{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QVYC3OQSKTCG2D5UZQ66WYVXBK","short_pith_number":"pith:QVYC3OQS","canonical_record":{"source":{"id":"1903.08487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-03-20T12:50:50Z","cross_cats_sorted":[],"title_canon_sha256":"5235e2ac9dafce030dfab77cf50ed53930c3efd1dcaf7075872413da84ef678a","abstract_canon_sha256":"07057dc136715da0dc3f21c06f68944b6234ef76de30100e892b72d377b272f6"},"schema_version":"1.0"},"canonical_sha256":"85702dba1254c46d0fb4cc3deb62b70a87edb157b6034f5fe8c5b0ebfe0be82c","source":{"kind":"arxiv","id":"1903.08487","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.08487","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1903.08487v1","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.08487","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"QVYC3OQSKTCG","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QVYC3OQSKTCG2D5U","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QVYC3OQS","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QVYC3OQSKTCG2D5UZQ66WYVXBK","target":"record","payload":{"canonical_record":{"source":{"id":"1903.08487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-03-20T12:50:50Z","cross_cats_sorted":[],"title_canon_sha256":"5235e2ac9dafce030dfab77cf50ed53930c3efd1dcaf7075872413da84ef678a","abstract_canon_sha256":"07057dc136715da0dc3f21c06f68944b6234ef76de30100e892b72d377b272f6"},"schema_version":"1.0"},"canonical_sha256":"85702dba1254c46d0fb4cc3deb62b70a87edb157b6034f5fe8c5b0ebfe0be82c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:47.970963Z","signature_b64":"xE6WPa6t4W/r8jM5zk0zkyMDpT3OSq/PzSaZUOBDD9v+ARWKVh98/Ivxh11MINzJ8nn18ped7cRGPwnKzbYgBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85702dba1254c46d0fb4cc3deb62b70a87edb157b6034f5fe8c5b0ebfe0be82c","last_reissued_at":"2026-05-17T23:50:47.970267Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:47.970267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.08487","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":"2026-05-17T23:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MXpp7LP5pGkIBJ/yJtHYGcaFAEKYPBP8k479XU2uW4T7u4iKc/EqGq8vUXm9EDEfq5eSrAgIatVLmKRHjKDeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:38:29.789790Z"},"content_sha256":"dead00b69462d38d55f7ef93259ba157de21c2c7f19acac65b3f2cc981932959","schema_version":"1.0","event_id":"sha256:dead00b69462d38d55f7ef93259ba157de21c2c7f19acac65b3f2cc981932959"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QVYC3OQSKTCG2D5UZQ66WYVXBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On integrals involving quotients of hyperbolic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"R B Paris, S A Dar","submitted_at":"2019-03-20T12:50:50Z","abstract_excerpt":"We evaluate some integrals over $[0,\\infty)$ of quotients of powers of the hyperbolic functions $\\sinh x$ and $\\cosh x$ using a hypergeometric approach. Some of these results appear to be new but several verify the entries in the table of integrals of Gradshteyn and Rhyzik."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08487","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":"2026-05-17T23:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eC8m7Jzi+NKpEGpgfWeuHott7fnpTwpGgmFmu+9MGu9+EZ+Hu8pD71tZ8kIaB0RvJgymb78JVAqpazF40TBPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:38:29.790535Z"},"content_sha256":"3451df239fa81d4954db456a0fe6c0ee05deb58d9d9a260f0f36101f15dad18c","schema_version":"1.0","event_id":"sha256:3451df239fa81d4954db456a0fe6c0ee05deb58d9d9a260f0f36101f15dad18c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVYC3OQSKTCG2D5UZQ66WYVXBK/bundle.json","state_url":"https://pith.science/pith/QVYC3OQSKTCG2D5UZQ66WYVXBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVYC3OQSKTCG2D5UZQ66WYVXBK/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":"2026-06-12T00:38:29Z","links":{"resolver":"https://pith.science/pith/QVYC3OQSKTCG2D5UZQ66WYVXBK","bundle":"https://pith.science/pith/QVYC3OQSKTCG2D5UZQ66WYVXBK/bundle.json","state":"https://pith.science/pith/QVYC3OQSKTCG2D5UZQ66WYVXBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVYC3OQSKTCG2D5UZQ66WYVXBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QVYC3OQSKTCG2D5UZQ66WYVXBK","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":"07057dc136715da0dc3f21c06f68944b6234ef76de30100e892b72d377b272f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-03-20T12:50:50Z","title_canon_sha256":"5235e2ac9dafce030dfab77cf50ed53930c3efd1dcaf7075872413da84ef678a"},"schema_version":"1.0","source":{"id":"1903.08487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.08487","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1903.08487v1","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.08487","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"QVYC3OQSKTCG","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QVYC3OQSKTCG2D5U","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QVYC3OQS","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:3451df239fa81d4954db456a0fe6c0ee05deb58d9d9a260f0f36101f15dad18c","target":"graph","created_at":"2026-05-17T23:50:47Z","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":"We evaluate some integrals over $[0,\\infty)$ of quotients of powers of the hyperbolic functions $\\sinh x$ and $\\cosh x$ using a hypergeometric approach. Some of these results appear to be new but several verify the entries in the table of integrals of Gradshteyn and Rhyzik.","authors_text":"R B Paris, S A Dar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-03-20T12:50:50Z","title":"On integrals involving quotients of hyperbolic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08487","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:dead00b69462d38d55f7ef93259ba157de21c2c7f19acac65b3f2cc981932959","target":"record","created_at":"2026-05-17T23:50:47Z","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":"07057dc136715da0dc3f21c06f68944b6234ef76de30100e892b72d377b272f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-03-20T12:50:50Z","title_canon_sha256":"5235e2ac9dafce030dfab77cf50ed53930c3efd1dcaf7075872413da84ef678a"},"schema_version":"1.0","source":{"id":"1903.08487","kind":"arxiv","version":1}},"canonical_sha256":"85702dba1254c46d0fb4cc3deb62b70a87edb157b6034f5fe8c5b0ebfe0be82c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85702dba1254c46d0fb4cc3deb62b70a87edb157b6034f5fe8c5b0ebfe0be82c","first_computed_at":"2026-05-17T23:50:47.970267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:47.970267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xE6WPa6t4W/r8jM5zk0zkyMDpT3OSq/PzSaZUOBDD9v+ARWKVh98/Ivxh11MINzJ8nn18ped7cRGPwnKzbYgBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:47.970963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.08487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dead00b69462d38d55f7ef93259ba157de21c2c7f19acac65b3f2cc981932959","sha256:3451df239fa81d4954db456a0fe6c0ee05deb58d9d9a260f0f36101f15dad18c"],"state_sha256":"833f6565f5da72e5166e5bfaa710eacba7a44f9ae865d84b78f370921a77808e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iKspYmo1LskIGae4Lo4lxx+ZS2ZW0tZO+OhkFWOB8DjJ+chX5dihcNaCoRIb1oBaF4pt3cK8yzSij9CRWvboCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:38:29.794416Z","bundle_sha256":"e5f968fb27d576e360fe3940d677961df23a10784a0073ad14f4f470ef23a7b4"}}