce70c"],"state_sha256":"98c4270f2381dbcbef5c813b413beda5fea33f969523e97be8ef3cfe7394f8cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/rbenT895ntQc2+LHs4PF3GgNpXfufINEPPpDVJcPx8eP/KjI944Zbc9gl+5iSNf6m6kniGtVofC8mm6Hgm1BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T10:13:06.643133Z","bundle_sha256":"40d45507c3bb925c2dbed01497d34946bd40a53ec3ccd33946536fc4be7825a1"}}