{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7FPAS3U2SXZ3LNEZCZAXQXNIHD","short_pith_number":"pith:7FPAS3U2","schema_version":"1.0","canonical_sha256":"f95e096e9a95f3b5b4991641785da838f51a75c4dea7e4940daa2fb89da4f352","source":{"kind":"arxiv","id":"1502.01793","version":3},"attestation_state":"computed","paper":{"title":"Rotational beta expansion: Ergodicity and Soficness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Jonathan Caalim, Shigeki Akiyama","submitted_at":"2015-02-06T04:54:25Z","abstract_excerpt":"We study a family of piecewise expanding maps on the plane, generated by composition of a rotation and an expansive similitude of expansion constant $\\beta$. We give two constants $B_1$ and $B_2$ depending only on the fundamental domain that if $\\beta>B_1$ then the expanding map has a unique absolutely continuous invariant probability measure, and if $\\beta>B_2$ then it is equivalent to $2$-dimensional Lebesgue measure. Restricting to a rotation generated by $q$-th root of unity $\\zeta$ with all parameters in $\\mathbb{Q}(\\zeta,\\beta)$, it gives a sofic system when $\\cos(2\\pi/q) \\in \\mathbb{Q}("},"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":"1502.01793","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-06T04:54:25Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"aa77e57011bcf6940b49046a29ac1cd869bc7f4c4e84a582ea56bc8c2148639b","abstract_canon_sha256":"0058476cd111434998c992cd12def54fc4f94d683073bdeaa9cb17a0e2af21e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:06.342295Z","signature_b64":"R4lqu7Hd6RGF8cNgdQwjve4flEAyJFpFK0/yebivBG8KbLA3R5zwIkzXokfxmk3hfpaRsJsXMlYpcScZuy7iCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f95e096e9a95f3b5b4991641785da838f51a75c4dea7e4940daa2fb89da4f352","last_reissued_at":"2026-05-18T01:33:06.341752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:06.341752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rotational beta expansion: Ergodicity and Soficness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Jonathan Caalim, Shigeki Akiyama","submitted_at":"2015-02-06T04:54:25Z","abstract_excerpt":"We study a family of piecewise expanding maps on the plane, generated by composition of a rotation and an expansive similitude of expansion constant $\\beta$. We give two constants $B_1$ and $B_2$ depending only on the fundamental domain that if $\\beta>B_1$ then the expanding map has a unique absolutely continuous invariant probability measure, and if $\\beta>B_2$ then it is equivalent to $2$-dimensional Lebesgue measure. Restricting to a rotation generated by $q$-th root of unity $\\zeta$ with all parameters in $\\mathbb{Q}(\\zeta,\\beta)$, it gives a sofic system when $\\cos(2\\pi/q) \\in \\mathbb{Q}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01793","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":"1502.01793","created_at":"2026-05-18T01:33:06.341833+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.01793v3","created_at":"2026-05-18T01:33:06.341833+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01793","created_at":"2026-05-18T01:33:06.341833+00:00"},{"alias_kind":"pith_short_12","alias_value":"7FPAS3U2SXZ3","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7FPAS3U2SXZ3LNEZ","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7FPAS3U2","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/7FPAS3U2SXZ3LNEZCZAXQXNIHD","json":"https://pith.science/pith/7FPAS3U2SXZ3LNEZCZAXQXNIHD.json","graph_json":"https://pith.science/api/pith-number/7FPAS3U2SXZ3LNEZCZAXQXNIHD/graph.json","events_json":"https://pith.science/api/pith-number/7FPAS3U2SXZ3LNEZCZAXQXNIHD/events.json","paper":"https://pith.science/paper/7FPAS3U2"},"agent_actions":{"view_html":"https://pith.science/pith/7FPAS3U2SXZ3LNEZCZAXQXNIHD","download_json":"https://pith.science/pith/7FPAS3U2SXZ3LNEZCZAXQXNIHD.json","view_paper":"https://pith.science/paper/7FPAS3U2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.01793&json=true","fetch_graph":"https://pith.science/api/pith-number/7FPAS3U2SXZ3LNEZCZAXQXNIHD/graph.json","fetch_events":"https://pith.science/api/pith-number/7FPAS3U2SXZ3LNEZCZAXQXNIHD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7FPAS3U2SXZ3LNEZCZAXQXNIHD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7FPAS3U2SXZ3LNEZCZAXQXNIHD/action/storage_attestation","attest_author":"https://pith.science/pith/7FPAS3U2SXZ3LNEZCZAXQXNIHD/action/author_attestation","sign_citation":"https://pith.science/pith/7FPAS3U2SXZ3LNEZCZAXQXNIHD/action/citation_signature","submit_replication":"https://pith.science/pith/7FPAS3U2SXZ3LNEZCZAXQXNIHD/action/replication_record"}},"created_at":"2026-05-18T01:33:06.341833+00:00","updated_at":"2026-05-18T01:33:06.341833+00:00"}