{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:Z4URL6MRTMI622VAMXACJP5TRR","short_pith_number":"pith:Z4URL6MR","schema_version":"1.0","canonical_sha256":"cf2915f9919b11ed6aa065c024bfb38c5b3f47e1658be837c27fe6a3bc2876bc","source":{"kind":"arxiv","id":"1404.5857","version":2},"attestation_state":"computed","paper":{"title":"On the asymptotics of the $\\alpha$-Farey transfer operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bernd O. Stratmann, Johannes Kautzsch, Marc Kesseb\\\"ohmer, Tony Samuel","submitted_at":"2014-04-23T15:12:38Z","abstract_excerpt":"We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic $\\alpha$-Farey maps. We provide a family of observables which are Riemann integrable, locally constant and of bounded variation, and for which the iterates of the transfer operator, when applied to one of these observables, is not asymptotic to a constant times the wandering rate on the first element of the partition $\\alpha$. Subsequently, sufficient conditions on observables are given under which this expected asymptotic holds. In particular, we obtain an extension theorem which establishes that, if th"},"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":"1404.5857","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-23T15:12:38Z","cross_cats_sorted":[],"title_canon_sha256":"c9a731c88058c6c733b32f8bc49c3c875db53e00fa357f8fc6ccb523a7ec11da","abstract_canon_sha256":"2649b2b98c9bfb1bc911d0d3b118dfb9945b4434346bd08893bc7d5c7cdc113c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:21.921373Z","signature_b64":"tsVHezzUAxT+zq66huCzoBE47w1E+3PvepOKJLzTGR/djk4Gn8elLnl/Y0m0v7tXrZE5GlvARIKJ6ELujHTUAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf2915f9919b11ed6aa065c024bfb38c5b3f47e1658be837c27fe6a3bc2876bc","last_reissued_at":"2026-05-18T00:32:21.920832Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:21.920832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the asymptotics of the $\\alpha$-Farey transfer operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bernd O. Stratmann, Johannes Kautzsch, Marc Kesseb\\\"ohmer, Tony Samuel","submitted_at":"2014-04-23T15:12:38Z","abstract_excerpt":"We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic $\\alpha$-Farey maps. We provide a family of observables which are Riemann integrable, locally constant and of bounded variation, and for which the iterates of the transfer operator, when applied to one of these observables, is not asymptotic to a constant times the wandering rate on the first element of the partition $\\alpha$. Subsequently, sufficient conditions on observables are given under which this expected asymptotic holds. In particular, we obtain an extension theorem which establishes that, if th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5857","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":"1404.5857","created_at":"2026-05-18T00:32:21.920904+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.5857v2","created_at":"2026-05-18T00:32:21.920904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5857","created_at":"2026-05-18T00:32:21.920904+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z4URL6MRTMI6","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z4URL6MRTMI622VA","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z4URL6MR","created_at":"2026-05-18T12:28:59.999130+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/Z4URL6MRTMI622VAMXACJP5TRR","json":"https://pith.science/pith/Z4URL6MRTMI622VAMXACJP5TRR.json","graph_json":"https://pith.science/api/pith-number/Z4URL6MRTMI622VAMXACJP5TRR/graph.json","events_json":"https://pith.science/api/pith-number/Z4URL6MRTMI622VAMXACJP5TRR/events.json","paper":"https://pith.science/paper/Z4URL6MR"},"agent_actions":{"view_html":"https://pith.science/pith/Z4URL6MRTMI622VAMXACJP5TRR","download_json":"https://pith.science/pith/Z4URL6MRTMI622VAMXACJP5TRR.json","view_paper":"https://pith.science/paper/Z4URL6MR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.5857&json=true","fetch_graph":"https://pith.science/api/pith-number/Z4URL6MRTMI622VAMXACJP5TRR/graph.json","fetch_events":"https://pith.science/api/pith-number/Z4URL6MRTMI622VAMXACJP5TRR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z4URL6MRTMI622VAMXACJP5TRR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z4URL6MRTMI622VAMXACJP5TRR/action/storage_attestation","attest_author":"https://pith.science/pith/Z4URL6MRTMI622VAMXACJP5TRR/action/author_attestation","sign_citation":"https://pith.science/pith/Z4URL6MRTMI622VAMXACJP5TRR/action/citation_signature","submit_replication":"https://pith.science/pith/Z4URL6MRTMI622VAMXACJP5TRR/action/replication_record"}},"created_at":"2026-05-18T00:32:21.920904+00:00","updated_at":"2026-05-18T00:32:21.920904+00:00"}