{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7ZTNQRTEYVLOMAOFU4PKXCQXVH","short_pith_number":"pith:7ZTNQRTE","schema_version":"1.0","canonical_sha256":"fe66d84664c556e601c5a71eab8a17a9f262830662bebf30e3872847e93bb37a","source":{"kind":"arxiv","id":"1812.04309","version":1},"attestation_state":"computed","paper":{"title":"An arithmetical function related to B\\'aez-Duarte's criterion for the Riemann hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michel Balazard (I2M)","submitted_at":"2018-12-11T10:01:50Z","abstract_excerpt":"In this mainly expository article, we revisit some formal aspects of B{\\'a}ez-Duarte's criterion for the Riemann hypothesis. In particular, starting from Weingartner's formulation of the criterion, we define an arithmetical function $\\nu$, which is equal to the M{\\\"o}bius function if, and only if the Riemann hypothesis is true. We record the basic properties of the Dirichlet series of $\\nu$, and state a few questions.\n  KEYWORDS: Riemann hypothesis, arithmetical functions, Dirichlet series, Hilbert space"},"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":"1812.04309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-11T10:01:50Z","cross_cats_sorted":[],"title_canon_sha256":"0bfa389d48ff07ac2eee75fb678113f5cf2ae685fcb86347e8dbc89c1e87ac7c","abstract_canon_sha256":"5137e642f097eef4c7fcd59b3a87a0eccfa597f3062bdd88a44be2395a212f6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:32.622310Z","signature_b64":"7vKNUTcDWgHJhqrNTP3+xiP4X4yICNRRQyIs5gbs2sGuLWkka74OLQ74tAbajcKrp64Rzsru6qoeTqrbG9DABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe66d84664c556e601c5a71eab8a17a9f262830662bebf30e3872847e93bb37a","last_reissued_at":"2026-05-17T23:58:32.621598Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:32.621598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An arithmetical function related to B\\'aez-Duarte's criterion for the Riemann hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michel Balazard (I2M)","submitted_at":"2018-12-11T10:01:50Z","abstract_excerpt":"In this mainly expository article, we revisit some formal aspects of B{\\'a}ez-Duarte's criterion for the Riemann hypothesis. In particular, starting from Weingartner's formulation of the criterion, we define an arithmetical function $\\nu$, which is equal to the M{\\\"o}bius function if, and only if the Riemann hypothesis is true. We record the basic properties of the Dirichlet series of $\\nu$, and state a few questions.\n  KEYWORDS: Riemann hypothesis, arithmetical functions, Dirichlet series, Hilbert space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04309","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":"1812.04309","created_at":"2026-05-17T23:58:32.621699+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.04309v1","created_at":"2026-05-17T23:58:32.621699+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04309","created_at":"2026-05-17T23:58:32.621699+00:00"},{"alias_kind":"pith_short_12","alias_value":"7ZTNQRTEYVLO","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"7ZTNQRTEYVLOMAOF","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"7ZTNQRTE","created_at":"2026-05-18T12:32:13.499390+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/7ZTNQRTEYVLOMAOFU4PKXCQXVH","json":"https://pith.science/pith/7ZTNQRTEYVLOMAOFU4PKXCQXVH.json","graph_json":"https://pith.science/api/pith-number/7ZTNQRTEYVLOMAOFU4PKXCQXVH/graph.json","events_json":"https://pith.science/api/pith-number/7ZTNQRTEYVLOMAOFU4PKXCQXVH/events.json","paper":"https://pith.science/paper/7ZTNQRTE"},"agent_actions":{"view_html":"https://pith.science/pith/7ZTNQRTEYVLOMAOFU4PKXCQXVH","download_json":"https://pith.science/pith/7ZTNQRTEYVLOMAOFU4PKXCQXVH.json","view_paper":"https://pith.science/paper/7ZTNQRTE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.04309&json=true","fetch_graph":"https://pith.science/api/pith-number/7ZTNQRTEYVLOMAOFU4PKXCQXVH/graph.json","fetch_events":"https://pith.science/api/pith-number/7ZTNQRTEYVLOMAOFU4PKXCQXVH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7ZTNQRTEYVLOMAOFU4PKXCQXVH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7ZTNQRTEYVLOMAOFU4PKXCQXVH/action/storage_attestation","attest_author":"https://pith.science/pith/7ZTNQRTEYVLOMAOFU4PKXCQXVH/action/author_attestation","sign_citation":"https://pith.science/pith/7ZTNQRTEYVLOMAOFU4PKXCQXVH/action/citation_signature","submit_replication":"https://pith.science/pith/7ZTNQRTEYVLOMAOFU4PKXCQXVH/action/replication_record"}},"created_at":"2026-05-17T23:58:32.621699+00:00","updated_at":"2026-05-17T23:58:32.621699+00:00"}