{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BCO6APO5OD2HEYYYEX6BDOILMY","short_pith_number":"pith:BCO6APO5","schema_version":"1.0","canonical_sha256":"089de03ddd70f472631825fc11b90b66372f8f899ec08d1db96246c304a55473","source":{"kind":"arxiv","id":"1205.1112","version":1},"attestation_state":"computed","paper":{"title":"A function Class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jamel El Kamel, Khaled Mehrez","submitted_at":"2012-05-05T08:22:29Z","abstract_excerpt":"In this paper we give some conditions for a class of functions related to Bessel functions to be positive definite or strictly positive definite . We present some properties and relationships involving logarithmically completely monotonic functions and strictly positive definite functions. In particular, we are interested with the modified Bessel functions."},"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":"1205.1112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-05T08:22:29Z","cross_cats_sorted":[],"title_canon_sha256":"52089447c205cc2822271998cad54dc4fcbf346ee227737991a352a62339ed6e","abstract_canon_sha256":"cdbd1c5477de989c1c4c4afad52c1905d8ae6918a7feaa73034e38eeb04570bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:12.082815Z","signature_b64":"siIkuLmgnlyv7bRq5SU5R4us42xjYXcGoPAJ1NhD6cC7ijF91NEbTBjkkBm8A4nsM7g/NU+FNunV/6VlXSFQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"089de03ddd70f472631825fc11b90b66372f8f899ec08d1db96246c304a55473","last_reissued_at":"2026-05-18T03:56:12.082181Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:12.082181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A function Class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jamel El Kamel, Khaled Mehrez","submitted_at":"2012-05-05T08:22:29Z","abstract_excerpt":"In this paper we give some conditions for a class of functions related to Bessel functions to be positive definite or strictly positive definite . We present some properties and relationships involving logarithmically completely monotonic functions and strictly positive definite functions. In particular, we are interested with the modified Bessel functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1112","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":"1205.1112","created_at":"2026-05-18T03:56:12.082281+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.1112v1","created_at":"2026-05-18T03:56:12.082281+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1112","created_at":"2026-05-18T03:56:12.082281+00:00"},{"alias_kind":"pith_short_12","alias_value":"BCO6APO5OD2H","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"BCO6APO5OD2HEYYY","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"BCO6APO5","created_at":"2026-05-18T12:26:58.693483+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/BCO6APO5OD2HEYYYEX6BDOILMY","json":"https://pith.science/pith/BCO6APO5OD2HEYYYEX6BDOILMY.json","graph_json":"https://pith.science/api/pith-number/BCO6APO5OD2HEYYYEX6BDOILMY/graph.json","events_json":"https://pith.science/api/pith-number/BCO6APO5OD2HEYYYEX6BDOILMY/events.json","paper":"https://pith.science/paper/BCO6APO5"},"agent_actions":{"view_html":"https://pith.science/pith/BCO6APO5OD2HEYYYEX6BDOILMY","download_json":"https://pith.science/pith/BCO6APO5OD2HEYYYEX6BDOILMY.json","view_paper":"https://pith.science/paper/BCO6APO5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.1112&json=true","fetch_graph":"https://pith.science/api/pith-number/BCO6APO5OD2HEYYYEX6BDOILMY/graph.json","fetch_events":"https://pith.science/api/pith-number/BCO6APO5OD2HEYYYEX6BDOILMY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BCO6APO5OD2HEYYYEX6BDOILMY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BCO6APO5OD2HEYYYEX6BDOILMY/action/storage_attestation","attest_author":"https://pith.science/pith/BCO6APO5OD2HEYYYEX6BDOILMY/action/author_attestation","sign_citation":"https://pith.science/pith/BCO6APO5OD2HEYYYEX6BDOILMY/action/citation_signature","submit_replication":"https://pith.science/pith/BCO6APO5OD2HEYYYEX6BDOILMY/action/replication_record"}},"created_at":"2026-05-18T03:56:12.082281+00:00","updated_at":"2026-05-18T03:56:12.082281+00:00"}