{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:NZQO7OJYTXPXZEXAW4LNIOPTSU","short_pith_number":"pith:NZQO7OJY","canonical_record":{"source":{"id":"math/0511677","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2005-11-28T13:07:43Z","cross_cats_sorted":[],"title_canon_sha256":"d5b4719625025667d9cc5b4c7533448d89e25ccc8aeb46cdb88b77ea41b88c69","abstract_canon_sha256":"ca67dd8fc9ead74d85507740ee2b986ae21d52f88f9cb2500f7152f710b3a1d3"},"schema_version":"1.0"},"canonical_sha256":"6e60efb9389ddf7c92e0b716d439f39538df1316f2000707b95e6f8731feda9a","source":{"kind":"arxiv","id":"math/0511677","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0511677","created_at":"2026-05-18T03:56:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0511677v1","created_at":"2026-05-18T03:56:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0511677","created_at":"2026-05-18T03:56:23Z"},{"alias_kind":"pith_short_12","alias_value":"NZQO7OJYTXPX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NZQO7OJYTXPXZEXA","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NZQO7OJY","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:NZQO7OJYTXPXZEXAW4LNIOPTSU","target":"record","payload":{"canonical_record":{"source":{"id":"math/0511677","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2005-11-28T13:07:43Z","cross_cats_sorted":[],"title_canon_sha256":"d5b4719625025667d9cc5b4c7533448d89e25ccc8aeb46cdb88b77ea41b88c69","abstract_canon_sha256":"ca67dd8fc9ead74d85507740ee2b986ae21d52f88f9cb2500f7152f710b3a1d3"},"schema_version":"1.0"},"canonical_sha256":"6e60efb9389ddf7c92e0b716d439f39538df1316f2000707b95e6f8731feda9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:23.253201Z","signature_b64":"pow6d7uIDXpmlA0yiP8k+dz+BL+itV6U8SQ23VQYaesd5sT+g8ycQBli24uhq+UOziEAa4FJWLBD+GwOGd6pCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e60efb9389ddf7c92e0b716d439f39538df1316f2000707b95e6f8731feda9a","last_reissued_at":"2026-05-18T03:56:23.252529Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:23.252529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0511677","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":"2026-05-18T03:56:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KlvJz0U94PqMshtNyDA58JbkZsTB7kObqb0nqZF3vtYCLzXmQn2JRtJZDEISb6y5yx83ZmMfbgZ+NHd5zcW2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:28:15.442520Z"},"content_sha256":"c85b53eb18fdc44eb4a327115d4a30c6af1e34b2919812776116719aaf91fc42","schema_version":"1.0","event_id":"sha256:c85b53eb18fdc44eb4a327115d4a30c6af1e34b2919812776116719aaf91fc42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:NZQO7OJYTXPXZEXAW4LNIOPTSU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the complexity of algebraic numbers II. Continued fractions","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Boris Adamczewski (ICJ), Yann Bugeaud (IRMA)","submitted_at":"2005-11-28T13:07:43Z","abstract_excerpt":"The continued fraction expansion of an irrational number $\\alpha$ is eventually periodic if and only if $\\alpha$ is a quadratic irrationality. However, very little is known regarding the size of the partial quotients of algebraic real numbers of degree at least three. Because of some numerical evidence and a belief that these numbers behave like most numbers in this respect, it is often conjectured that their partial quotients form an unbounded sequence. More modestly, we may expect that if the sequence of partial quotients of an irrational number $\\alpha$ is, in some sense, \"simple\", then $\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511677","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":"2026-05-18T03:56:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DhdgJSlHRb5/6O+uUxVPgZLnYqVkmK1KT9HucFVdi3YueZP8ZvQAT2lOc+4gDLIz4DLFiyXCXMqdM2PUYUXRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:28:15.442862Z"},"content_sha256":"1c6703b2e648dd14ff4c85762076ade656289bcd71f79ae325c5e92f4f339884","schema_version":"1.0","event_id":"sha256:1c6703b2e648dd14ff4c85762076ade656289bcd71f79ae325c5e92f4f339884"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZQO7OJYTXPXZEXAW4LNIOPTSU/bundle.json","state_url":"https://pith.science/pith