{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WQ33LJRENXLC4JLRTPC4MLIBMI","short_pith_number":"pith:WQ33LJRE","canonical_record":{"source":{"id":"1504.04789","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-19T04:26:09Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"a65c09442249b5b19d1e88398b540def324f2e5a9a562e0f3a1b3f326d23b18b","abstract_canon_sha256":"abc145b198d341d569cf6b9e151be121b2f534cd6fb1155ef210fc78a952ae52"},"schema_version":"1.0"},"canonical_sha256":"b437b5a6246dd62e25719bc5c62d01622653a9b59081a6c6f69f747823208a4a","source":{"kind":"arxiv","id":"1504.04789","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04789","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04789v2","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04789","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"pith_short_12","alias_value":"WQ33LJRENXLC","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WQ33LJRENXLC4JLR","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WQ33LJRE","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WQ33LJRENXLC4JLRTPC4MLIBMI","target":"record","payload":{"canonical_record":{"source":{"id":"1504.04789","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-19T04:26:09Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"a65c09442249b5b19d1e88398b540def324f2e5a9a562e0f3a1b3f326d23b18b","abstract_canon_sha256":"abc145b198d341d569cf6b9e151be121b2f534cd6fb1155ef210fc78a952ae52"},"schema_version":"1.0"},"canonical_sha256":"b437b5a6246dd62e25719bc5c62d01622653a9b59081a6c6f69f747823208a4a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:38.259992Z","signature_b64":"z5JUx9zlIkkxsbQpAt8SWS/ModYk+kXPwxjHaTvX89hyNOmhn2ED4+BqvIC35lRaEUpbl/TCPEQLOjqlQx8LCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b437b5a6246dd62e25719bc5c62d01622653a9b59081a6c6f69f747823208a4a","last_reissued_at":"2026-05-18T00:56:38.259252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:38.259252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.04789","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DtN9Z5r1GWb2yuEPG1gGWZxRmYQiz76GVQJkAGCWuETuxOFnWQaPCb80htrvjfMxjGiU6VeV/sXHTjp/KzAqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:41:34.485992Z"},"content_sha256":"09035e1fbb9a21cc858861e095d8312a27edbfdc58ace9954261636843029258","schema_version":"1.0","event_id":"sha256:09035e1fbb9a21cc858861e095d8312a27edbfdc58ace9954261636843029258"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WQ33LJRENXLC4JLRTPC4MLIBMI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Restrictions of H\\\"older continuous functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Andr\\'as M\\'ath\\'e, Omer Angel, Rich\\'ard Balka, Yuval Peres","submitted_at":"2015-04-19T04:26:09Z","abstract_excerpt":"For $0<\\alpha<1$ let $V(\\alpha)$ denote the supremum of the numbers $v$ such that every $\\alpha$-H\\\"older continuous function is of bounded variation on a set of Hausdorff dimension $v$. Kahane and Katznelson (2009) proved the estimate $1/2 \\leq V(\\alpha)\\leq 1/(2-\\alpha)$ and asked whether the upper bound is sharp. We show that in fact $V(\\alpha)=\\max\\{1/2,\\alpha\\}$. Let $\\dim_{H}$ and $\\overline{\\dim}_{M}$ denote the Hausdorff and upper Minkowski dimension, respectively. The upper bound on $V(\\alpha)$ is a consequence of the following theorem. Let $\\{B(t): t\\in [0,1]\\}$ be a fractional Brown"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04789","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qUcKphmeseLXIbTwsWzIxJyM2VX+/fwUQLLFnI3UlaqiIJipJIiLaR968KgmfTT8kfzdQEzH/BIwz7QFhctTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:41:34.486680Z"},"content_sha256":"9792aec5c51a8b8ea4eb609de83c01fda71bee65fccf61e8cc06517ba7d0b91b","schema_version":"1.0","event_id":"sha256:9792aec5c51a8b8ea4eb609de83c01fda71bee65fccf61e8cc06517ba7d0b91b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WQ33LJRENXLC4JLRTPC4MLIBMI/bundle.json","state_url":"https://pith.science/pith/WQ33LJRENXLC4JLRTPC4MLIBMI