{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KUALHS6T6EMMBMQORJL3DUF6RP","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":"13258d55c6a6c5bd4c8fd6a4dfbb334a8e11e48d0230dcb09e5869b8db2d86b5","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-02T10:37:04Z","title_canon_sha256":"d2aea41fb43aa312e3110f349f424c875d8f79eb78b8150da7bd3bbd1dc01b88"},"schema_version":"1.0","source":{"id":"1503.00475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00475","created_at":"2026-05-18T02:25:54Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00475v1","created_at":"2026-05-18T02:25:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00475","created_at":"2026-05-18T02:25:54Z"},{"alias_kind":"pith_short_12","alias_value":"KUALHS6T6EMM","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KUALHS6T6EMMBMQO","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KUALHS6T","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:2ac73a1a998889990c5443d2bdb4b984c1d1d1bd4183e2dd6dad9a7a30a0028d","target":"graph","created_at":"2026-05-18T02:25:54Z","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":"We fix a positive integer $M$, and we consider expansions in arbitrary real bases $q>1$ over the alphabet $\\{0,1,...,M\\}$. We denote by $U_q$ the set of real numbers having a unique expansion. Completing many former investigations, we give a formula for the Hausdorff dimension $D(q)$ of $U_q$ for each $q\\in (1,\\infty)$. Furthermore, we prove that the dimension function $D:(1,\\infty)\\to[0,1]$ is continuous, and has a bounded variation. Moreover, it has a Devil's staircase behavior in $(q',\\infty)$, where $q'$ denotes the Komornik--Loreti constant: although $D(q)>D(q')$ for all $q>q'$, we have $","authors_text":"Derong Kong, Vilmos Komornik, Wenxia Li","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-02T10:37:04Z","title":"Hausdorff dimension of univoque sets and Devil's staircase"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00475","kind":"arxiv","version":1},"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:ddb82885729bf5c528776fa135df5402fb61382fbc0e04bf3fb83f87f7431ffe","target":"record","created_at":"2026-05-18T02:25:54Z","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":"13258d55c6a6c5bd4c8fd6a4dfbb334a8e11e48d0230dcb09e5869b8db2d86b5","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-02T10:37:04Z","title_canon_sha256":"d2aea41fb43aa312e3110f349f424c875d8f79eb78b8150da7bd3bbd1dc01b88"},"schema_version":"1.0","source":{"id":"1503.00475","kind":"arxiv","version":1}},"canonical_sha256":"5500b3cbd3f118c0b20e8a57b1d0be8bc460dd50f054b403fed21c93584b5a45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5500b3cbd3f118c0b20e8a57b1d0be8bc460dd50f054b403fed21c93584b5a45","first_computed_at":"2026-05-18T02:25:54.376490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:54.376490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WhI7oGwrSb4h4/Guqkhg/+j8b3cyYfJ5JLeuFpY+DA2EXmco0QYSv2VZL6WiwL5DLiMMMBTeGV7OAJoSOlyyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:54.376856Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddb82885729bf5c528776fa135df5402fb61382fbc0e04bf3fb83f87f7431ffe","sha256:2ac73a1a998889990c5443d2bdb4b984c1d1d1bd4183e2dd6dad9a7a30a0028d"],"state_sha256":"135ef5947747ee6469121bb67f3ba99b228b4219adc8e9923c5d13f592dac78b"}