{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:J5AFO37B32VO2RLVSB4BBBT5Y6","short_pith_number":"pith:J5AFO37B","canonical_record":{"source":{"id":"1904.02577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-04T14:28:56Z","cross_cats_sorted":[],"title_canon_sha256":"fda954ba7788bccb24618417740b3341473f7190fba21ae8d09a8dbf20cf9741","abstract_canon_sha256":"3863c724aa752d33d0df57ff4e159816d0a40f5604b273d96e11ff6d1ef34139"},"schema_version":"1.0"},"canonical_sha256":"4f40576fe1deaaed4575907810867dc7b073afb9446fe3a2e003f13489ab7dff","source":{"kind":"arxiv","id":"1904.02577","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02577","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02577v1","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02577","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"pith_short_12","alias_value":"J5AFO37B32VO","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"J5AFO37B32VO2RLV","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"J5AFO37B","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:J5AFO37B32VO2RLVSB4BBBT5Y6","target":"record","payload":{"canonical_record":{"source":{"id":"1904.02577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-04T14:28:56Z","cross_cats_sorted":[],"title_canon_sha256":"fda954ba7788bccb24618417740b3341473f7190fba21ae8d09a8dbf20cf9741","abstract_canon_sha256":"3863c724aa752d33d0df57ff4e159816d0a40f5604b273d96e11ff6d1ef34139"},"schema_version":"1.0"},"canonical_sha256":"4f40576fe1deaaed4575907810867dc7b073afb9446fe3a2e003f13489ab7dff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:23.259977Z","signature_b64":"sNjOAdxo7GFJViomZ5OrpGSi2uP7z63hwv7Hu7wvYbLXTF2b1OWp2h1F0+lO5gYJTsnF4W2Q1VVMD+/fgACzDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f40576fe1deaaed4575907810867dc7b073afb9446fe3a2e003f13489ab7dff","last_reissued_at":"2026-05-17T23:49:23.259574Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:23.259574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.02577","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":"2026-05-17T23:49:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gLC+phRopfL1Fbyitg778/FbfL2pd53IhlH32wfXACgLINH3quDYqg3H9wewFeKAYMPr8DsvWN7Ik1ivYDwbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T11:48:18.133384Z"},"content_sha256":"1b4e7aaebd90aacefacfc8de59cf62635cba73e64b487201a131a68524bdd9fb","schema_version":"1.0","event_id":"sha256:1b4e7aaebd90aacefacfc8de59cf62635cba73e64b487201a131a68524bdd9fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:J5AFO37B32VO2RLVSB4BBBT5Y6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytical Development of Incomplete Riemann-Liouville Fractional Calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Arran Fernandez, Ceren Ustao\\u{g}lu, Mehmet Ali \\\"Ozarslan","submitted_at":"2019-04-04T14:28:56Z","abstract_excerpt":"The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus into the fractional scenario; the application of fractional differintegrals to assorted special functions. Recently, a new variant of fractional calculus has arisen, namely incomplete fractional calculus. In two very recent papers, incomplete versions of the Riemann-Liouville and Caputo fractional differintegrals have been formulated and applied to several "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02577","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":"2026-05-17T23:49:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uN4QmYReyNkENA06fcJqkhKCbe+qKbXwNXwoWLz94LJibvDhfnK2IkSGBleVaMK7Yv8rak+kdn8XJMzUVIMKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T11:48:18.133739Z"},"content_sha256":"576c293007fe75e58a1c1111d67fc92e5cc0eab2489278bb13e766ce5bf6eac6","schema_version":"1.0","event_id":"sha256:576c293007fe75e58a1c1111d67fc92e5cc0eab2489278bb13e766ce5bf6eac6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J5AFO37B32VO2RLVSB4BBBT5Y6/bundle.json","state_url":"https://pith.science/pith/J5AFO37B32VO2RLVSB4BBBT5Y6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J5AFO37B32VO2RLVSB4BBBT5Y6/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":"2026-07-01T11:48:18Z","links":{"resolver":"https://pith.science/pith/J5AFO37B32VO2RLVSB4BBBT5Y6","bundle":"https://pith.science/pith/J5AFO37B32VO2RLVSB4BBBT5Y6/bundle.json","state":"https://pith.science/pith/J5AFO37B32VO2RLVSB4BBBT5Y6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J5AFO37B32VO2RLVSB4BBBT5Y6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:J5AFO37B32VO2RLVSB4BBBT5Y6","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":"3863c724aa752d33d0df57ff4e159816d0a40f5604b273d96e11ff6d1ef34139","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-04T14:28:56Z","title_canon_sha256":"fda954ba7788bccb24618417740b3341473f7190fba21ae8d09a8dbf20cf9741"},"schema_version":"1.0","source":{"id":"1904.02577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02577","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02577v1","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02577","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"pith_short_12","alias_value":"J5AFO37B32VO","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"J5AFO37B32VO2RLV","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"J5AFO37B","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:576c293007fe75e58a1c1111d67fc92e5cc0eab2489278bb13e766ce5bf6eac6","target":"graph","created_at":"2026-05-17T23:49:23Z","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 theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus into the fractional scenario; the application of fractional differintegrals to assorted special functions. Recently, a new variant of fractional calculus has arisen, namely incomplete fractional calculus. In two very recent papers, incomplete versions of the Riemann-Liouville and Caputo fractional differintegrals have been formulated and applied to several ","authors_text":"Arran Fernandez, Ceren Ustao\\u{g}lu, Mehmet Ali \\\"Ozarslan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-04T14:28:56Z","title":"Analytical Development of Incomplete Riemann-Liouville Fractional Calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02577","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":"sha256:1b4e7aaebd90aacefacfc8de59cf62635cba73e64b487201a131a68524bdd9fb","target":"record","created_at":"2026-05-17T23:49:23Z","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":"3863c724aa752d33d0df57ff4e159816d0a40f5604b273d96e11ff6d1ef34139","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-04T14:28:56Z","title_canon_sha256":"fda954ba7788bccb24618417740b3341473f7190fba21ae8d09a8dbf20cf9741"},"schema_version":"1.0","source":{"id":"1904.02577","kind":"arxiv","version":1}},"canonical_sha256":"4f40576fe1deaaed4575907810867dc7b073afb9446fe3a2e003f13489ab7dff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f40576fe1deaaed4575907810867dc7b073afb9446fe3a2e003f13489ab7dff","first_computed_at":"2026-05-17T23:49:23.259574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:23.259574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sNjOAdxo7GFJViomZ5OrpGSi2uP7z63hwv7Hu7wvYbLXTF2b1OWp2h1F0+lO5gYJTsnF4W2Q1VVMD+/fgACzDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:23.259977Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b4e7aaebd90aacefacfc8de59cf62635cba73e64b487201a131a68524bdd9fb","sha256:576c293007fe75e58a1c1111d67fc92e5cc0eab2489278bb13e766ce5bf6eac6"],"state_sha256":"c4e70314a4870a357a75af332654172a93c68039805320056eab073170500874"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zZbszMHOt7GUXYW2IKd6eMVU/Orc/u1+rWYUm0xk2sywhA8ZVqq/m4N6V5uh2hDSY4Egv/MxQepC+8r/HgxcCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T11:48:18.135678Z","bundle_sha256":"c25179452327a978f533e480767bd0bd03356a443aaf96ba6c93b20f48ddff78"}}