{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XYRKZV3WQ26ANEG555LL4TXMP5","short_pith_number":"pith:XYRKZV3W","schema_version":"1.0","canonical_sha256":"be22acd77686bc0690ddef56be4eec7f594f907d170306843ace76737660d5be","source":{"kind":"arxiv","id":"1601.06737","version":1},"attestation_state":"computed","paper":{"title":"C^m Eigenfunctions of Perron-Frobenius Operators and a New Approach to Numerical Computation of Hausdorff Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Richard S. Falk, Roger D. Nussbaum","submitted_at":"2016-01-25T19:32:49Z","abstract_excerpt":"We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case, our methods require only C^3 regularity of the maps in the IFS. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family of positive, linear, Perron-Frobenius operators L_s. The operators L_s can typically be studied in many different Banach spaces. Here, unlike most of the literature, we study L_s in a Banach space of real-valued, C^k functions, k >= 2; and we"},"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":"1601.06737","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-25T19:32:49Z","cross_cats_sorted":[],"title_canon_sha256":"6dae75179a3dc573f22a4473eeec521fe77779b6a27c98356e09485c9f1943c4","abstract_canon_sha256":"0f1e9a1142f7dc9db86a9f412a2a53fcbb274598ce2df02458335589f0398b75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:03.836068Z","signature_b64":"4/io3ecdoqLu+3un9AxT+z/xfhsqbFXv+6Gu2qORxet8+/DytcU5QkCvYhR6LCTeedmnIAS+I7fmi+ZbMGgGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be22acd77686bc0690ddef56be4eec7f594f907d170306843ace76737660d5be","last_reissued_at":"2026-05-18T01:22:03.835575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:03.835575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"C^m Eigenfunctions of Perron-Frobenius Operators and a New Approach to Numerical Computation of Hausdorff Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Richard S. Falk, Roger D. Nussbaum","submitted_at":"2016-01-25T19:32:49Z","abstract_excerpt":"We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case, our methods require only C^3 regularity of the maps in the IFS. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family of positive, linear, Perron-Frobenius operators L_s. The operators L_s can typically be studied in many different Banach spaces. Here, unlike most of the literature, we study L_s in a Banach space of real-valued, C^k functions, k >= 2; and we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06737","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":"1601.06737","created_at":"2026-05-18T01:22:03.835652+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.06737v1","created_at":"2026-05-18T01:22:03.835652+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06737","created_at":"2026-05-18T01:22:03.835652+00:00"},{"alias_kind":"pith_short_12","alias_value":"XYRKZV3WQ26A","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XYRKZV3WQ26ANEG5","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XYRKZV3W","created_at":"2026-05-18T12:30:51.357362+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/XYRKZV3WQ26ANEG555LL4TXMP5","json":"https://pith.science/pith/XYRKZV3WQ26ANEG555LL4TXMP5.json","graph_json":"https://pith.science/api/pith-number/XYRKZV3WQ26ANEG555LL4TXMP5/graph.json","events_json":"https://pith.science/api/pith-number/XYRKZV3WQ26ANEG555LL4TXMP5/events.json","paper":"https://pith.science/paper/XYRKZV3W"},"agent_actions":{"view_html":"https://pith.science/pith/XYRKZV3WQ26ANEG555LL4TXMP5","download_json":"https://pith.science/pith/XYRKZV3WQ26ANEG555LL4TXMP5.json","view_paper":"https://pith.science/paper/XYRKZV3W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.06737&json=true","fetch_graph":"https://pith.science/api/pith-number/XYRKZV3WQ26ANEG555LL4TXMP5/graph.json","fetch_events":"https://pith.science/api/pith-number/XYRKZV3WQ26ANEG555LL4TXMP5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XYRKZV3WQ26ANEG555LL4TXMP5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XYRKZV3WQ26ANEG555LL4TXMP5/action/storage_attestation","attest_author":"https://pith.science/pith/XYRKZV3WQ26ANEG555LL4TXMP5/action/author_attestation","sign_citation":"https://pith.science/pith/XYRKZV3WQ26ANEG555LL4TXMP5/action/citation_signature","submit_replication":"https://pith.science/pith/XYRKZV3WQ26ANEG555LL4TXMP5/action/replication_record"}},"created_at":"2026-05-18T01:22:03.835652+00:00","updated_at":"2026-05-18T01:22:03.835652+00:00"}