{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:Z6MYZPIMKHRPZZHJ7PK2IBTHME","short_pith_number":"pith:Z6MYZPIM","schema_version":"1.0","canonical_sha256":"cf998cbd0c51e2fce4e9fbd5a4066761398109725db6df3509a30b4748a937cc","source":{"kind":"arxiv","id":"1011.5940","version":1},"attestation_state":"computed","paper":{"title":"Unimodal sequences show Lambert W is Bernstein","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D.J. Jeffrey, G.A. Kalugin","submitted_at":"2010-11-27T00:10:11Z","abstract_excerpt":"We consider a sequence of polynomials appearing in expressions for the derivatives of the Lambert W function. The coefficients of each polynomial are shown to form a positive sequence that is log-concave and unimodal. This property implies that the positive real branch of the Lambert W function is a Bernstein 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":"1011.5940","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-27T00:10:11Z","cross_cats_sorted":[],"title_canon_sha256":"ee76e99b7669c3c118e7231aebed459b87ec4fc57961db8f232018d7020d60aa","abstract_canon_sha256":"8ea4422b7ce735d0f7a3f47057d044ae6ab0668eb72eff562c1016548ebd2a6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:37.867423Z","signature_b64":"94pLL3Or1OyMz3pLuNYwuIBvpeGViJu5+1zH/iHTLm/q+ZzpB04FnxqXgLLRCpIwZNFCVAMmQxEXxQsnHeH1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf998cbd0c51e2fce4e9fbd5a4066761398109725db6df3509a30b4748a937cc","last_reissued_at":"2026-05-18T04:34:37.866745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:37.866745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unimodal sequences show Lambert W is Bernstein","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D.J. Jeffrey, G.A. Kalugin","submitted_at":"2010-11-27T00:10:11Z","abstract_excerpt":"We consider a sequence of polynomials appearing in expressions for the derivatives of the Lambert W function. The coefficients of each polynomial are shown to form a positive sequence that is log-concave and unimodal. This property implies that the positive real branch of the Lambert W function is a Bernstein function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5940","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":"1011.5940","created_at":"2026-05-18T04:34:37.866850+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.5940v1","created_at":"2026-05-18T04:34:37.866850+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5940","created_at":"2026-05-18T04:34:37.866850+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z6MYZPIMKHRP","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z6MYZPIMKHRPZZHJ","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z6MYZPIM","created_at":"2026-05-18T12:26:17.028572+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/Z6MYZPIMKHRPZZHJ7PK2IBTHME","json":"https://pith.science/pith/Z6MYZPIMKHRPZZHJ7PK2IBTHME.json","graph_json":"https://pith.science/api/pith-number/Z6MYZPIMKHRPZZHJ7PK2IBTHME/graph.json","events_json":"https://pith.science/api/pith-number/Z6MYZPIMKHRPZZHJ7PK2IBTHME/events.json","paper":"https://pith.science/paper/Z6MYZPIM"},"agent_actions":{"view_html":"https://pith.science/pith/Z6MYZPIMKHRPZZHJ7PK2IBTHME","download_json":"https://pith.science/pith/Z6MYZPIMKHRPZZHJ7PK2IBTHME.json","view_paper":"https://pith.science/paper/Z6MYZPIM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.5940&json=true","fetch_graph":"https://pith.science/api/pith-number/Z6MYZPIMKHRPZZHJ7PK2IBTHME/graph.json","fetch_events":"https://pith.science/api/pith-number/Z6MYZPIMKHRPZZHJ7PK2IBTHME/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z6MYZPIMKHRPZZHJ7PK2IBTHME/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z6MYZPIMKHRPZZHJ7PK2IBTHME/action/storage_attestation","attest_author":"https://pith.science/pith/Z6MYZPIMKHRPZZHJ7PK2IBTHME/action/author_attestation","sign_citation":"https://pith.science/pith/Z6MYZPIMKHRPZZHJ7PK2IBTHME/action/citation_signature","submit_replication":"https://pith.science/pith/Z6MYZPIMKHRPZZHJ7PK2IBTHME/action/replication_record"}},"created_at":"2026-05-18T04:34:37.866850+00:00","updated_at":"2026-05-18T04:34:37.866850+00:00"}