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WQ33LJRENXLC4JLRTPC4MLIBMI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T20:41:34Z","links":{"resolver":"https://pith.science/pith/WQ33LJRENXLC4JLRTPC4MLIBMI","bundle":"https://pith.science/pith/WQ33LJRENXLC4JLRTPC4MLIBMI/bundle.json","state":"https://pith.science/pith/WQ33LJRENXLC4JLRTPC4MLIBMI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WQ33LJRENXLC4JLRTPC4MLIBMI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WQ33LJRENXLC4JLRTPC4MLIBMI","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":"abc145b198d341d569cf6b9e151be121b2f534cd6fb1155ef210fc78a952ae52","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-19T04:26:09Z","title_canon_sha256":"a65c09442249b5b19d1e88398b540def324f2e5a9a562e0f3a1b3f326d23b18b"},"schema_version":"1.0","source":{"id":"1504.04789","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04789","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04789v2","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04789","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"pith_short_12","alias_value":"WQ33LJRENXLC","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WQ33LJRENXLC4JLR","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WQ33LJRE","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:9792aec5c51a8b8ea4eb609de83c01fda71bee65fccf61e8cc06517ba7d0b91b","target":"graph","created_at":"2026-05-18T00:56:38Z","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":"For $0<\\alpha<1$ let $V(\\alpha)$ denote the supremum of the numbers $v$ such that every $\\alpha$-H\\\"older continuous function is of bounded variation on a set of Hausdorff dimension $v$. Kahane and Katznelson (2009) proved the estimate $1/2 \\leq V(\\alpha)\\leq 1/(2-\\alpha)$ and asked whether the upper bound is sharp. We show that in fact $V(\\alpha)=\\max\\{1/2,\\alpha\\}$. Let $\\dim_{H}$ and $\\overline{\\dim}_{M}$ denote the Hausdorff and upper Minkowski dimension, respectively. The upper bound on $V(\\alpha)$ is a consequence of the following theorem. Let $\\{B(t): t\\in [0,1]\\}$ be a fractional Brown","authors_text":"Andr\\'as M\\'ath\\'e, Omer Angel, 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":"2015-04-19T04:26:09Z","title":"Restrictions of H\\\"older continuous functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04789","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":"sha256:09035e1fbb9a21cc858861e095d8312a27edbfdc58ace9954261636843029258","target":"record","created_at":"2026-05-18T00:56:38Z","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":"abc145b198d341d569cf6b9e151be121b2f534cd6fb1155ef210fc78a952ae52","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-19T04:26:09Z","title_canon_sha256":"a65c09442249b5b19d1e88398b540def324f2e5a9a562e0f3a1b3f326d23b18b"},"schema_version":"1.0","source":{"id":"1504.04789","kind":"arxiv","version":2}},"canonical_sha256":"b437b5a6246dd62e25719bc5c62d01622653a9b59081a6c6f69f747823208a4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b437b5a6246dd62e25719bc5c62d01622653a9b59081a6c6f69f747823208a4a","first_computed_at":"2026-05-18T00:56:38.259252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:38.259252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z5JUx9zlIkkxsbQpAt8SWS/ModYk+kXPwxjHaTvX89hyNOmhn2ED4+BqvIC35lRaEUpbl/TCPEQLOjqlQx8LCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:38.259992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04789","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09035e1fbb9a21cc858861e095d8312a27edbfdc58ace9954261636843029258","sha256:9792aec5c51a8b8ea4eb609de83c01fda71bee65fccf61e8cc06517ba7d0b91b"],"state_sha256":"a66d200edd0f346159a33ff642e485cc28b0e83651465354c743ff354612fcef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WLOJ3rh6qJMiRsQDrBPH268L1qfkEGjgfJhIjKmbI13TKUqP2X0WRSyrscTCd9TGV47IizVsbtfXKKpEU9/pCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:41:34.490349Z","bundle_sha256":"d97344c0590783a5f9b7544a36c81428d068e3658e5afb41a04dc42a422c4658"}}