{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IIM5CAH4X7T2VHDOZRL3IMLXRS","short_pith_number":"pith:IIM5CAH4","schema_version":"1.0","canonical_sha256":"4219d100fcbfe7aa9c6ecc57b431778c94fefd08cf47ceb379ce57d1130e7dc0","source":{"kind":"arxiv","id":"1302.5008","version":3},"attestation_state":"computed","paper":{"title":"Classical homogeneous multidimensional continued fraction algorithms are ergodic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Arnaldo Nogueira, Jonathan Chaika","submitted_at":"2013-02-20T15:59:52Z","abstract_excerpt":"Homogeneous continued fraction algorithms are multidimensional generalizations of the classical Euclidean algorithm, the dissipative map $$ (x_1,x_2) \\in \\mathbb{R}_+^2 \\longmapsto \\left\\{\\begin{array}{ll}\n  (x_1 - x_2, x_2), & \\mbox{if $x_1 \\geq x_2$}\n  (x_1, x_2 - x_1), & \\mbox{otherwise.} \\end{array} \\right. $$ We focus on those which act piecewise linearly on finitely many copies of positive cones which we call Rauzy induction type algorithms.\n  In particular, a variation Selmer algorithm belongs to this class. We prove that Rauzy induction type algorithms, as well as Selmer algorithms, ar"},"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":"1302.5008","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-20T15:59:52Z","cross_cats_sorted":[],"title_canon_sha256":"a6d4806eeaad53ee327ca77c35d87a45702fee5eb92e921fe98e69fb504943d8","abstract_canon_sha256":"d221c9d40be3122704c8e64ae4cf6f7e8f7ac33d164e3cdd6afb5bd716cf0054"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:22.256884Z","signature_b64":"emuHiFTENMo7zokzcZ0E0T+6IbY0/pHcJcV4szelyaVEOKMIIYD/O9Ny/DTfrJ/Fmim8zbtZoP2SYuQIFrjYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4219d100fcbfe7aa9c6ecc57b431778c94fefd08cf47ceb379ce57d1130e7dc0","last_reissued_at":"2026-05-18T03:19:22.256203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:22.256203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classical homogeneous multidimensional continued fraction algorithms are ergodic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Arnaldo Nogueira, Jonathan Chaika","submitted_at":"2013-02-20T15:59:52Z","abstract_excerpt":"Homogeneous continued fraction algorithms are multidimensional generalizations of the classical Euclidean algorithm, the dissipative map $$ (x_1,x_2) \\in \\mathbb{R}_+^2 \\longmapsto \\left\\{\\begin{array}{ll}\n  (x_1 - x_2, x_2), & \\mbox{if $x_1 \\geq x_2$}\n  (x_1, x_2 - x_1), & \\mbox{otherwise.} \\end{array} \\right. $$ We focus on those which act piecewise linearly on finitely many copies of positive cones which we call Rauzy induction type algorithms.\n  In particular, a variation Selmer algorithm belongs to this class. We prove that Rauzy induction type algorithms, as well as Selmer algorithms, ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5008","kind":"arxiv","version":3},"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":"1302.5008","created_at":"2026-05-18T03:19:22.256309+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.5008v3","created_at":"2026-05-18T03:19:22.256309+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5008","created_at":"2026-05-18T03:19:22.256309+00:00"},{"alias_kind":"pith_short_12","alias_value":"IIM5CAH4X7T2","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"IIM5CAH4X7T2VHDO","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"IIM5CAH4","created_at":"2026-05-18T12:27:46.883200+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/IIM5CAH4X7T2VHDOZRL3IMLXRS","json":"https://pith.science/pith/IIM5CAH4X7T2VHDOZRL3IMLXRS.json","graph_json":"https://pith.science/api/pith-number/IIM5CAH4X7T2VHDOZRL3IMLXRS/graph.json","events_json":"https://pith.science/api/pith-number/IIM5CAH4X7T2VHDOZRL3IMLXRS/events.json","paper":"https://pith.science/paper/IIM5CAH4"},"agent_actions":{"view_html":"https://pith.science/pith/IIM5CAH4X7T2VHDOZRL3IMLXRS","download_json":"https://pith.science/pith/IIM5CAH4X7T2VHDOZRL3IMLXRS.json","view_paper":"https://pith.science/paper/IIM5CAH4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.5008&json=true","fetch_graph":"https://pith.science/api/pith-number/IIM5CAH4X7T2VHDOZRL3IMLXRS/graph.json","fetch_events":"https://pith.science/api/pith-number/IIM5CAH4X7T2VHDOZRL3IMLXRS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IIM5CAH4X7T2VHDOZRL3IMLXRS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IIM5CAH4X7T2VHDOZRL3IMLXRS/action/storage_attestation","attest_author":"https://pith.science/pith/IIM5CAH4X7T2VHDOZRL3IMLXRS/action/author_attestation","sign_citation":"https://pith.science/pith/IIM5CAH4X7T2VHDOZRL3IMLXRS/action/citation_signature","submit_replication":"https://pith.science/pith/IIM5CAH4X7T2VHDOZRL3IMLXRS/action/replication_record"}},"created_at":"2026-05-18T03:19:22.256309+00:00","updated_at":"2026-05-18T03:19:22.256309+00:00"}