{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:DEWKSE2BADHXRTRTIQDG7PMLP4","short_pith_number":"pith:DEWKSE2B","schema_version":"1.0","canonical_sha256":"192ca9134100cf78ce3344066fbd8b7f2e1faa0aa90b2b17b9675c8d76fe64a0","source":{"kind":"arxiv","id":"1109.2784","version":1},"attestation_state":"computed","paper":{"title":"Moebius-Walsh correlation bounds and an estimate of Mauduit and Rivat","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean Bourgain","submitted_at":"2011-09-13T13:44:07Z","abstract_excerpt":"We establish small correlation bounds for the Moebius function and the Walsh system, answering affirmatively a question posed by G.Kalai [Ka]. The argument is based on generalizing the approach of Mauduit and Rivat [M-R] in order to treat Walsh functions of `large weight', while the `small weight' case follows from recent work due to B.Green [Gr]. The conclusion is an estimate uniform over the full Walsh system. A similar result also holds for the Liouville function."},"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":"1109.2784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-13T13:44:07Z","cross_cats_sorted":[],"title_canon_sha256":"e93421b6be9a74991996419753643be979ada2dd8a412b8e2267c27e7b3ed4a6","abstract_canon_sha256":"291731eb6149eac0c88a8b1436cf3c9d0175a014672185f79ab3ffb43b3c94fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:07.713437Z","signature_b64":"aZu0JTyYTQq6T5qds4UN7hOIRx0bQYt96R1XzccJADnChlS7oJbiJQSdfGXnDOgx3e/rPU8gRq23FrQ/tTp7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"192ca9134100cf78ce3344066fbd8b7f2e1faa0aa90b2b17b9675c8d76fe64a0","last_reissued_at":"2026-05-18T04:13:07.712795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:07.712795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moebius-Walsh correlation bounds and an estimate of Mauduit and Rivat","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean Bourgain","submitted_at":"2011-09-13T13:44:07Z","abstract_excerpt":"We establish small correlation bounds for the Moebius function and the Walsh system, answering affirmatively a question posed by G.Kalai [Ka]. The argument is based on generalizing the approach of Mauduit and Rivat [M-R] in order to treat Walsh functions of `large weight', while the `small weight' case follows from recent work due to B.Green [Gr]. The conclusion is an estimate uniform over the full Walsh system. A similar result also holds for the Liouville function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2784","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":"1109.2784","created_at":"2026-05-18T04:13:07.712879+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.2784v1","created_at":"2026-05-18T04:13:07.712879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2784","created_at":"2026-05-18T04:13:07.712879+00:00"},{"alias_kind":"pith_short_12","alias_value":"DEWKSE2BADHX","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DEWKSE2BADHXRTRT","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DEWKSE2B","created_at":"2026-05-18T12:26:26.731475+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/DEWKSE2BADHXRTRTIQDG7PMLP4","json":"https://pith.science/pith/DEWKSE2BADHXRTRTIQDG7PMLP4.json","graph_json":"https://pith.science/api/pith-number/DEWKSE2BADHXRTRTIQDG7PMLP4/graph.json","events_json":"https://pith.science/api/pith-number/DEWKSE2BADHXRTRTIQDG7PMLP4/events.json","paper":"https://pith.science/paper/DEWKSE2B"},"agent_actions":{"view_html":"https://pith.science/pith/DEWKSE2BADHXRTRTIQDG7PMLP4","download_json":"https://pith.science/pith/DEWKSE2BADHXRTRTIQDG7PMLP4.json","view_paper":"https://pith.science/paper/DEWKSE2B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.2784&json=true","fetch_graph":"https://pith.science/api/pith-number/DEWKSE2BADHXRTRTIQDG7PMLP4/graph.json","fetch_events":"https://pith.science/api/pith-number/DEWKSE2BADHXRTRTIQDG7PMLP4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DEWKSE2BADHXRTRTIQDG7PMLP4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DEWKSE2BADHXRTRTIQDG7PMLP4/action/storage_attestation","attest_author":"https://pith.science/pith/DEWKSE2BADHXRTRTIQDG7PMLP4/action/author_attestation","sign_citation":"https://pith.science/pith/DEWKSE2BADHXRTRTIQDG7PMLP4/action/citation_signature","submit_replication":"https://pith.science/pith/DEWKSE2BADHXRTRTIQDG7PMLP4/action/replication_record"}},"created_at":"2026-05-18T04:13:07.712879+00:00","updated_at":"2026-05-18T04:13:07.712879+00:00"}