{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WFY72ZYHCALJ2MLNGX2ON7PP7N","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9a04bcf83029a0de61dc6ab3d2b6abf1abf5eb9ddc6b4b52db83c393ca591373","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2014-06-12T15:25:02Z","title_canon_sha256":"15e689046a3059d5907b47fbbab7bf5ab93b490845984ba297a7eb16b6efdc1f"},"schema_version":"1.0","source":{"id":"1406.3263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3263","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3263v2","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3263","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"WFY72ZYHCALJ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WFY72ZYHCALJ2MLN","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WFY72ZYH","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:1fcbadebf71dc2dad85545505ffc14ac7c524ed2cda3b8200a98b4e4381948e1","target":"graph","created_at":"2026-05-18T02:48:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $K\\subseteq\\mathbb{R}$ be the unique attractor of an iterated function system. We consider the case where $K$ is an interval and study those elements of $K$ with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence of this, we can show that the set of points with a unique coding is a graph-directed self-similar set in the sense of Mauldin and Williams \\cite{MW}. The theory of Mauldin and Williams then provides a method by which we can explicitly calculate the Hausdorff dimension of thi","authors_text":"Kan Jiang, Karma Dajani, Simon Baker","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2014-06-12T15:25:02Z","title":"On univoque points for self-similar sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3263","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0730065429de573af80374248cd108a930b0c35b14be7f105592f8ee52d4d4b9","target":"record","created_at":"2026-05-18T02:48:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9a04bcf83029a0de61dc6ab3d2b6abf1abf5eb9ddc6b4b52db83c393ca591373","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2014-06-12T15:25:02Z","title_canon_sha256":"15e689046a3059d5907b47fbbab7bf5ab93b490845984ba297a7eb16b6efdc1f"},"schema_version":"1.0","source":{"id":"1406.3263","kind":"arxiv","version":2}},"canonical_sha256":"b171fd670710169d316d35f4e6fdeffb5e90b56018d3f93831471d7598a51fa3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b171fd670710169d316d35f4e6fdeffb5e90b56018d3f93831471d7598a51fa3","first_computed_at":"2026-05-18T02:48:45.823434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:45.823434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ksuyYhC3wxxqDGr8ADP2Md16C+tTFEzNHcJq48mw6LCFfFuqWD3t5moMssRwQ1JNQbwEF4B5eFk6Ut34C1qvBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:45.824170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0730065429de573af80374248cd108a930b0c35b14be7f105592f8ee52d4d4b9","sha256:1fcbadebf71dc2dad85545505ffc14ac7c524ed2cda3b8200a98b4e4381948e1"],"state_sha256":"5d02732f275baf9030044ea7d4f5d876006aefba9e6ba80ff9ec9376729c12a3"}