{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZZLISAWFYKIJXLIMAQC3Y5RUDZ","short_pith_number":"pith:ZZLISAWF","schema_version":"1.0","canonical_sha256":"ce568902c5c2909bad0c0405bc76341e6d7e5814e225a0df8eb84e549c03ca26","source":{"kind":"arxiv","id":"1206.4950","version":3},"attestation_state":"computed","paper":{"title":"Construction of \\mu-normal sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance, Manfred G. Madritsch","submitted_at":"2012-06-21T17:31:58Z","abstract_excerpt":"In the present paper we extend Champernowne's construction of normal numbers to provide sequences which are generic for a given invariant probability measure, which need not be the maximal one. We present a construction together with estimates and examples for normal numbers with respect to L\\\"uroth series expansion, continued fractions expansion or $\\beta$-expansion."},"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":"1206.4950","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-21T17:31:58Z","cross_cats_sorted":[],"title_canon_sha256":"f47635b24ec68a9293a7847fc7aebb6a2304e7f7c281cbf6c7808a298725ab19","abstract_canon_sha256":"8a9803fe004ce9b5d7a7b5e5aa908a5843d8722c0782a20570fbe7a173824fd1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:09.254916Z","signature_b64":"CzK384Jq+eyVKeGwo/ROMVL/FtNWrCzKCiwCsRCAf+0FAXZjeOXPI9DuCbgPwz5KvYkvf+6ys82N6ifqIbPQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce568902c5c2909bad0c0405bc76341e6d7e5814e225a0df8eb84e549c03ca26","last_reissued_at":"2026-05-18T02:41:09.254361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:09.254361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Construction of \\mu-normal sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance, Manfred G. Madritsch","submitted_at":"2012-06-21T17:31:58Z","abstract_excerpt":"In the present paper we extend Champernowne's construction of normal numbers to provide sequences which are generic for a given invariant probability measure, which need not be the maximal one. We present a construction together with estimates and examples for normal numbers with respect to L\\\"uroth series expansion, continued fractions expansion or $\\beta$-expansion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4950","kind":"arxiv","version":3},"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":"1206.4950","created_at":"2026-05-18T02:41:09.254452+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.4950v3","created_at":"2026-05-18T02:41:09.254452+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4950","created_at":"2026-05-18T02:41:09.254452+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZZLISAWFYKIJ","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZZLISAWFYKIJXLIM","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZZLISAWF","created_at":"2026-05-18T12:27:30.460161+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/ZZLISAWFYKIJXLIMAQC3Y5RUDZ","json":"https://pith.science/pith/ZZLISAWFYKIJXLIMAQC3Y5RUDZ.json","graph_json":"https://pith.science/api/pith-number/ZZLISAWFYKIJXLIMAQC3Y5RUDZ/graph.json","events_json":"https://pith.science/api/pith-number/ZZLISAWFYKIJXLIMAQC3Y5RUDZ/events.json","paper":"https://pith.science/paper/ZZLISAWF"},"agent_actions":{"view_html":"https://pith.science/pith/ZZLISAWFYKIJXLIMAQC3Y5RUDZ","download_json":"https://pith.science/pith/ZZLISAWFYKIJXLIMAQC3Y5RUDZ.json","view_paper":"https://pith.science/paper/ZZLISAWF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.4950&json=true","fetch_graph":"https://pith.science/api/pith-number/ZZLISAWFYKIJXLIMAQC3Y5RUDZ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZZLISAWFYKIJXLIMAQC3Y5RUDZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZZLISAWFYKIJXLIMAQC3Y5RUDZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZZLISAWFYKIJXLIMAQC3Y5RUDZ/action/storage_attestation","attest_author":"https://pith.science/pith/ZZLISAWFYKIJXLIMAQC3Y5RUDZ/action/author_attestation","sign_citation":"https://pith.science/pith/ZZLISAWFYKIJXLIMAQC3Y5RUDZ/action/citation_signature","submit_replication":"https://pith.science/pith/ZZLISAWFYKIJXLIMAQC3Y5RUDZ/action/replication_record"}},"created_at":"2026-05-18T02:41:09.254452+00:00","updated_at":"2026-05-18T02:41:09.254452+00:00"}