{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OIIB752KSLZFKGNQLGD5X4GIGG","short_pith_number":"pith:OIIB752K","schema_version":"1.0","canonical_sha256":"72101ff74a92f25519b05987dbf0c831984e2c407d765ed5d0be1e3f6bb7586b","source":{"kind":"arxiv","id":"1303.1582","version":1},"attestation_state":"computed","paper":{"title":"Complete monotonicity of a difference between the exponential and trigamma functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Feng Qi, Xiao-Jing Zhang","submitted_at":"2013-03-07T00:49:41Z","abstract_excerpt":"In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function $e^{1/t}$ and the trigamma function $\\psi'(t)$ on $(0,\\infty)$."},"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":"1303.1582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-07T00:49:41Z","cross_cats_sorted":[],"title_canon_sha256":"6d4192590a3ff95288b1404545170b1f0abb4b9d7bf83722ac517d9f1f03c931","abstract_canon_sha256":"615e3bd49414f1afcae0af28a29ad1d45c2765125fed85dc7baab0b2b3161b95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:34.173039Z","signature_b64":"YWAYQTM73SD1Inc6MjwoVILe4Yhi6nrzeFQhQpUN3X1x1PXXH0F645hzSzPQMvgtf6rWyZgOUagkC3IzPMg3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72101ff74a92f25519b05987dbf0c831984e2c407d765ed5d0be1e3f6bb7586b","last_reissued_at":"2026-05-18T02:50:34.172485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:34.172485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete monotonicity of a difference between the exponential and trigamma functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Feng Qi, Xiao-Jing Zhang","submitted_at":"2013-03-07T00:49:41Z","abstract_excerpt":"In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function $e^{1/t}$ and the trigamma function $\\psi'(t)$ on $(0,\\infty)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1582","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":"1303.1582","created_at":"2026-05-18T02:50:34.172574+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.1582v1","created_at":"2026-05-18T02:50:34.172574+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1582","created_at":"2026-05-18T02:50:34.172574+00:00"},{"alias_kind":"pith_short_12","alias_value":"OIIB752KSLZF","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OIIB752KSLZFKGNQ","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OIIB752K","created_at":"2026-05-18T12:27:54.935989+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/OIIB752KSLZFKGNQLGD5X4GIGG","json":"https://pith.science/pith/OIIB752KSLZFKGNQLGD5X4GIGG.json","graph_json":"https://pith.science/api/pith-number/OIIB752KSLZFKGNQLGD5X4GIGG/graph.json","events_json":"https://pith.science/api/pith-number/OIIB752KSLZFKGNQLGD5X4GIGG/events.json","paper":"https://pith.science/paper/OIIB752K"},"agent_actions":{"view_html":"https://pith.science/pith/OIIB752KSLZFKGNQLGD5X4GIGG","download_json":"https://pith.science/pith/OIIB752KSLZFKGNQLGD5X4GIGG.json","view_paper":"https://pith.science/paper/OIIB752K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.1582&json=true","fetch_graph":"https://pith.science/api/pith-number/OIIB752KSLZFKGNQLGD5X4GIGG/graph.json","fetch_events":"https://pith.science/api/pith-number/OIIB752KSLZFKGNQLGD5X4GIGG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OIIB752KSLZFKGNQLGD5X4GIGG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OIIB752KSLZFKGNQLGD5X4GIGG/action/storage_attestation","attest_author":"https://pith.science/pith/OIIB752KSLZFKGNQLGD5X4GIGG/action/author_attestation","sign_citation":"https://pith.science/pith/OIIB752KSLZFKGNQLGD5X4GIGG/action/citation_signature","submit_replication":"https://pith.science/pith/OIIB752KSLZFKGNQLGD5X4GIGG/action/replication_record"}},"created_at":"2026-05-18T02:50:34.172574+00:00","updated_at":"2026-05-18T02:50:34.172574+00:00"}