{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:B2AYGCXMMY7273CXVZUWVNM3OZ","short_pith_number":"pith:B2AYGCXM","canonical_record":{"source":{"id":"1801.08032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-22T05:44:11Z","cross_cats_sorted":[],"title_canon_sha256":"adda81741b0a369c2a2428ecaf2bdba89078cd79e67eed8d42de89c562acafc9","abstract_canon_sha256":"bc24af4895f1ca009c33caf3be20176b242f153a8baba9e4c01dbdf5fd307636"},"schema_version":"1.0"},"canonical_sha256":"0e81830aec663fafec57ae696ab59b765c72400da7c0f4cd3733de44bf9fc86b","source":{"kind":"arxiv","id":"1801.08032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08032","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08032v1","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08032","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"pith_short_12","alias_value":"B2AYGCXMMY72","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"B2AYGCXMMY7273CX","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"B2AYGCXM","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:B2AYGCXMMY7273CXVZUWVNM3OZ","target":"record","payload":{"canonical_record":{"source":{"id":"1801.08032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-22T05:44:11Z","cross_cats_sorted":[],"title_canon_sha256":"adda81741b0a369c2a2428ecaf2bdba89078cd79e67eed8d42de89c562acafc9","abstract_canon_sha256":"bc24af4895f1ca009c33caf3be20176b242f153a8baba9e4c01dbdf5fd307636"},"schema_version":"1.0"},"canonical_sha256":"0e81830aec663fafec57ae696ab59b765c72400da7c0f4cd3733de44bf9fc86b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:08.502807Z","signature_b64":"QUfJRrEkhrfBZW2nrPiN7+efiDbsWDRmV2fcf03XnuUC3Ex3mRRTNFvyt78K+PRedmrZKSZbMfDH0thRetGhCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e81830aec663fafec57ae696ab59b765c72400da7c0f4cd3733de44bf9fc86b","last_reissued_at":"2026-05-18T00:25:08.502366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:08.502366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.08032","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":"2026-05-18T00:25:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YVlD+3wReTuN/k9oBWsqnjw+3XN3reXgMGrzR3baakpZ+AJnS0ubCPEAZhgKcwVl9u1t3IFjx2feebdhmihaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:45:44.523158Z"},"content_sha256":"888d5a52fa32974e7fbef6cbb0d1b447e3729f7854d8d7a3c28c7cae7301ea93","schema_version":"1.0","event_id":"sha256:888d5a52fa32974e7fbef6cbb0d1b447e3729f7854d8d7a3c28c7cae7301ea93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:B2AYGCXMMY7273CXVZUWVNM3OZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An extension of the Whittaker function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Gauhar Rahman, Junesang Choi, Kottakkaran Sooppy Nisar","submitted_at":"2018-01-22T05:44:11Z","abstract_excerpt":"The Whittaker function and its diverse extensions have been actively investigated. Here we introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function $\\Phi_{p,v}$ and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08032","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":"2026-05-18T00:25:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C3xiyBNKr888FUaZrgrl0Iuyl8dskeGsT4v/Rl8mBCiPXMUJcReAej7VRAB438pJpuHx97azOdMPxarJXk/fBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:45:44.523524Z"},"content_sha256":"ebbd56bb1aeed4721effb82f9cf084b8669b9542fd605e9fb3d35216eb60498e","schema_version":"1.0","event_id":"sha256:ebbd56bb1aeed4721effb82f9cf084b8669b9542fd605e9fb3d35216eb60498e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B2AYGCXMMY7273CXVZUWVNM3OZ/bundle.json","state_url":"https://pith.science/pith/B2AYGCXMMY7273CXVZUWVNM3OZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B2AYGCXMMY7273CXVZUWVNM3OZ/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":"2026-06-22T11:45:44Z","links":{"resolver":"https://pith.science/pith/B2AYGCXMMY7273CXVZUWVNM3OZ","bundle":"https://pith.science/pith/B2AYGCXMMY7273CXVZUWVNM3OZ/bundle.json","state":"https://pith.science/pith/B2AYGCXMMY7273CXVZUWVNM3OZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B2AYGCXMMY7273CXVZUWVNM3OZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:B2AYGCXMMY7273CXVZUWVNM3OZ","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":"bc24af4895f1ca009c33caf3be20176b242f153a8baba9e4c01dbdf5fd307636","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-22T05:44:11Z","title_canon_sha256":"adda81741b0a369c2a2428ecaf2bdba89078cd79e67eed8d42de89c562acafc9"},"schema_version":"1.0","source":{"id":"1801.08032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08032","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08032v1","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08032","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"pith_short_12","alias_value":"B2AYGCXMMY72","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"B2AYGCXMMY7273CX","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"B2AYGCXM","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:ebbd56bb1aeed4721effb82f9cf084b8669b9542fd605e9fb3d35216eb60498e","target":"graph","created_at":"2026-05-18T00:25:08Z","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":"The Whittaker function and its diverse extensions have been actively investigated. Here we introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function $\\Phi_{p,v}$ and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered.","authors_text":"Gauhar Rahman, Junesang Choi, Kottakkaran Sooppy Nisar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-22T05:44:11Z","title":"An extension of the Whittaker function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08032","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":"sha256:888d5a52fa32974e7fbef6cbb0d1b447e3729f7854d8d7a3c28c7cae7301ea93","target":"record","created_at":"2026-05-18T00:25:08Z","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":"bc24af4895f1ca009c33caf3be20176b242f153a8baba9e4c01dbdf5fd307636","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-22T05:44:11Z","title_canon_sha256":"adda81741b0a369c2a2428ecaf2bdba89078cd79e67eed8d42de89c562acafc9"},"schema_version":"1.0","source":{"id":"1801.08032","kind":"arxiv","version":1}},"canonical_sha256":"0e81830aec663fafec57ae696ab59b765c72400da7c0f4cd3733de44bf9fc86b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e81830aec663fafec57ae696ab59b765c72400da7c0f4cd3733de44bf9fc86b","first_computed_at":"2026-05-18T00:25:08.502366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:08.502366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QUfJRrEkhrfBZW2nrPiN7+efiDbsWDRmV2fcf03XnuUC3Ex3mRRTNFvyt78K+PRedmrZKSZbMfDH0thRetGhCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:08.502807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:888d5a52fa32974e7fbef6cbb0d1b447e3729f7854d8d7a3c28c7cae7301ea93","sha256:ebbd56bb1aeed4721effb82f9cf084b8669b9542fd605e9fb3d35216eb60498e"],"state_sha256":"248f08d6ff890e2fe4348a2369a0b799bbf63145f7aa6d24c944265e8536fc4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/CS/MvaQvdyyFAy2t6yjmhNV7lLQn955lj8hy7YX++J0odClaAZaZNBqVZwMudE3A0KSVCehjleE2a56C4GBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:45:44.525415Z","bundle_sha256":"0569d455d45c09f434351a74575cad121d0c06e876046113e5423ed198b8a1c4"}}