{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GKRAIMKRYTERAWE7HST6C34OBI","short_pith_number":"pith:GKRAIMKR","schema_version":"1.0","canonical_sha256":"32a2043151c4c910589f3ca7e16f8e0a15aa1158315ba27c22be006c352a7676","source":{"kind":"arxiv","id":"1509.04900","version":2},"attestation_state":"computed","paper":{"title":"Subshift of finite type and self-similar sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kan Jiang, Karma Dajani","submitted_at":"2015-09-16T12:18:15Z","abstract_excerpt":"Let $K\\subset \\mathbb{R}$ be a self-similar set generated by some iterated function system. In this paper we prove, under some assumptions, that $K$ can be identified with a subshift of finite type. With this identification, we can calculate the Hausdorff dimension of $K$ as well as the set of elements in $K$ with unique codings using the machinery of Mauldin and Williams \\cite{MW}. We give three different applications of our main result. Firstly, we calculate the Hausdorff dimension of the set of points of $K$ with multiple codings. Secondly, in the setting of $\\beta$-expansions, when the set"},"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":"1509.04900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-16T12:18:15Z","cross_cats_sorted":[],"title_canon_sha256":"23a0198ea23087afe342085af62817c4fd2082bd71461c2f1ff4401b87aa376f","abstract_canon_sha256":"5422f54b6db7a879b376d918f60a6629eaa6f0cc1fdb20108cd68f31ac17a44f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:25.607122Z","signature_b64":"5p+Sp+Gmw0iBedFHu51n1PQVxDrbZursu0OTxnG5EGqwB63xx8c4FwokMyY5Q1ILigFQeOKroN7JVov73x+8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32a2043151c4c910589f3ca7e16f8e0a15aa1158315ba27c22be006c352a7676","last_reissued_at":"2026-05-18T00:55:25.606366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:25.606366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subshift of finite type and self-similar sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kan Jiang, Karma Dajani","submitted_at":"2015-09-16T12:18:15Z","abstract_excerpt":"Let $K\\subset \\mathbb{R}$ be a self-similar set generated by some iterated function system. In this paper we prove, under some assumptions, that $K$ can be identified with a subshift of finite type. With this identification, we can calculate the Hausdorff dimension of $K$ as well as the set of elements in $K$ with unique codings using the machinery of Mauldin and Williams \\cite{MW}. We give three different applications of our main result. Firstly, we calculate the Hausdorff dimension of the set of points of $K$ with multiple codings. Secondly, in the setting of $\\beta$-expansions, when the set"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04900","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":"1509.04900","created_at":"2026-05-18T00:55:25.606497+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.04900v2","created_at":"2026-05-18T00:55:25.606497+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04900","created_at":"2026-05-18T00:55:25.606497+00:00"},{"alias_kind":"pith_short_12","alias_value":"GKRAIMKRYTER","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GKRAIMKRYTERAWE7","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GKRAIMKR","created_at":"2026-05-18T12:29:22.688609+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/GKRAIMKRYTERAWE7HST6C34OBI","json":"https://pith.science/pith/GKRAIMKRYTERAWE7HST6C34OBI.json","graph_json":"https://pith.science/api/pith-number/GKRAIMKRYTERAWE7HST6C34OBI/graph.json","events_json":"https://pith.science/api/pith-number/GKRAIMKRYTERAWE7HST6C34OBI/events.json","paper":"https://pith.science/paper/GKRAIMKR"},"agent_actions":{"view_html":"https://pith.science/pith/GKRAIMKRYTERAWE7HST6C34OBI","download_json":"https://pith.science/pith/GKRAIMKRYTERAWE7HST6C34OBI.json","view_paper":"https://pith.science/paper/GKRAIMKR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.04900&json=true","fetch_graph":"https://pith.science/api/pith-number/GKRAIMKRYTERAWE7HST6C34OBI/graph.json","fetch_events":"https://pith.science/api/pith-number/GKRAIMKRYTERAWE7HST6C34OBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GKRAIMKRYTERAWE7HST6C34OBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GKRAIMKRYTERAWE7HST6C34OBI/action/storage_attestation","attest_author":"https://pith.science/pith/GKRAIMKRYTERAWE7HST6C34OBI/action/author_attestation","sign_citation":"https://pith.science/pith/GKRAIMKRYTERAWE7HST6C34OBI/action/citation_signature","submit_replication":"https://pith.science/pith/GKRAIMKRYTERAWE7HST6C34OBI/action/replication_record"}},"created_at":"2026-05-18T00:55:25.606497+00:00","updated_at":"2026-05-18T00:55:25.606497+00:00"}