{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:THIHTFR5BSYVUX6CHAK3Y52W7C","short_pith_number":"pith:THIHTFR5","schema_version":"1.0","canonical_sha256":"99d079963d0cb15a5fc23815bc7756f884589a2d2880f78ec6416159775f4f41","source":{"kind":"arxiv","id":"0912.2329","version":1},"attestation_state":"computed","paper":{"title":"The entropy of alpha-continued fractions: numerical results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Alessandro Profeti, Carlo Carminati, Giulio Tiozzo, Stefano Marmi","submitted_at":"2009-12-11T20:03:18Z","abstract_excerpt":"We consider the one-parameter family of interval maps arising from generalized continued fraction expansions known as alpha-continued fractions. For such maps, we perform a numerical study of the behaviour of metric entropy as a function of the parameter. The behaviour of entropy is known to be quite regular for parameters for which a matching condition on the orbits of the endpoints holds. We give a detailed description of the set M where this condition is met: it consists of a countable union of open intervals, corresponding to different combinatorial data, which appear to be arranged in a h"},"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":"0912.2329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-11T20:03:18Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"e5496c71d226d6607c3c488fab509d050b9263d9fd71143ada01ddf71041dbf4","abstract_canon_sha256":"2b6a7e859b8ea8aed6ed12cd6929271793871c9c4eb8a2a4909a61ade1d14707"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:24.359672Z","signature_b64":"OkhhkNZzDYC+g+9fURyIg/yj4/EtNdbTq7TaFChz6bEKW97D44gGBMHwOtc5SRFrGUIE5qZi3sqvPoDANSjfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99d079963d0cb15a5fc23815bc7756f884589a2d2880f78ec6416159775f4f41","last_reissued_at":"2026-05-18T02:10:24.358960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:24.358960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The entropy of alpha-continued fractions: numerical results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Alessandro Profeti, Carlo Carminati, Giulio Tiozzo, Stefano Marmi","submitted_at":"2009-12-11T20:03:18Z","abstract_excerpt":"We consider the one-parameter family of interval maps arising from generalized continued fraction expansions known as alpha-continued fractions. For such maps, we perform a numerical study of the behaviour of metric entropy as a function of the parameter. The behaviour of entropy is known to be quite regular for parameters for which a matching condition on the orbits of the endpoints holds. We give a detailed description of the set M where this condition is met: it consists of a countable union of open intervals, corresponding to different combinatorial data, which appear to be arranged in a h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2329","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":"0912.2329","created_at":"2026-05-18T02:10:24.359064+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.2329v1","created_at":"2026-05-18T02:10:24.359064+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2329","created_at":"2026-05-18T02:10:24.359064+00:00"},{"alias_kind":"pith_short_12","alias_value":"THIHTFR5BSYV","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"THIHTFR5BSYVUX6C","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"THIHTFR5","created_at":"2026-05-18T12:26:01.383474+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/THIHTFR5BSYVUX6CHAK3Y52W7C","json":"https://pith.science/pith/THIHTFR5BSYVUX6CHAK3Y52W7C.json","graph_json":"https://pith.science/api/pith-number/THIHTFR5BSYVUX6CHAK3Y52W7C/graph.json","events_json":"https://pith.science/api/pith-number/THIHTFR5BSYVUX6CHAK3Y52W7C/events.json","paper":"https://pith.science/paper/THIHTFR5"},"agent_actions":{"view_html":"https://pith.science/pith/THIHTFR5BSYVUX6CHAK3Y52W7C","download_json":"https://pith.science/pith/THIHTFR5BSYVUX6CHAK3Y52W7C.json","view_paper":"https://pith.science/paper/THIHTFR5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.2329&json=true","fetch_graph":"https://pith.science/api/pith-number/THIHTFR5BSYVUX6CHAK3Y52W7C/graph.json","fetch_events":"https://pith.science/api/pith-number/THIHTFR5BSYVUX6CHAK3Y52W7C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/THIHTFR5BSYVUX6CHAK3Y52W7C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/THIHTFR5BSYVUX6CHAK3Y52W7C/action/storage_attestation","attest_author":"https://pith.science/pith/THIHTFR5BSYVUX6CHAK3Y52W7C/action/author_attestation","sign_citation":"https://pith.science/pith/THIHTFR5BSYVUX6CHAK3Y52W7C/action/citation_signature","submit_replication":"https://pith.science/pith/THIHTFR5BSYVUX6CHAK3Y52W7C/action/replication_record"}},"created_at":"2026-05-18T02:10:24.359064+00:00","updated_at":"2026-05-18T02:10:24.359064+00:00"}