{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MCIX6EGTQRUE4YLPQ4AB4UWQMR","short_pith_number":"pith:MCIX6EGT","canonical_record":{"source":{"id":"1309.0760","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-03T18:07:37Z","cross_cats_sorted":[],"title_canon_sha256":"51cd3ae9f88ae6590a749f8b1cb0cdca8d46a843536c651ef00925c812ece94b","abstract_canon_sha256":"7c82b28ea5a974944dd2fc28a0c1f16882edcab418fa408cfe87b34ca1258127"},"schema_version":"1.0"},"canonical_sha256":"60917f10d384684e616f87001e52d0647522481e0945cd118f54c8236743a980","source":{"kind":"arxiv","id":"1309.0760","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0760","created_at":"2026-05-18T03:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0760v1","created_at":"2026-05-18T03:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0760","created_at":"2026-05-18T03:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"MCIX6EGTQRUE","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MCIX6EGTQRUE4YLP","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MCIX6EGT","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MCIX6EGTQRUE4YLPQ4AB4UWQMR","target":"record","payload":{"canonical_record":{"source":{"id":"1309.0760","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-03T18:07:37Z","cross_cats_sorted":[],"title_canon_sha256":"51cd3ae9f88ae6590a749f8b1cb0cdca8d46a843536c651ef00925c812ece94b","abstract_canon_sha256":"7c82b28ea5a974944dd2fc28a0c1f16882edcab418fa408cfe87b34ca1258127"},"schema_version":"1.0"},"canonical_sha256":"60917f10d384684e616f87001e52d0647522481e0945cd118f54c8236743a980","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:18.056865Z","signature_b64":"DKVbxoCWfAcuLX72J5lKOUNCzpqponqqsTwuvNU0luVuzYjzVtKwvE681/8gi+nDLOe+lnmzNYMnmFem6qZvDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60917f10d384684e616f87001e52d0647522481e0945cd118f54c8236743a980","last_reissued_at":"2026-05-18T03:14:18.056139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:18.056139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.0760","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":"2026-05-18T03:14:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cCOiAXlZapUZ/W3soiQN5JUsDJz5gSRwb+LJ7RqaGda+X9u73QZntX94rHfTRC+hEhziQXMpcv3ETqWkGrHTAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:41:25.465188Z"},"content_sha256":"6a53daf246732741f11aa0feb2fa6fdea068afb44d481c6aced9f1b10967ee3a","schema_version":"1.0","event_id":"sha256:6a53daf246732741f11aa0feb2fa6fdea068afb44d481c6aced9f1b10967ee3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MCIX6EGTQRUE4YLPQ4AB4UWQMR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Commensurable continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Pierre Arnoux, Thomas A. Schmidt","submitted_at":"2013-09-03T18:07:37Z","abstract_excerpt":"We compare two families of continued fractions algorithms, the symmetrized Rosen algorithm and the Veech algorithm. Each of these algorithms expands real numbers in terms of certain algebraic integers. We give explicit models of the natural extension of the maps associated with these algorithms; prove that these natural extensions are in fact conjugate to the first return map of the geodesic flow on a related surface; and, deduce that, up to a conjugacy, almost every real number has an infinite number of common approximants for both algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0760","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":"2026-05-18T03:14:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j4jwDI2eYG7U0t39hXoHuP71CE+SzZ0o0W74lUZ5RfmSobmR5h2YUbECagNq+XFUAifVfpVueetkjLHuJQNUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:41:25.465830Z"},"content_sha256":"6a283cb93a686d77c0d4bb2471460d8fbfa1f6ef305be9e8718ed235a77a55c2","schema_version":"1.0","event_id":"sha256:6a283cb93a686d77c0d4bb2471460d8fbfa1f6ef305be9e8718ed235a77a55c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MCIX6EGTQRUE4YLPQ4AB4UWQMR/bundle.json","state_url":"https://pith.science/pith/MCIX6EGTQRUE4YLPQ4AB4UWQMR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MCIX6EGTQRUE4YLPQ4AB4UWQMR/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":"2026-05-27T14:41:25Z","links":{"resolver":"https://pith.science/pith/MCIX6EGTQRUE4YLPQ4AB4UWQMR","bundle":"https://pith.science/pith/MCIX6EGTQRUE4YLPQ4AB4UWQMR/bundle.json","state":"https://pith.science/pith/MCIX6EGTQRUE4YLPQ4AB4UWQMR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MCIX6EGTQRUE4YLPQ4AB4UWQMR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MCIX6EGTQRUE4YLPQ4AB4UWQMR","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":"7c82b28ea5a974944dd2fc28a0c1f16882edcab418fa408cfe87b34ca1258127","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-03T18:07:37Z","title_canon_sha256":"51cd3ae9f88ae6590a749f8b1cb0cdca8d46a843536c651ef00925c812ece94b"},"schema_version":"1.0","source":{"id":"1309.0760","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0760","created_at":"2026-05-18T03:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0760v1","created_at":"2026-05-18T03:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0760","created_at":"2026-05-18T03:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"MCIX6EGTQRUE","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MCIX6EGTQRUE4YLP","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MCIX6EGT","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:6a283cb93a686d77c0d4bb2471460d8fbfa1f6ef305be9e8718ed235a77a55c2","target":"graph","created_at":"2026-05-18T03:14:18Z","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 compare two families of continued fractions algorithms, the symmetrized Rosen algorithm and the Veech algorithm. Each of these algorithms expands real numbers in terms of certain algebraic integers. We give explicit models of the natural extension of the maps associated with these algorithms; prove that these natural extensions are in fact conjugate to the first return map of the geodesic flow on a related surface; and, deduce that, up to a conjugacy, almost every real number has an infinite number of common approximants for both algorithms.","authors_text":"Pierre Arnoux, Thomas A. Schmidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-03T18:07:37Z","title":"Commensurable continued fractions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0760","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":"sha256:6a53daf246732741f11aa0feb2fa6fdea068afb44d481c6aced9f1b10967ee3a","target":"record","created_at":"2026-05-18T03:14:18Z","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":"7c82b28ea5a974944dd2fc28a0c1f16882edcab418fa408cfe87b34ca1258127","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-03T18:07:37Z","title_canon_sha256":"51cd3ae9f88ae6590a749f8b1cb0cdca8d46a843536c651ef00925c812ece94b"},"schema_version":"1.0","source":{"id":"1309.0760","kind":"arxiv","version":1}},"canonical_sha256":"60917f10d384684e616f87001e52d0647522481e0945cd118f54c8236743a980","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60917f10d384684e616f87001e52d0647522481e0945cd118f54c8236743a980","first_computed_at":"2026-05-18T03:14:18.056139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:18.056139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DKVbxoCWfAcuLX72J5lKOUNCzpqponqqsTwuvNU0luVuzYjzVtKwvE681/8gi+nDLOe+lnmzNYMnmFem6qZvDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:18.056865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0760","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a53daf246732741f11aa0feb2fa6fdea068afb44d481c6aced9f1b10967ee3a","sha256:6a283cb93a686d77c0d4bb2471460d8fbfa1f6ef305be9e8718ed235a77a55c2"],"state_sha256":"89fe5863aea9d11ab8522792cfcdbeb062676b192dde9a3cc7a912fd44d5a4b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mTF/99jM6/4sS9+6F1KuzbiADZM6WS15eXIzL1FeiT3YIiFg0QaV69TlLg8myVA9UuAUJw6htm1Br1xkqvMjBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:41:25.469264Z","bundle_sha256":"03fff76ed06c89959cfd69c9a33a95fab86ff614da413a96e59d19a1a2b722d6"}}