{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:I74A5CQBWMN3MTN6GB2FL2KIHE","short_pith_number":"pith:I74A5CQB","canonical_record":{"source":{"id":"1612.08596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-22T16:48:32Z","cross_cats_sorted":[],"title_canon_sha256":"6f77036b571c1e075273b367f7b095272d16a39410d9e6604d0ac9f61e2c9a4a","abstract_canon_sha256":"c887bc543f602d8e0d6c2e826ce06e382e3342f2f3dbbfa55c271f8cab4781ee"},"schema_version":"1.0"},"canonical_sha256":"47f80e8a01b31bb64dbe307455e9483923e7d1c09bcc95c755415a1157849e2b","source":{"kind":"arxiv","id":"1612.08596","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08596","created_at":"2026-05-18T00:53:52Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08596v1","created_at":"2026-05-18T00:53:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08596","created_at":"2026-05-18T00:53:52Z"},{"alias_kind":"pith_short_12","alias_value":"I74A5CQBWMN3","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I74A5CQBWMN3MTN6","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I74A5CQB","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:I74A5CQBWMN3MTN6GB2FL2KIHE","target":"record","payload":{"canonical_record":{"source":{"id":"1612.08596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-22T16:48:32Z","cross_cats_sorted":[],"title_canon_sha256":"6f77036b571c1e075273b367f7b095272d16a39410d9e6604d0ac9f61e2c9a4a","abstract_canon_sha256":"c887bc543f602d8e0d6c2e826ce06e382e3342f2f3dbbfa55c271f8cab4781ee"},"schema_version":"1.0"},"canonical_sha256":"47f80e8a01b31bb64dbe307455e9483923e7d1c09bcc95c755415a1157849e2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:52.579254Z","signature_b64":"7CHkjfjNI0NpWmALu8G3sMqdpK3/sOuo3GI0hVTFwY6IcjhoBIiCQcB/eP4DadEAp83pKkhhpqumdgnhCZbKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47f80e8a01b31bb64dbe307455e9483923e7d1c09bcc95c755415a1157849e2b","last_reissued_at":"2026-05-18T00:53:52.578650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:52.578650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.08596","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":"2026-05-18T00:53:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Wtxb20j78KdXzh/3glKii0GEqIb2wfghhAy3ar8P713FFHGEUbGbGqcZEM+Nq2h7H67OslAoK4fynGISl2tDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:56:28.533629Z"},"content_sha256":"0a48f9e3ce44d74804af054338805a0266ee2141a0dedda6bd45ea816654537a","schema_version":"1.0","event_id":"sha256:0a48f9e3ce44d74804af054338805a0266ee2141a0dedda6bd45ea816654537a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:I74A5CQBWMN3MTN6GB2FL2KIHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New fractional integral unifying six existing fractional integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Udita N. Katugampola","submitted_at":"2016-12-22T16:48:32Z","abstract_excerpt":"In this paper we introduce a new fractional integral that generalizes six existing fractional integrals, namely, Riemann-Liouville, Hadamard, Erd\\'elyi-Kober, Katugampola, Weyl and Liouville fractional integrals in to one form. Such a generalization takes the form \\[\n  \\left({}^{\\rho}\\mathcal{I}^{\\alpha, \\beta}_{a+;\\eta, \\kappa}f\\right)(x)=\\frac{\\rho^{1-\\beta}x^{\\kappa}}{\\Gamma(\\alpha)}\\int_a^x \\frac{\\tau^{\\rho \\eta +\\rho-1}}{(x^\\rho-\\tau^\\rho)^{1-\\alpha}}f(\\tau)\\text{d}\\tau, \\quad 0\\leq a < x < b \\leq \\infty. \\] A similar generalization is not possible with the Erd\\'elyi-Kober operator though"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08596","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":"2026-05-18T00:53:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"un7xZ9S5F80IT3Z8/oj/l4QEOeqnEQ2ARjg7oj4SE5FZGNhpg5Hg+Qo2jAWf0Cy5Ti6Zj/3Y6IzLmozbfzd+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:56:28.534002Z"},"content_sha256":"d94257038627b65ae7b5e3bfa3e19d554170939226f762ae954666ba78f2eb37","schema_version":"1.0","event_id":"sha256:d94257038627b65ae7b5e3bfa3e19d554170939226f762ae954666ba78f2eb37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I74A5CQBWMN3MTN6GB2FL2KIHE/bundle.json","state_url":"https://pith.science/pith/I74A5CQBWMN3MTN6GB2FL2KIHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I74A5CQBWMN3MTN6GB2FL2KIHE/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":"2026-05-28T20:56:28Z","links":{"resolver":"https://pith.science/pith/I74A5CQBWMN3MTN6GB2FL2KIHE","bundle":"https://pith.science/pith/I74A5CQBWMN3MTN6GB2FL2KIHE/bundle.json","state":"https://pith.science/pith/I74A5CQBWMN3MTN6GB2FL2KIHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I74A5CQBWMN3MTN6GB2FL2KIHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I74A5CQBWMN3MTN6GB2FL2KIHE","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":"c887bc543f602d8e0d6c2e826ce06e382e3342f2f3dbbfa55c271f8cab4781ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-22T16:48:32Z","title_canon_sha256":"6f77036b571c1e075273b367f7b095272d16a39410d9e6604d0ac9f61e2c9a4a"},"schema_version":"1.0","source":{"id":"1612.08596","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08596","created_at":"2026-05-18T00:53:52Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08596v1","created_at":"2026-05-18T00:53:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08596","created_at":"2026-05-18T00:53:52Z"},{"alias_kind":"pith_short_12","alias_value":"I74A5CQBWMN3","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I74A5CQBWMN3MTN6","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I74A5CQB","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:d94257038627b65ae7b5e3bfa3e19d554170939226f762ae954666ba78f2eb37","target":"graph","created_at":"2026-05-18T00:53:52Z","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 introduce a new fractional integral that generalizes six existing fractional integrals, namely, Riemann-Liouville, Hadamard, Erd\\'elyi-Kober, Katugampola, Weyl and Liouville fractional integrals in to one form. Such a generalization takes the form \\[\n  \\left({}^{\\rho}\\mathcal{I}^{\\alpha, \\beta}_{a+;\\eta, \\kappa}f\\right)(x)=\\frac{\\rho^{1-\\beta}x^{\\kappa}}{\\Gamma(\\alpha)}\\int_a^x \\frac{\\tau^{\\rho \\eta +\\rho-1}}{(x^\\rho-\\tau^\\rho)^{1-\\alpha}}f(\\tau)\\text{d}\\tau, \\quad 0\\leq a < x < b \\leq \\infty. \\] A similar generalization is not possible with the Erd\\'elyi-Kober operator though","authors_text":"Udita N. Katugampola","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-22T16:48:32Z","title":"New fractional integral unifying six existing fractional integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08596","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":"sha256:0a48f9e3ce44d74804af054338805a0266ee2141a0dedda6bd45ea816654537a","target":"record","created_at":"2026-05-18T00:53:52Z","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":"c887bc543f602d8e0d6c2e826ce06e382e3342f2f3dbbfa55c271f8cab4781ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-22T16:48:32Z","title_canon_sha256":"6f77036b571c1e075273b367f7b095272d16a39410d9e6604d0ac9f61e2c9a4a"},"schema_version":"1.0","source":{"id":"1612.08596","kind":"arxiv","version":1}},"canonical_sha256":"47f80e8a01b31bb64dbe307455e9483923e7d1c09bcc95c755415a1157849e2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47f80e8a01b31bb64dbe307455e9483923e7d1c09bcc95c755415a1157849e2b","first_computed_at":"2026-05-18T00:53:52.578650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:52.578650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7CHkjfjNI0NpWmALu8G3sMqdpK3/sOuo3GI0hVTFwY6IcjhoBIiCQcB/eP4DadEAp83pKkhhpqumdgnhCZbKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:52.579254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.08596","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a48f9e3ce44d74804af054338805a0266ee2141a0dedda6bd45ea816654537a","sha256:d94257038627b65ae7b5e3bfa3e19d554170939226f762ae954666ba78f2eb37"],"state_sha256":"8f9e219c0d252250a58f1d3a4a415408b742f470fb74b58161cff45f815fd01e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"06zTGWTp2vGRK783HZAB30P49cOU/0HrXbqudSQAWbfPcW5vrBVNkJRfG6CpAzUFw+KhdJWge4d7MySNWn6RAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:56:28.536439Z","bundle_sha256":"8160d6e49d5ae6ceace13aa064f9731edcfc7bac3bf896cc69c154943ee2cf37"}}