{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:LLBV7PQS5TERZVE47EZKXRXDGM","short_pith_number":"pith:LLBV7PQS","schema_version":"1.0","canonical_sha256":"5ac35fbe12ecc91cd49cf932abc6e33305b8c5241f222217a97794f6bcc3334a","source":{"kind":"arxiv","id":"1907.07664","version":1},"attestation_state":"computed","paper":{"title":"The Landau function and the Riemann Hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean-Louis Nicolas, Marc Deleglise","submitted_at":"2019-07-17T17:50:03Z","abstract_excerpt":"The Landau function $g(n)$ is the maximal order of an element of the symmetric group of degree $n$; it is also the largest product of powers of primes whose sum is $\\le n$. The main result of this article is that the property \" For all $n > 0$ , $log g(n) < li^{-1} (n))$ \" (where $li^{-1}(n)$ denotes the inverse function of the logarithmic integral) is equivalent to the Riemann hypothesis."},"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":"1907.07664","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-17T17:50:03Z","cross_cats_sorted":[],"title_canon_sha256":"ecc8b52837e3717f9e4cd182a6a4bbf8ca5a230520a88c9982df2941e0ae16cf","abstract_canon_sha256":"d0d3a3c5537aaadc61136a1c8e661eab848c6c15fb273f42670ac2a450a1eec7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:21.351428Z","signature_b64":"wcJ/f6xjOL2ensanH43Cjgr6o5Dt8l5mjhBMGhc3JViqY0fczBKNTlXiXaExbaETZ/TzE0Z60oVPn9rCX1G9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ac35fbe12ecc91cd49cf932abc6e33305b8c5241f222217a97794f6bcc3334a","last_reissued_at":"2026-05-17T23:40:21.350824Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:21.350824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Landau function and the Riemann Hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean-Louis Nicolas, Marc Deleglise","submitted_at":"2019-07-17T17:50:03Z","abstract_excerpt":"The Landau function $g(n)$ is the maximal order of an element of the symmetric group of degree $n$; it is also the largest product of powers of primes whose sum is $\\le n$. The main result of this article is that the property \" For all $n > 0$ , $log g(n) < li^{-1} (n))$ \" (where $li^{-1}(n)$ denotes the inverse function of the logarithmic integral) is equivalent to the Riemann hypothesis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07664","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":"1907.07664","created_at":"2026-05-17T23:40:21.350903+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.07664v1","created_at":"2026-05-17T23:40:21.350903+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07664","created_at":"2026-05-17T23:40:21.350903+00:00"},{"alias_kind":"pith_short_12","alias_value":"LLBV7PQS5TER","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"LLBV7PQS5TERZVE4","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"LLBV7PQS","created_at":"2026-05-18T12:33:21.387695+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/LLBV7PQS5TERZVE47EZKXRXDGM","json":"https://pith.science/pith/LLBV7PQS5TERZVE47EZKXRXDGM.json","graph_json":"https://pith.science/api/pith-number/LLBV7PQS5TERZVE47EZKXRXDGM/graph.json","events_json":"https://pith.science/api/pith-number/LLBV7PQS5TERZVE47EZKXRXDGM/events.json","paper":"https://pith.science/paper/LLBV7PQS"},"agent_actions":{"view_html":"https://pith.science/pith/LLBV7PQS5TERZVE47EZKXRXDGM","download_json":"https://pith.science/pith/LLBV7PQS5TERZVE47EZKXRXDGM.json","view_paper":"https://pith.science/paper/LLBV7PQS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.07664&json=true","fetch_graph":"https://pith.science/api/pith-number/LLBV7PQS5TERZVE47EZKXRXDGM/graph.json","fetch_events":"https://pith.science/api/pith-number/LLBV7PQS5TERZVE47EZKXRXDGM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LLBV7PQS5TERZVE47EZKXRXDGM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LLBV7PQS5TERZVE47EZKXRXDGM/action/storage_attestation","attest_author":"https://pith.science/pith/LLBV7PQS5TERZVE47EZKXRXDGM/action/author_attestation","sign_citation":"https://pith.science/pith/LLBV7PQS5TERZVE47EZKXRXDGM/action/citation_signature","submit_replication":"https://pith.science/pith/LLBV7PQS5TERZVE47EZKXRXDGM/action/replication_record"}},"created_at":"2026-05-17T23:40:21.350903+00:00","updated_at":"2026-05-17T23:40:21.350903+00:00"}