{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SDRPAAXTB7FDHL5VSU5AQRNPNR","short_pith_number":"pith:SDRPAAXT","canonical_record":{"source":{"id":"1502.02877","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-10T12:12:33Z","cross_cats_sorted":[],"title_canon_sha256":"14d7c494e457b2d6ff8f56d0a5782277a51cd2797794e948647810d8843bfece","abstract_canon_sha256":"a12e808d7093a232a89e79b742ee114a7e797cddfac79d62c60111620fa04ed6"},"schema_version":"1.0"},"canonical_sha256":"90e2f002f30fca33afb5953a0845af6c45c0c0c79ecb68d24c601acbb4f0288c","source":{"kind":"arxiv","id":"1502.02877","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02877","created_at":"2026-05-18T02:27:30Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02877v1","created_at":"2026-05-18T02:27:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02877","created_at":"2026-05-18T02:27:30Z"},{"alias_kind":"pith_short_12","alias_value":"SDRPAAXTB7FD","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"SDRPAAXTB7FDHL5V","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"SDRPAAXT","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SDRPAAXTB7FDHL5VSU5AQRNPNR","target":"record","payload":{"canonical_record":{"source":{"id":"1502.02877","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-10T12:12:33Z","cross_cats_sorted":[],"title_canon_sha256":"14d7c494e457b2d6ff8f56d0a5782277a51cd2797794e948647810d8843bfece","abstract_canon_sha256":"a12e808d7093a232a89e79b742ee114a7e797cddfac79d62c60111620fa04ed6"},"schema_version":"1.0"},"canonical_sha256":"90e2f002f30fca33afb5953a0845af6c45c0c0c79ecb68d24c601acbb4f0288c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:30.554209Z","signature_b64":"e0vRXIIwQ/hq9HgYI+569nf01smScgvNcs3mDeoG1eXunuWpEx/m0+J6rR7M8L3DoodID7hmGA3kd02UTMtuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90e2f002f30fca33afb5953a0845af6c45c0c0c79ecb68d24c601acbb4f0288c","last_reissued_at":"2026-05-18T02:27:30.553594Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:30.553594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.02877","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0rXJlLUOTJqmW42xFdfVA1qfPcehqsJfBYHcnc/tY0eVoOvBrv3bXh7kYLZLLv/sc9rN26GhAOzS/QL99aZcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:51:59.605093Z"},"content_sha256":"6e2897a8182f3d3f300f39a8e11b48c7c06d2441ef8f3b5f96a09d46b121071c","schema_version":"1.0","event_id":"sha256:6e2897a8182f3d3f300f39a8e11b48c7c06d2441ef8f3b5f96a09d46b121071c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SDRPAAXTB7FDHL5VSU5AQRNPNR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tur\\'an type inequalities for general Bessel functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"\\'Arp\\'ad Baricz, Saminathan Ponnusamy, Sanjeev Singh","submitted_at":"2015-02-10T12:12:33Z","abstract_excerpt":"In this paper some Tur\\'an type inequalities for the general Bessel function, monotonicity and bounds for its logarithmic derivative are derived. Moreover we find the series representation and the relative extrema of the Tur\\'anian of general Bessel functions. The key tools in the proofs are the recurrence relations together with some asymptotic relations for Bessel functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02877","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NcnLE3JH8MyelQy+JNfuBQufvsTJJwMLs0Qtak2lzX2unskapjHoQHnYnamA0MPltK+Ef/RBFrBrkBTnU9DxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:51:59.605450Z"},"content_sha256":"380377b3a6d6dc3a395a0ec40e2d1b4c159d4c6e45d34d1bf7de00c7c9bf1883","schema_version":"1.0","event_id":"sha256:380377b3a6d6dc3a395a0ec40e2d1b4c159d4c6e45d34d1bf7de00c7c9bf1883"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SDRPAAXTB7FDHL5VSU5AQRNPNR/bundle.json","state_url":"https://pith.science/pith/SDRPAAXTB7FDHL5VSU5AQRNPNR