{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:JXLPKMEIS5OOZU2UD2S2WSHROT","short_pith_number":"pith:JXLPKMEI","schema_version":"1.0","canonical_sha256":"4dd6f53088975cecd3541ea5ab48f174c950aaacf85a485afe3cb838ecfbfe04","source":{"kind":"arxiv","id":"2312.06012","version":2},"attestation_state":"computed","paper":{"title":"On Correlations of Liouville-like Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yichen You","submitted_at":"2023-12-10T21:52:46Z","abstract_excerpt":"Let $\\mathcal{A}$ be a set of mutually coprime positive integers, satisfying \\begin{align*}\n  \\sum\\limits_{a\\in\\mathcal{A}}\\frac{1}{a} = \\infty. \\end{align*} Define the (possibly non-multiplicative) \"Liouville-like\" functions \\begin{align*}\n  \\lambda_{\\mathcal{A}}(n) = (-1)^{\\#\\{a:a|n, a \\in \\mathcal{A}\\}} \\text{ or } (-1)^{\\#\\{a:a^\\nu\\parallel n, a \\in \\mathcal{A}, \\nu \\in \\mathbb{N}\\}}. \\end{align*} We show that \\begin{align*}\n  \\lim\\limits_{x\\to\\infty}\\frac{1}{x}\\sum\\limits_{n \\leq x} \\lambda_\\mathcal{A}(n) = 0 \\end{align*} holds, answering a question of de la Rue."},"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":"2312.06012","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-12-10T21:52:46Z","cross_cats_sorted":[],"title_canon_sha256":"e7dc8e9a66ad3927918f12bbe908e2f85ece91c08a5ba0692381b611ec458ac9","abstract_canon_sha256":"cc0d2b726bdf2b32295a3a0219f8ab2d5e1cecd935cd8fac0af7c81f709f4f3b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:23:11.000597Z","signature_b64":"Jl1xXYq3C6qNuExWkP4yocpPK+arh3fKXZjmRtxoFLG6j8epDlvI9bvPI6ZyMfvhGN5ZG0n7jgQ8E91FcshECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4dd6f53088975cecd3541ea5ab48f174c950aaacf85a485afe3cb838ecfbfe04","last_reissued_at":"2026-07-05T07:23:11.000174Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:23:11.000174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Correlations of Liouville-like Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yichen You","submitted_at":"2023-12-10T21:52:46Z","abstract_excerpt":"Let $\\mathcal{A}$ be a set of mutually coprime positive integers, satisfying \\begin{align*}\n  \\sum\\limits_{a\\in\\mathcal{A}}\\frac{1}{a} = \\infty. \\end{align*} Define the (possibly non-multiplicative) \"Liouville-like\" functions \\begin{align*}\n  \\lambda_{\\mathcal{A}}(n) = (-1)^{\\#\\{a:a|n, a \\in \\mathcal{A}\\}} \\text{ or } (-1)^{\\#\\{a:a^\\nu\\parallel n, a \\in \\mathcal{A}, \\nu \\in \\mathbb{N}\\}}. \\end{align*} We show that \\begin{align*}\n  \\lim\\limits_{x\\to\\infty}\\frac{1}{x}\\sum\\limits_{n \\leq x} \\lambda_\\mathcal{A}(n) = 0 \\end{align*} holds, answering a question of de la Rue."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.06012","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.06012/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2312.06012","created_at":"2026-07-05T07:23:11.000238+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.06012v2","created_at":"2026-07-05T07:23:11.000238+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.06012","created_at":"2026-07-05T07:23:11.000238+00:00"},{"alias_kind":"pith_short_12","alias_value":"JXLPKMEIS5OO","created_at":"2026-07-05T07:23:11.000238+00:00"},{"alias_kind":"pith_short_16","alias_value":"JXLPKMEIS5OOZU2U","created_at":"2026-07-05T07:23:11.000238+00:00"},{"alias_kind":"pith_short_8","alias_value":"JXLPKMEI","created_at":"2026-07-05T07:23:11.000238+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/JXLPKMEIS5OOZU2UD2S2WSHROT","json":"https://pith.science/pith/JXLPKMEIS5OOZU2UD2S2WSHROT.json","graph_json":"https://pith.science/api/pith-number/JXLPKMEIS5OOZU2UD2S2WSHROT/graph.json","events_json":"https://pith.science/api/pith-number/JXLPKMEIS5OOZU2UD2S2WSHROT/events.json","paper":"https://pith.science/paper/JXLPKMEI"},"agent_actions":{"view_html":"https://pith.science/pith/JXLPKMEIS5OOZU2UD2S2WSHROT","download_json":"https://pith.science/pith/JXLPKMEIS5OOZU2UD2S2WSHROT.json","view_paper":"https://pith.science/paper/JXLPKMEI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.06012&json=true","fetch_graph":"https://pith.science/api/pith-number/JXLPKMEIS5OOZU2UD2S2WSHROT/graph.json","fetch_events":"https://pith.science/api/pith-number/JXLPKMEIS5OOZU2UD2S2WSHROT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JXLPKMEIS5OOZU2UD2S2WSHROT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JXLPKMEIS5OOZU2UD2S2WSHROT/action/storage_attestation","attest_author":"https://pith.science/pith/JXLPKMEIS5OOZU2UD2S2WSHROT/action/author_attestation","sign_citation":"https://pith.science/pith/JXLPKMEIS5OOZU2UD2S2WSHROT/action/citation_signature","submit_replication":"https://pith.science/pith/JXLPKMEIS5OOZU2UD2S2WSHROT/action/replication_record"}},"created_at":"2026-07-05T07:23:11.000238+00:00","updated_at":"2026-07-05T07:23:11.000238+00:00"}