{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:HWSD3FXUZ5K6UFHBWPDNPB5YY2","short_pith_number":"pith:HWSD3FXU","schema_version":"1.0","canonical_sha256":"3da43d96f4cf55ea14e1b3c6d787b8c6b5fdfb98e88152e89bc866f6c1a05e68","source":{"kind":"arxiv","id":"1106.0577","version":1},"attestation_state":"computed","paper":{"title":"1/2-Heavy Sequences Driven By Rotation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"David Ralston","submitted_at":"2011-06-03T07:38:16Z","abstract_excerpt":"We investigate the set of $x \\in S^1$ such that for every positive integer $N$, the first $N$ points in the orbit of $x$ under rotation by irrational $\\theta$ contain at least as many values in the interval $[0,1/2]$ as in the complement. By using a renormalization procedure, we show both that the Hausdorff dimension of this set is the same constant (strictly between zero and one) for almost-every $\\theta$, and that for every $d \\in [0,1]$ there is a dense set of $\\theta$ for which the Hausdorff dimension of this set is $d$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.0577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-03T07:38:16Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"26c65296f4da9c56ae738f74cdd20de8c4a0b5cf238cc493c4e515e61d27755f","abstract_canon_sha256":"e69a05ccaba1a38ce2381661042aa844ce2de0f3ae79a76ad10ae97005f374ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:49.141621Z","signature_b64":"TqXQOKSNRNIup3lYGcxWlDzVDoEJlJ3jzdUVGQa0SgD71RORB3LBrJsaRu3bOO8I5zNbDD0G12u4FZkkP5SbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3da43d96f4cf55ea14e1b3c6d787b8c6b5fdfb98e88152e89bc866f6c1a05e68","last_reissued_at":"2026-05-18T04:20:49.141003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:49.141003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"1/2-Heavy Sequences Driven By Rotation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"David Ralston","submitted_at":"2011-06-03T07:38:16Z","abstract_excerpt":"We investigate the set of $x \\in S^1$ such that for every positive integer $N$, the first $N$ points in the orbit of $x$ under rotation by irrational $\\theta$ contain at least as many values in the interval $[0,1/2]$ as in the complement. By using a renormalization procedure, we show both that the Hausdorff dimension of this set is the same constant (strictly between zero and one) for almost-every $\\theta$, and that for every $d \\in [0,1]$ there is a dense set of $\\theta$ for which the Hausdorff dimension of this set is $d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0577","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1106.0577","created_at":"2026-05-18T04:20:49.141078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.0577v1","created_at":"2026-05-18T04:20:49.141078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0577","created_at":"2026-05-18T04:20:49.141078+00:00"},{"alias_kind":"pith_short_12","alias_value":"HWSD3FXUZ5K6","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"HWSD3FXUZ5K6UFHB","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"HWSD3FXU","created_at":"2026-05-18T12:26:30.835961+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HWSD3FXUZ5K6UFHBWPDNPB5YY2","json":"https://pith.science/pith/HWSD3FXUZ5K6UFHBWPDNPB5YY2.json","graph_json":"https://pith.science/api/pith-number/HWSD3FXUZ5K6UFHBWPDNPB5YY2/graph.json","events_json":"https://pith.science/api/pith-number/HWSD3FXUZ5K6UFHBWPDNPB5YY2/events.json","paper":"https://pith.science/paper/HWSD3FXU"},"agent_actions":{"view_html":"https://pith.science/pith/HWSD3FXUZ5K6UFHBWPDNPB5YY2","download_json":"https://pith.science/pith/HWSD3FXUZ5K6UFHBWPDNPB5YY2.json","view_paper":"https://pith.science/paper/HWSD3FXU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.0577&json=true","fetch_graph":"https://pith.science/api/pith-number/HWSD3FXUZ5K6UFHBWPDNPB5YY2/graph.json","fetch_events":"https://pith.science/api/pith-number/HWSD3FXUZ5K6UFHBWPDNPB5YY2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HWSD3FXUZ5K6UFHBWPDNPB5YY2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HWSD3FXUZ5K6UFHBWPDNPB5YY2/action/storage_attestation","attest_author":"https://pith.science/pith/HWSD3FXUZ5K6UFHBWPDNPB5YY2/action/author_attestation","sign_citation":"https://pith.science/pith/HWSD3FXUZ5K6UFHBWPDNPB5YY2/action/citation_signature","submit_replication":"https://pith.science/pith/HWSD3FXUZ5K6UFHBWPDNPB5YY2/action/replication_record"}},"created_at":"2026-05-18T04:20:49.141078+00:00","updated_at":"2026-05-18T04:20:49.141078+00:00"}