{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:BSWQWX6VI2ME3UG6GJFN2U7D2J","short_pith_number":"pith:BSWQWX6V","schema_version":"1.0","canonical_sha256":"0cad0b5fd546984dd0de324add53e3d249dc1e812e746b25b8dd50e1672bdbd7","source":{"kind":"arxiv","id":"2502.06511","version":2},"attestation_state":"computed","paper":{"title":"Spectral and dynamical results related to certain non-integer base expansions on the unit interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.SP","authors_text":"Giovanna Marcelli, Horia D. Cornean, Ira W. Herbst","submitted_at":"2025-02-10T14:26:44Z","abstract_excerpt":"We consider certain non-integer base $\\beta$-expansions of Parry's type and we study various properties of the transfer (Perron-Frobenius) operator $\\mathcal{P}:L^p([0,1])\\mapsto L^p([0,1])$ with $p\\geq 1$ and its associated composition (Koopman) operator, which are induced by a discrete dynamical system on the unit interval related to these $\\beta$-expansions. We show that if $f$ is Lipschitz, then the iterated sequence $\\{\\mathcal{P}^N f\\}_{N\\geq 1}$ converges exponentially fast (in the $L^1$ norm) to an invariant state corresponding to the eigenvalue $1$ of $\\mathcal{P}$. This \"attracting\" "},"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":"2502.06511","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-02-10T14:26:44Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"98bfa8652118208d1575ed97b0e1d9c9b23e8639f52ec879bcbdbbd48c3d47f8","abstract_canon_sha256":"cba4f3a4abc1c173dd86026c8d1afc0a07634374fe4477b83e1c4d298114dddf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:48.328081Z","signature_b64":"K/TAUVNvt5RFVLUWOe8kVJBX4KtXJX4oNkfNUzhsdfy0NygE0L2+AqY/JBd0U8BO/yQQfniVcqau/J43Yu2hAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cad0b5fd546984dd0de324add53e3d249dc1e812e746b25b8dd50e1672bdbd7","last_reissued_at":"2026-05-20T00:02:48.327122Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:48.327122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral and dynamical results related to certain non-integer base expansions on the unit interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.SP","authors_text":"Giovanna Marcelli, Horia D. Cornean, Ira W. Herbst","submitted_at":"2025-02-10T14:26:44Z","abstract_excerpt":"We consider certain non-integer base $\\beta$-expansions of Parry's type and we study various properties of the transfer (Perron-Frobenius) operator $\\mathcal{P}:L^p([0,1])\\mapsto L^p([0,1])$ with $p\\geq 1$ and its associated composition (Koopman) operator, which are induced by a discrete dynamical system on the unit interval related to these $\\beta$-expansions. We show that if $f$ is Lipschitz, then the iterated sequence $\\{\\mathcal{P}^N f\\}_{N\\geq 1}$ converges exponentially fast (in the $L^1$ norm) to an invariant state corresponding to the eigenvalue $1$ of $\\mathcal{P}$. This \"attracting\" "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06511","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.06511/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2502.06511","created_at":"2026-05-20T00:02:48.327262+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.06511v2","created_at":"2026-05-20T00:02:48.327262+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06511","created_at":"2026-05-20T00:02:48.327262+00:00"},{"alias_kind":"pith_short_12","alias_value":"BSWQWX6VI2ME","created_at":"2026-05-20T00:02:48.327262+00:00"},{"alias_kind":"pith_short_16","alias_value":"BSWQWX6VI2ME3UG6","created_at":"2026-05-20T00:02:48.327262+00:00"},{"alias_kind":"pith_short_8","alias_value":"BSWQWX6V","created_at":"2026-05-20T00:02:48.327262+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.17113","citing_title":"Sharp iteration asymptotics for transfer operators induced by greedy $\\beta$-expansions","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BSWQWX6VI2ME3UG6GJFN2U7D2J","json":"https://pith.science/pith/BSWQWX6VI2ME3UG6GJFN2U7D2J.json","graph_json":"https://pith.science/api/pith-number/BSWQWX6VI2ME3UG6GJFN2U7D2J/graph.json","events_json":"https://pith.science/api/pith-number/BSWQWX6VI2ME3UG6GJFN2U7D2J/events.json","paper":"https://pith.science/paper/BSWQWX6V"},"agent_actions":{"view_html":"https://pith.science/pith/BSWQWX6VI2ME3UG6GJFN2U7D2J","download_json":"https://pith.science/pith/BSWQWX6VI2ME3UG6GJFN2U7D2J.json","view_paper":"https://pith.science/paper/BSWQWX6V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.06511&json=true","fetch_graph":"https://pith.science/api/pith-number/BSWQWX6VI2ME3UG6GJFN2U7D2J/graph.json","fetch_events":"https://pith.science/api/pith-number/BSWQWX6VI2ME3UG6GJFN2U7D2J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BSWQWX6VI2ME3UG6GJFN2U7D2J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BSWQWX6VI2ME3UG6GJFN2U7D2J/action/storage_attestation","attest_author":"https://pith.science/pith/BSWQWX6VI2ME3UG6GJFN2U7D2J/action/author_attestation","sign_citation":"https://pith.science/pith/BSWQWX6VI2ME3UG6GJFN2U7D2J/action/citation_signature","submit_replication":"https://pith.science/pith/BSWQWX6VI2ME3UG6GJFN2U7D2J/action/replication_record"}},"created_at":"2026-05-20T00:02:48.327262+00:00","updated_at":"2026-05-20T00:02:48.327262+00:00"}