{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TDEICF4LVAH3PLIWVIYOLZTRWT","short_pith_number":"pith:TDEICF4L","canonical_record":{"source":{"id":"1601.01007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-05T22:41:00Z","cross_cats_sorted":[],"title_canon_sha256":"41f6431306928a077ad3bf7bc80b9ea85c58e9bf08eb4ddbf0766bb85ebe9b69","abstract_canon_sha256":"9bb22cea56aa5ed1ae3875063341b8bcec854a868c9687851c23ecebb5e4ccac"},"schema_version":"1.0"},"canonical_sha256":"98c881178ba80fb7ad16aa30e5e671b4ed61753693af6e83ae66a4b3797d6893","source":{"kind":"arxiv","id":"1601.01007","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01007","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01007v1","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01007","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"pith_short_12","alias_value":"TDEICF4LVAH3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TDEICF4LVAH3PLIW","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TDEICF4L","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TDEICF4LVAH3PLIWVIYOLZTRWT","target":"record","payload":{"canonical_record":{"source":{"id":"1601.01007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-05T22:41:00Z","cross_cats_sorted":[],"title_canon_sha256":"41f6431306928a077ad3bf7bc80b9ea85c58e9bf08eb4ddbf0766bb85ebe9b69","abstract_canon_sha256":"9bb22cea56aa5ed1ae3875063341b8bcec854a868c9687851c23ecebb5e4ccac"},"schema_version":"1.0"},"canonical_sha256":"98c881178ba80fb7ad16aa30e5e671b4ed61753693af6e83ae66a4b3797d6893","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:18.236434Z","signature_b64":"PBxBpiLpuwdK/uO9nrzNyKzF8IELOawg/DvdcFQEg10UrOZhjdB07GDwdsULQBaUu9bHEzjlMD7YuBrQK1j0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98c881178ba80fb7ad16aa30e5e671b4ed61753693af6e83ae66a4b3797d6893","last_reissued_at":"2026-05-18T01:23:18.235797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:18.235797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.01007","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":"2026-05-18T01:23:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HIPVZIkhgY1wCsCHeuD1+OXehjytBE1esgQPZd+d9xhMaqsKCtDx5Ht4I+TPhpbwfYkXE1IDALXgcO9TfglFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T16:24:26.638759Z"},"content_sha256":"4527111197dc4724d65f6690e8f31979fb8151f1be99d6e6e8a93e6ab1a3eb80","schema_version":"1.0","event_id":"sha256:4527111197dc4724d65f6690e8f31979fb8151f1be99d6e6e8a93e6ab1a3eb80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TDEICF4LVAH3PLIWVIYOLZTRWT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Huygens types inequalities for Bessel and modified Bessel functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Khaled Mehrez","submitted_at":"2016-01-05T22:41:00Z","abstract_excerpt":"In this paper, we present a generalization of the Huygens types inequalities involving Bessel and modified Bessel functions of the first kind."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01007","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":"2026-05-18T01:23:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9gcvJq9ggrz/DF8AKu0sgU23FoVP5UgUxe1Qy01K2BasUJtkC8OhlS31uw9ObqRftRRYPC4ZBXMzxW3KmgMEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T16:24:26.639084Z"},"content_sha256":"fff88b97c28833a3f89a516f88beb0288dba171dd6be060f6b043251bf12ef14","schema_version":"1.0","event_id":"sha256:fff88b97c28833a3f89a516f88beb0288dba171dd6be060f6b043251bf12ef14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TDEICF4LVAH3PLIWVIYOLZTRWT/bundle.json","state_url":"https://pith.science/pith/TDEICF4LVAH3PLIWVIYOLZTRWT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TDEICF4LVAH3PLIWVIYOLZTRWT/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":"2026-07-03T16:24:26Z","links":{"resolver":"https://pith.science/pith/TDEICF4LVAH3PLIWVIYOLZTRWT","bundle":"https://pith.science/pith/TDEICF4LVAH3PLIWVIYOLZTRWT/bundle.json","state":"https://pith.science/pith/TDEICF4LVAH3PLIWVIYOLZTRWT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TDEICF4LVAH3PLIWVIYOLZTRWT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TDEICF4LVAH3PLIWVIYOLZTRWT","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":"9bb22cea56aa5ed1ae3875063341b8bcec854a868c9687851c23ecebb5e4ccac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-05T22:41:00Z","title_canon_sha256":"41f6431306928a077ad3bf7bc80b9ea85c58e9bf08eb4ddbf0766bb85ebe9b69"},"schema_version":"1.0","source":{"id":"1601.01007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01007","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01007v1","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01007","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"pith_short_12","alias_value":"TDEICF4LVAH3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TDEICF4LVAH3PLIW","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TDEICF4L","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:fff88b97c28833a3f89a516f88beb0288dba171dd6be060f6b043251bf12ef14","target":"graph","created_at":"2026-05-18T01:23:18Z","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, we present a generalization of the Huygens types inequalities involving Bessel and modified Bessel functions of the first kind.","authors_text":"Khaled Mehrez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-05T22:41:00Z","title":"Generalized Huygens types inequalities for Bessel and modified Bessel functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01007","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":"sha256:4527111197dc4724d65f6690e8f31979fb8151f1be99d6e6e8a93e6ab1a3eb80","target":"record","created_at":"2026-05-18T01:23:18Z","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":"9bb22cea56aa5ed1ae3875063341b8bcec854a868c9687851c23ecebb5e4ccac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-05T22:41:00Z","title_canon_sha256":"41f6431306928a077ad3bf7bc80b9ea85c58e9bf08eb4ddbf0766bb85ebe9b69"},"schema_version":"1.0","source":{"id":"1601.01007","kind":"arxiv","version":1}},"canonical_sha256":"98c881178ba80fb7ad16aa30e5e671b4ed61753693af6e83ae66a4b3797d6893","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98c881178ba80fb7ad16aa30e5e671b4ed61753693af6e83ae66a4b3797d6893","first_computed_at":"2026-05-18T01:23:18.235797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:18.235797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PBxBpiLpuwdK/uO9nrzNyKzF8IELOawg/DvdcFQEg10UrOZhjdB07GDwdsULQBaUu9bHEzjlMD7YuBrQK1j0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:18.236434Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4527111197dc4724d65f6690e8f31979fb8151f1be99d6e6e8a93e6ab1a3eb80","sha256:fff88b97c28833a3f89a516f88beb0288dba171dd6be060f6b043251bf12ef14"],"state_sha256":"cca2276a2e70a76b71219c7216e0ba482e39ad05fbc44d9053b969264ef6bdfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stIgtO4NLoheLQutSgwNqyc9Pm76cLGGl97SnIlhqwXg2cJcY/UbDM/a8H8CzHMAyhb4NBgly4iL4ggNQpz2Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T16:24:26.640923Z","bundle_sha256":"9c77344b6506a54b594433815019f63ba25153b3417d0d71269fd240a4542cf3"}}