{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:27AOCP7B75YN6DDVSSOOY4A5LN","short_pith_number":"pith:27AOCP7B","schema_version":"1.0","canonical_sha256":"d7c0e13fe1ff70df0c75949cec701d5b5383dc08852f5b7db6511545a7703969","source":{"kind":"arxiv","id":"1810.10668","version":2},"attestation_state":"computed","paper":{"title":"The Boca-Cobeli-Zaharescu Map Analogue for the Hecke Triangle Groups $G_q$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Diaaeldin Taha","submitted_at":"2018-10-25T00:52:52Z","abstract_excerpt":"The Farey sequence $\\mathcal{F}(Q)$ at level $Q$ is the sequence of irreducible fractions in $[0, 1]$ with denominators not exceeding $Q$, arranged in increasing order of magnitude. A simple ``next-term'' algorithm exists for generating the elements of $\\mathcal{F}(Q)$ in increasing or decreasing order. That algorithm, along with a number of other properties of the Farey sequence, was encoded by F. Boca, C. Cobeli, and A. Zaharescu into what is now known as the Boca-Cobeli-Zaharescu (BCZ) map, and used to attack several problems that can be described using the statistics of subsets of the Fare"},"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":"1810.10668","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-25T00:52:52Z","cross_cats_sorted":[],"title_canon_sha256":"9a43c2a3c063c2f476948561eb9e36010dcef1035dd8d5907b23cf210e4acced","abstract_canon_sha256":"f4c88826fae37e04e289380cebae4ad8f83242c0b6922fc42c0a0d7653e90dca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:50.665248Z","signature_b64":"CLMxmyG7LIsKBOjsMiBpML5GS2Z6ABN2lXv3RuPmvYVgHPf2FaLAdPnwwcK3LGAPoak034/M8YK4z1T/ODF3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7c0e13fe1ff70df0c75949cec701d5b5383dc08852f5b7db6511545a7703969","last_reissued_at":"2026-05-17T23:49:50.664602Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:50.664602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Boca-Cobeli-Zaharescu Map Analogue for the Hecke Triangle Groups $G_q$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Diaaeldin Taha","submitted_at":"2018-10-25T00:52:52Z","abstract_excerpt":"The Farey sequence $\\mathcal{F}(Q)$ at level $Q$ is the sequence of irreducible fractions in $[0, 1]$ with denominators not exceeding $Q$, arranged in increasing order of magnitude. A simple ``next-term'' algorithm exists for generating the elements of $\\mathcal{F}(Q)$ in increasing or decreasing order. That algorithm, along with a number of other properties of the Farey sequence, was encoded by F. Boca, C. Cobeli, and A. Zaharescu into what is now known as the Boca-Cobeli-Zaharescu (BCZ) map, and used to attack several problems that can be described using the statistics of subsets of the Fare"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10668","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.10668","created_at":"2026-05-17T23:49:50.664703+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.10668v2","created_at":"2026-05-17T23:49:50.664703+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10668","created_at":"2026-05-17T23:49:50.664703+00:00"},{"alias_kind":"pith_short_12","alias_value":"27AOCP7B75YN","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"27AOCP7B75YN6DDV","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"27AOCP7B","created_at":"2026-05-18T12:31:59.375834+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/27AOCP7B75YN6DDVSSOOY4A5LN","json":"https://pith.science/pith/27AOCP7B75YN6DDVSSOOY4A5LN.json","graph_json":"https://pith.science/api/pith-number/27AOCP7B75YN6DDVSSOOY4A5LN/graph.json","events_json":"https://pith.science/api/pith-number/27AOCP7B75YN6DDVSSOOY4A5LN/events.json","paper":"https://pith.science/paper/27AOCP7B"},"agent_actions":{"view_html":"https://pith.science/pith/27AOCP7B75YN6DDVSSOOY4A5LN","download_json":"https://pith.science/pith/27AOCP7B75YN6DDVSSOOY4A5LN.json","view_paper":"https://pith.science/paper/27AOCP7B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.10668&json=true","fetch_graph":"https://pith.science/api/pith-number/27AOCP7B75YN6DDVSSOOY4A5LN/graph.json","fetch_events":"https://pith.science/api/pith-number/27AOCP7B75YN6DDVSSOOY4A5LN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/27AOCP7B75YN6DDVSSOOY4A5LN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/27AOCP7B75YN6DDVSSOOY4A5LN/action/storage_attestation","attest_author":"https://pith.science/pith/27AOCP7B75YN6DDVSSOOY4A5LN/action/author_attestation","sign_citation":"https://pith.science/pith/27AOCP7B75YN6DDVSSOOY4A5LN/action/citation_signature","submit_replication":"https://pith.science/pith/27AOCP7B75YN6DDVSSOOY4A5LN/action/replication_record"}},"created_at":"2026-05-17T23:49:50.664703+00:00","updated_at":"2026-05-17T23:49:50.664703+00:00"}