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SDRPAAXTB7FDHL5VSU5AQRNPNR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T09:51:59Z","links":{"resolver":"https://pith.science/pith/SDRPAAXTB7FDHL5VSU5AQRNPNR","bundle":"https://pith.science/pith/SDRPAAXTB7FDHL5VSU5AQRNPNR/bundle.json","state":"https://pith.science/pith/SDRPAAXTB7FDHL5VSU5AQRNPNR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SDRPAAXTB7FDHL5VSU5AQRNPNR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SDRPAAXTB7FDHL5VSU5AQRNPNR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a12e808d7093a232a89e79b742ee114a7e797cddfac79d62c60111620fa04ed6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-10T12:12:33Z","title_canon_sha256":"14d7c494e457b2d6ff8f56d0a5782277a51cd2797794e948647810d8843bfece"},"schema_version":"1.0","source":{"id":"1502.02877","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02877","created_at":"2026-05-18T02:27:30Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02877v1","created_at":"2026-05-18T02:27:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02877","created_at":"2026-05-18T02:27:30Z"},{"alias_kind":"pith_short_12","alias_value":"SDRPAAXTB7FD","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"SDRPAAXTB7FDHL5V","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"SDRPAAXT","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:380377b3a6d6dc3a395a0ec40e2d1b4c159d4c6e45d34d1bf7de00c7c9bf1883","target":"graph","created_at":"2026-05-18T02:27:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper some Tur\\'an type inequalities for the general Bessel function, monotonicity and bounds for its logarithmic derivative are derived. Moreover we find the series representation and the relative extrema of the Tur\\'anian of general Bessel functions. The key tools in the proofs are the recurrence relations together with some asymptotic relations for Bessel functions.","authors_text":"\\'Arp\\'ad Baricz, Saminathan Ponnusamy, Sanjeev Singh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-10T12:12:33Z","title":"Tur\\'an type inequalities for general Bessel functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02877","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6e2897a8182f3d3f300f39a8e11b48c7c06d2441ef8f3b5f96a09d46b121071c","target":"record","created_at":"2026-05-18T02:27:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a12e808d7093a232a89e79b742ee114a7e797cddfac79d62c60111620fa04ed6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-10T12:12:33Z","title_canon_sha256":"14d7c494e457b2d6ff8f56d0a5782277a51cd2797794e948647810d8843bfece"},"schema_version":"1.0","source":{"id":"1502.02877","kind":"arxiv","version":1}},"canonical_sha256":"90e2f002f30fca33afb5953a0845af6c45c0c0c79ecb68d24c601acbb4f0288c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90e2f002f30fca33afb5953a0845af6c45c0c0c79ecb68d24c601acbb4f0288c","first_computed_at":"2026-05-18T02:27:30.553594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:30.553594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e0vRXIIwQ/hq9HgYI+569nf01smScgvNcs3mDeoG1eXunuWpEx/m0+J6rR7M8L3DoodID7hmGA3kd02UTMtuDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:30.554209Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02877","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e2897a8182f3d3f300f39a8e11b48c7c06d2441ef8f3b5f96a09d46b121071c","sha256:380377b3a6d6dc3a395a0ec40e2d1b4c159d4c6e45d34d1bf7de00c7c9bf1883"],"state_sha256":"3c3517d8065af6788651fdcc4d378e1960b62c929cf126edd69bb102e814e6be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2IBY7Tw+iRI1kqu8BqgMcHcU16lSDp4tDQOrHJD6E0OZ4RSQghRdjVXf0JYOzhRgMuzGEeVGLmqajWeK16aGBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:51:59.607283Z","bundle_sha256":"a1fd758f03e9fa5fef8d89933c756312c246d47e1ac4bdf3ec6d1b135a985e29"}}