{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UZAUGKAGDIWYGYV4HLWLMDQJNR","short_pith_number":"pith:UZAUGKAG","schema_version":"1.0","canonical_sha256":"a6414328061a2d8362bc3aecb60e096c41246a4c5ab6d6a5df1fc8aed8f50624","source":{"kind":"arxiv","id":"1601.07281","version":2},"attestation_state":"computed","paper":{"title":"Optimal $L_p$-discrepancy bounds for second order digital sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.NA"],"primary_cat":"math.NT","authors_text":"Aicke Hinrichs, Friedrich Pillichshammer, Josef Dick, Lev Markhasin","submitted_at":"2016-01-27T07:42:55Z","abstract_excerpt":"The $L_p$-discrepancy is a quantitative measure for the irregularity of distribution modulo one of infinite sequences. In 1986 Proinov proved for all $p>1$ a lower bound for the $L_p$-discrepancy of general infinite sequences in the $d$-dimensional unit cube, but it remained an open question whether this lower bound is best possible in the order of magnitude until recently. In 2014 Dick and Pillichshammer gave a first construction of an infinite sequence whose order of $L_2$-discrepancy matches the lower bound of Proinov. Here we give a complete solution to this problem for all finite $p > 1$."},"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":"1601.07281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-27T07:42:55Z","cross_cats_sorted":["math.FA","math.NA"],"title_canon_sha256":"e8f81f15e74895d3caa803176e395c44a897ddb72e8f815d00b637cc9f0238c3","abstract_canon_sha256":"22c12870369f3863b38c188d9217422336962d6b9115b8ac661e262f5a0ac73a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:15.263347Z","signature_b64":"Y85XTDAcYA0Lrbbm4X3r41nDxKz5+Vw/ebdYicsYLAoyVQn04zlIcjSJYlAiUXK3aWwBlDlXf+1gEXcjqpoGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6414328061a2d8362bc3aecb60e096c41246a4c5ab6d6a5df1fc8aed8f50624","last_reissued_at":"2026-05-18T00:32:15.262833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:15.262833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal $L_p$-discrepancy bounds for second order digital sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.NA"],"primary_cat":"math.NT","authors_text":"Aicke Hinrichs, Friedrich Pillichshammer, Josef Dick, Lev Markhasin","submitted_at":"2016-01-27T07:42:55Z","abstract_excerpt":"The $L_p$-discrepancy is a quantitative measure for the irregularity of distribution modulo one of infinite sequences. In 1986 Proinov proved for all $p>1$ a lower bound for the $L_p$-discrepancy of general infinite sequences in the $d$-dimensional unit cube, but it remained an open question whether this lower bound is best possible in the order of magnitude until recently. In 2014 Dick and Pillichshammer gave a first construction of an infinite sequence whose order of $L_2$-discrepancy matches the lower bound of Proinov. Here we give a complete solution to this problem for all finite $p > 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07281","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1601.07281","created_at":"2026-05-18T00:32:15.262923+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.07281v2","created_at":"2026-05-18T00:32:15.262923+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07281","created_at":"2026-05-18T00:32:15.262923+00:00"},{"alias_kind":"pith_short_12","alias_value":"UZAUGKAGDIWY","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UZAUGKAGDIWYGYV4","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UZAUGKAG","created_at":"2026-05-18T12:30:46.583412+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/UZAUGKAGDIWYGYV4HLWLMDQJNR","json":"https://pith.science/pith/UZAUGKAGDIWYGYV4HLWLMDQJNR.json","graph_json":"https://pith.science/api/pith-number/UZAUGKAGDIWYGYV4HLWLMDQJNR/graph.json","events_json":"https://pith.science/api/pith-number/UZAUGKAGDIWYGYV4HLWLMDQJNR/events.json","paper":"https://pith.science/paper/UZAUGKAG"},"agent_actions":{"view_html":"https://pith.science/pith/UZAUGKAGDIWYGYV4HLWLMDQJNR","download_json":"https://pith.science/pith/UZAUGKAGDIWYGYV4HLWLMDQJNR.json","view_paper":"https://pith.science/paper/UZAUGKAG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.07281&json=true","fetch_graph":"https://pith.science/api/pith-number/UZAUGKAGDIWYGYV4HLWLMDQJNR/graph.json","fetch_events":"https://pith.science/api/pith-number/UZAUGKAGDIWYGYV4HLWLMDQJNR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UZAUGKAGDIWYGYV4HLWLMDQJNR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UZAUGKAGDIWYGYV4HLWLMDQJNR/action/storage_attestation","attest_author":"https://pith.science/pith/UZAUGKAGDIWYGYV4HLWLMDQJNR/action/author_attestation","sign_citation":"https://pith.science/pith/UZAUGKAGDIWYGYV4HLWLMDQJNR/action/citation_signature","submit_replication":"https://pith.science/pith/UZAUGKAGDIWYGYV4HLWLMDQJNR/action/replication_record"}},"created_at":"2026-05-18T00:32:15.262923+00:00","updated_at":"2026-05-18T00:32:15.262923+00:00"}