{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ASFPFU3PSWZ7I2KRJBPNXBYAAP","short_pith_number":"pith:ASFPFU3P","schema_version":"1.0","canonical_sha256":"048af2d36f95b3f46951485edb870003e512613e5435753434856546303fe9e7","source":{"kind":"arxiv","id":"1511.08399","version":1},"attestation_state":"computed","paper":{"title":"$3$-dimensional Continued Fraction Algorithms Cheat Sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.DS","authors_text":"S\\'ebastien Labb\\'e","submitted_at":"2015-11-26T14:34:50Z","abstract_excerpt":"Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applications on some subcone of $\\mathbb{R}^d$. We consider multidimensional continued fraction algorithms that acts symmetrically on the positive cone $\\mathbb{R}^d_+$ for $d=3$. We include well-known and old ones (Poincar\\'e, Brun, Selmer, Fully Subtractive) and new ones (Arnoux-Rauzy-Poincar\\'e, Reverse, Cassaigne).\n  For each algorithm, one page (called cheat sheet) gathers a handful of informations most of them generated"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.08399","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-26T14:34:50Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"21098750509db0f6cd6017dd407d2c9b48cc5d1a2ac08c286a4d8f4c459e0a8b","abstract_canon_sha256":"5b300102fd2dfb72d6173a283dc7a5c47e74aa84d0739ca80ae11e35dd5547ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:54.167931Z","signature_b64":"2nKCuZISF12m2iDNm3U4xvIGW9HpDENP3/1COT2WMhoH9x/jB4OrTsn5XyfDhEX5cqJsYL/0xFSMc6sSctxTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"048af2d36f95b3f46951485edb870003e512613e5435753434856546303fe9e7","last_reissued_at":"2026-05-18T01:25:54.167146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:54.167146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$3$-dimensional Continued Fraction Algorithms Cheat Sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.DS","authors_text":"S\\'ebastien Labb\\'e","submitted_at":"2015-11-26T14:34:50Z","abstract_excerpt":"Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applications on some subcone of $\\mathbb{R}^d$. We consider multidimensional continued fraction algorithms that acts symmetrically on the positive cone $\\mathbb{R}^d_+$ for $d=3$. We include well-known and old ones (Poincar\\'e, Brun, Selmer, Fully Subtractive) and new ones (Arnoux-Rauzy-Poincar\\'e, Reverse, Cassaigne).\n  For each algorithm, one page (called cheat sheet) gathers a handful of informations most of them generated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08399","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.08399","created_at":"2026-05-18T01:25:54.167274+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.08399v1","created_at":"2026-05-18T01:25:54.167274+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08399","created_at":"2026-05-18T01:25:54.167274+00:00"},{"alias_kind":"pith_short_12","alias_value":"ASFPFU3PSWZ7","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"ASFPFU3PSWZ7I2KR","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"ASFPFU3P","created_at":"2026-05-18T12:29:10.953037+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ASFPFU3PSWZ7I2KRJBPNXBYAAP","json":"https://pith.science/pith/ASFPFU3PSWZ7I2KRJBPNXBYAAP.json","graph_json":"https://pith.science/api/pith-number/ASFPFU3PSWZ7I2KRJBPNXBYAAP/graph.json","events_json":"https://pith.science/api/pith-number/ASFPFU3PSWZ7I2KRJBPNXBYAAP/events.json","paper":"https://pith.science/paper/ASFPFU3P"},"agent_actions":{"view_html":"https://pith.science/pith/ASFPFU3PSWZ7I2KRJBPNXBYAAP","download_json":"https://pith.science/pith/ASFPFU3PSWZ7I2KRJBPNXBYAAP.json","view_paper":"https://pith.science/paper/ASFPFU3P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.08399&json=true","fetch_graph":"https://pith.science/api/pith-number/ASFPFU3PSWZ7I2KRJBPNXBYAAP/graph.json","fetch_events":"https://pith.science/api/pith-number/ASFPFU3PSWZ7I2KRJBPNXBYAAP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ASFPFU3PSWZ7I2KRJBPNXBYAAP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ASFPFU3PSWZ7I2KRJBPNXBYAAP/action/storage_attestation","attest_author":"https://pith.science/pith/ASFPFU3PSWZ7I2KRJBPNXBYAAP/action/author_attestation","sign_citation":"https://pith.science/pith/ASFPFU3PSWZ7I2KRJBPNXBYAAP/action/citation_signature","submit_replication":"https://pith.science/pith/ASFPFU3PSWZ7I2KRJBPNXBYAAP/action/replication_record"}},"created_at":"2026-05-18T01:25:54.167274+00:00","updated_at":"2026-05-18T01:25:54.167274+00:00"}