{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FC2EKLLRD342PDDWWTXBPVTZE6","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":"2b564c3adfb140f3cc00f1ec79aa164df47550128a65588401d034cf407f2857","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-09T09:25:45Z","title_canon_sha256":"84f5270f3112722d460ceecb206ef1edcb57a5c6a86faf75089fd2aa8f878399"},"schema_version":"1.0","source":{"id":"1804.02879","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.02879","created_at":"2026-05-17T23:39:58Z"},{"alias_kind":"arxiv_version","alias_value":"1804.02879v1","created_at":"2026-05-17T23:39:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.02879","created_at":"2026-05-17T23:39:58Z"},{"alias_kind":"pith_short_12","alias_value":"FC2EKLLRD342","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FC2EKLLRD342PDDW","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FC2EKLLR","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:049c23b3b482cbcee53273214c80128ba8305adf8ec01ba28089c7496a4f78b2","target":"graph","created_at":"2026-05-17T23:39:58Z","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":"In a recent paper [Adv. Math. 305:165--196, 2017], Komornik et al.~proved a long-conjectured formula for the Hausdorff dimension of the set $\\mathcal{U}_q$ of numbers having a unique expansion in the (non-integer) base $q$, and showed that this Hausdorff dimension is continuous in $q$. Unfortunately, their proof contained a gap which appears difficult to fix. This article gives a completely different proof of these results, using a more direct combinatorial approach.","authors_text":"Derong Kong, Pieter Allaart","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-09T09:25:45Z","title":"On the continuity of the Hausdorff dimension of the univoque set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02879","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":"sha256:182f4cf3a9b558c5221d4329842bd39774e2c5f3802f4e490201a21989a730de","target":"record","created_at":"2026-05-17T23:39:58Z","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":"2b564c3adfb140f3cc00f1ec79aa164df47550128a65588401d034cf407f2857","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-09T09:25:45Z","title_canon_sha256":"84f5270f3112722d460ceecb206ef1edcb57a5c6a86faf75089fd2aa8f878399"},"schema_version":"1.0","source":{"id":"1804.02879","kind":"arxiv","version":1}},"canonical_sha256":"28b4452d711ef9a78c76b4ee17d67927a4ec75ec5d31b18698f4d18b127f9850","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28b4452d711ef9a78c76b4ee17d67927a4ec75ec5d31b18698f4d18b127f9850","first_computed_at":"2026-05-17T23:39:58.682613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:58.682613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ScIOnYBJvLFgIC1ixPCPiHbD3EKWklz38vzNcrHjhR0gDhTktGWZLQSbsw321kiR4mzwmKqTk/U99EBGg8bFDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:58.683170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.02879","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:182f4cf3a9b558c5221d4329842bd39774e2c5f3802f4e490201a21989a730de","sha256:049c23b3b482cbcee53273214c80128ba8305adf8ec01ba28089c7496a4f78b2"],"state_sha256":"2f414d275e4cc6a757eb3c22afa3089338d8b6fa951fb0d83581b7ea324db263"}