/NZQO7OJYTXPXZEXAW4LNIOPTSU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZQO7OJYTXPXZEXAW4LNIOPTSU/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":"2026-06-25T06:28:15Z","links":{"resolver":"https://pith.science/pith/NZQO7OJYTXPXZEXAW4LNIOPTSU","bundle":"https://pith.science/pith/NZQO7OJYTXPXZEXAW4LNIOPTSU/bundle.json","state":"https://pith.science/pith/NZQO7OJYTXPXZEXAW4LNIOPTSU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZQO7OJYTXPXZEXAW4LNIOPTSU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:NZQO7OJYTXPXZEXAW4LNIOPTSU","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":"ca67dd8fc9ead74d85507740ee2b986ae21d52f88f9cb2500f7152f710b3a1d3","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2005-11-28T13:07:43Z","title_canon_sha256":"d5b4719625025667d9cc5b4c7533448d89e25ccc8aeb46cdb88b77ea41b88c69"},"schema_version":"1.0","source":{"id":"math/0511677","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0511677","created_at":"2026-05-18T03:56:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0511677v1","created_at":"2026-05-18T03:56:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0511677","created_at":"2026-05-18T03:56:23Z"},{"alias_kind":"pith_short_12","alias_value":"NZQO7OJYTXPX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NZQO7OJYTXPXZEXA","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NZQO7OJY","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:1c6703b2e648dd14ff4c85762076ade656289bcd71f79ae325c5e92f4f339884","target":"graph","created_at":"2026-05-18T03:56:23Z","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":"The continued fraction expansion of an irrational number $\\alpha$ is eventually periodic if and only if $\\alpha$ is a quadratic irrationality. However, very little is known regarding the size of the partial quotients of algebraic real numbers of degree at least three. Because of some numerical evidence and a belief that these numbers behave like most numbers in this respect, it is often conjectured that their partial quotients form an unbounded sequence. More modestly, we may expect that if the sequence of partial quotients of an irrational number $\\alpha$ is, in some sense, \"simple\", then $\\a","authors_text":"Boris Adamczewski (ICJ), Yann Bugeaud (IRMA)","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2005-11-28T13:07:43Z","title":"On the complexity of algebraic numbers II. Continued fractions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511677","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:c85b53eb18fdc44eb4a327115d4a30c6af1e34b2919812776116719aaf91fc42","target":"record","created_at":"2026-05-18T03:56:23Z","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":"ca67dd8fc9ead74d85507740ee2b986ae21d52f88f9cb2500f7152f710b3a1d3","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2005-11-28T13:07:43Z","title_canon_sha256":"d5b4719625025667d9cc5b4c7533448d89e25ccc8aeb46cdb88b77ea41b88c69"},"schema_version":"1.0","source":{"id":"math/0511677","kind":"arxiv","version":1}},"canonical_sha256":"6e60efb9389ddf7c92e0b716d439f39538df1316f2000707b95e6f8731feda9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e60efb9389ddf7c92e0b716d439f39538df1316f2000707b95e6f8731feda9a","first_computed_at":"2026-05-18T03:56:23.252529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:23.252529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pow6d7uIDXpmlA0yiP8k+dz+BL+itV6U8SQ23VQYaesd5sT+g8ycQBli24uhq+UOziEAa4FJWLBD+GwOGd6pCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:23.253201Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0511677","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c85b53eb18fdc44eb4a327115d4a30c6af1e34b2919812776116719aaf91fc42","sha256:1c6703b2e648dd14ff4c85762076ade656289bcd71f79ae325c5e92f4f339884"],"state_sha256":"db36a9bd59598bed2474bce466aa9bddcde5375a9c7095e5882efbe99ad4dbd5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Na3m4bD+8vgmFumi39UzbRJHsdlgiKaa74fHmSiMKMgBjqtG6TU/5mUDhu67GOjKdFIXepEuUW1/zq8tXBYeBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T06:28:15.444768Z","bundle_sha256":"cea4b9f9269d7e554b53d9d22f796bc3c14a07797e0175acb039274e76c79b4d"}}