{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GAWW6OEQCYDLSNYIZ3I2ZCLIRQ","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":"848a397f1cdcc995224940557ffeb168782251424b552b8d2370af26363d4bdb","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-11T06:12:47Z","title_canon_sha256":"c774870b402855e52d1fd71971362f74f7294a83bba89026dea2598d732d7c35"},"schema_version":"1.0","source":{"id":"1406.2789","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2789","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2789v2","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2789","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"pith_short_12","alias_value":"GAWW6OEQCYDL","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GAWW6OEQCYDLSNYI","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GAWW6OEQ","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:bbf5f363345b731223936ffcfbc3a225cf95ddc22896f9c72ad7f33bf3eb27c8","target":"graph","created_at":"2026-05-18T02:33:01Z","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 $\\{ B(t) \\colon 0\\leq t\\leq 1\\}$ be a linear Brownian motion and let $\\dim$ denote the Hausdorff dimension. Let $\\alpha>\\frac12$ and $1\\leq \\beta \\leq 2$. We prove that, almost surely, there exists no set $A\\subset[0,1]$ such that $\\dim A>\\frac12$ and $B\\colon A\\to\\mathbb{R}$ is $\\alpha$-H\\\"older continuous. The proof is an application of Kaufman's dimension doubling theorem. As a corollary of the above theorem, we show that, almost surely, there exists no set $A\\subset[0,1]$ such that $\\dim A>\\frac{\\beta}{2}$ and $B\\colon A\\to\\mathbb{R}$ has finite $\\beta$-variation. The zero set of $B$ a","authors_text":"Rich\\'ard Balka, Yuval Peres","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-11T06:12:47Z","title":"Restrictions of Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2789","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":"sha256:27112b8b56db368af2ac4583e0e5d0f261849da3c19190e42ce73d4997712d7f","target":"record","created_at":"2026-05-18T02:33:01Z","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":"848a397f1cdcc995224940557ffeb168782251424b552b8d2370af26363d4bdb","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-11T06:12:47Z","title_canon_sha256":"c774870b402855e52d1fd71971362f74f7294a83bba89026dea2598d732d7c35"},"schema_version":"1.0","source":{"id":"1406.2789","kind":"arxiv","version":2}},"canonical_sha256":"302d6f38901606b93708ced1ac89688c0ec92b2379286bdc968d341f5076f9d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"302d6f38901606b93708ced1ac89688c0ec92b2379286bdc968d341f5076f9d4","first_computed_at":"2026-05-18T02:33:01.141444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:01.141444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rImPlwqPQqcJX0Kv6gyPS08iiPSUfsEKoKAHrpMPSheXpry+zyfhnGSNSOkedVKyuJALxuHfyX55CBYClJPqAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:01.141785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2789","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27112b8b56db368af2ac4583e0e5d0f261849da3c19190e42ce73d4997712d7f","sha256:bbf5f363345b731223936ffcfbc3a225cf95ddc22896f9c72ad7f33bf3eb27c8"],"state_sha256":"84f52d68730d1062166063aed49285845fd92b505c41e998cfab7b976a29fc66"}