{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3SSOPHKDOLDHP65RYB2YRNNOJC","short_pith_number":"pith:3SSOPHKD","schema_version":"1.0","canonical_sha256":"dca4e79d4372c677fbb1c07588b5ae488f8a438637d4fa5dd8244aad3c371c01","source":{"kind":"arxiv","id":"1211.7325","version":2},"attestation_state":"computed","paper":{"title":"Inequalities for modified Bessel functions and their integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Robert E. Gaunt","submitted_at":"2012-11-30T17:46:15Z","abstract_excerpt":"Simple inequalities for some integrals involving the modified Bessel functions $I_{\\nu}(x)$ and $K_{\\nu}(x)$ are established. We also obtain a monotonicity result for $K_{\\nu}(x)$ and a new lower bound, that involves gamma functions, for $K_0(x)$."},"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":"1211.7325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-30T17:46:15Z","cross_cats_sorted":[],"title_canon_sha256":"aaa0eef17e9f561d9b5f91b4d4939d7962d5841605147d6ce6391a9436eb8b92","abstract_canon_sha256":"35adb3bc8d7e65ee2c9fcb02d2b5c72ea5f8a806e1280d3d280256f2c6dd3d9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:29.025791Z","signature_b64":"/mjjLLEbzqyPjRnrSEnK8YmwkIjnnUwPCVgZ+XA2T4bo6Lp+NtW06t0AljFgdPeJjrn7PTn0gs6rISOCdK7DCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dca4e79d4372c677fbb1c07588b5ae488f8a438637d4fa5dd8244aad3c371c01","last_reissued_at":"2026-05-18T00:48:29.025087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:29.025087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inequalities for modified Bessel functions and their integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Robert E. Gaunt","submitted_at":"2012-11-30T17:46:15Z","abstract_excerpt":"Simple inequalities for some integrals involving the modified Bessel functions $I_{\\nu}(x)$ and $K_{\\nu}(x)$ are established. We also obtain a monotonicity result for $K_{\\nu}(x)$ and a new lower bound, that involves gamma functions, for $K_0(x)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7325","kind":"arxiv","version":2},"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":"1211.7325","created_at":"2026-05-18T00:48:29.025190+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.7325v2","created_at":"2026-05-18T00:48:29.025190+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7325","created_at":"2026-05-18T00:48:29.025190+00:00"},{"alias_kind":"pith_short_12","alias_value":"3SSOPHKDOLDH","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3SSOPHKDOLDHP65R","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3SSOPHKD","created_at":"2026-05-18T12:26:53.410803+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/3SSOPHKDOLDHP65RYB2YRNNOJC","json":"https://pith.science/pith/3SSOPHKDOLDHP65RYB2YRNNOJC.json","graph_json":"https://pith.science/api/pith-number/3SSOPHKDOLDHP65RYB2YRNNOJC/graph.json","events_json":"https://pith.science/api/pith-number/3SSOPHKDOLDHP65RYB2YRNNOJC/events.json","paper":"https://pith.science/paper/3SSOPHKD"},"agent_actions":{"view_html":"https://pith.science/pith/3SSOPHKDOLDHP65RYB2YRNNOJC","download_json":"https://pith.science/pith/3SSOPHKDOLDHP65RYB2YRNNOJC.json","view_paper":"https://pith.science/paper/3SSOPHKD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.7325&json=true","fetch_graph":"https://pith.science/api/pith-number/3SSOPHKDOLDHP65RYB2YRNNOJC/graph.json","fetch_events":"https://pith.science/api/pith-number/3SSOPHKDOLDHP65RYB2YRNNOJC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3SSOPHKDOLDHP65RYB2YRNNOJC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3SSOPHKDOLDHP65RYB2YRNNOJC/action/storage_attestation","attest_author":"https://pith.science/pith/3SSOPHKDOLDHP65RYB2YRNNOJC/action/author_attestation","sign_citation":"https://pith.science/pith/3SSOPHKDOLDHP65RYB2YRNNOJC/action/citation_signature","submit_replication":"https://pith.science/pith/3SSOPHKDOLDHP65RYB2YRNNOJC/action/replication_record"}},"created_at":"2026-05-18T00:48:29.025190+00:00","updated_at":"2026-05-18T00:48:29.025190+00:00"}