{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ABGUF5EIVJUS6M6YZ5B6CMTWB4","short_pith_number":"pith:ABGUF5EI","canonical_record":{"source":{"id":"1601.06121","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-11T21:12:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"907336cbffc11edb9c54a642642541598328e8c124d65bfa1b808d90f4ac0be6","abstract_canon_sha256":"20ea032fc7e78d73c08a97af779d21fbc67053db92e0e42b53e898a632f16317"},"schema_version":"1.0"},"canonical_sha256":"004d42f488aa692f33d8cf43e132760f377b619a511125969e9d379d1356c350","source":{"kind":"arxiv","id":"1601.06121","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06121","created_at":"2026-05-18T01:16:43Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06121v1","created_at":"2026-05-18T01:16:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06121","created_at":"2026-05-18T01:16:43Z"},{"alias_kind":"pith_short_12","alias_value":"ABGUF5EIVJUS","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ABGUF5EIVJUS6M6Y","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ABGUF5EI","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ABGUF5EIVJUS6M6YZ5B6CMTWB4","target":"record","payload":{"canonical_record":{"source":{"id":"1601.06121","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-11T21:12:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"907336cbffc11edb9c54a642642541598328e8c124d65bfa1b808d90f4ac0be6","abstract_canon_sha256":"20ea032fc7e78d73c08a97af779d21fbc67053db92e0e42b53e898a632f16317"},"schema_version":"1.0"},"canonical_sha256":"004d42f488aa692f33d8cf43e132760f377b619a511125969e9d379d1356c350","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:43.222332Z","signature_b64":"C/FX5YqQpAaWgpAhiPJy2V4Uowqt/M6aVJ4e5OmWNTI5TffLA8euXp03grEoWqxyvlQCnuPdWQ0TYesQlVAqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"004d42f488aa692f33d8cf43e132760f377b619a511125969e9d379d1356c350","last_reissued_at":"2026-05-18T01:16:43.221839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:43.221839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.06121","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":"2026-05-18T01:16:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4zNhV7DiWQPKsKPxm/bL6y5U1DpenE0UWjtlNFOZH8LKZAMD/Spjf0V/3qdseIS3QLk4oyn2h4Of1yuhRDhjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T11:25:21.408716Z"},"content_sha256":"a4a1281eb8cdfec50cfc1bc81b6fb3d6839c15216ee5b8d4e01a9416edc4ae3d","schema_version":"1.0","event_id":"sha256:a4a1281eb8cdfec50cfc1bc81b6fb3d6839c15216ee5b8d4e01a9416edc4ae3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ABGUF5EIVJUS6M6YZ5B6CMTWB4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Derivatives on Fractal Subset of Real-line","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Alireza Khalili Golmankhaneh, Dumitru Baleanu","submitted_at":"2015-12-11T21:12:28Z","abstract_excerpt":"In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on fractals subset of real-line lies in the fact that they are used for better modelling of processes with memory effect."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06121","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":"2026-05-18T01:16:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F0SGA832bG8bHGIrXIc+N2jgSTv/1AV9njcRHEijrvtOmOJqsJK2FxYKOkwt1e4orntT19hLiVhYrx3rDKYBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T11:25:21.409059Z"},"content_sha256":"1b9b079cf1bbc2b861485289fb9ce2b1c8f9abb6d52851025573a0edd2bae6ff","schema_version":"1.0","event_id":"sha256:1b9b079cf1bbc2b861485289fb9ce2b1c8f9abb6d52851025573a0edd2bae6ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABGUF5EIVJUS6M6YZ5B6CMTWB4/bundle.json","state_url":"https://pith.science/pith/ABGUF5EIVJUS6M6YZ5B6CMTWB4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABGUF5EIVJUS6M6YZ5B6CMTWB4/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":"2026-06-08T11:25:21Z","links":{"resolver":"https://pith.science/pith/ABGUF5EIVJUS6M6YZ5B6CMTWB4","bundle":"https://pith.science/pith/ABGUF5EIVJUS6M6YZ5B6CMTWB4/bundle.json","state":"https://pith.science/pith/ABGUF5EIVJUS6M6YZ5B6CMTWB4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABGUF5EIVJUS6M6YZ5B6CMTWB4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ABGUF5EIVJUS6M6YZ5B6CMTWB4","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":"20ea032fc7e78d73c08a97af779d21fbc67053db92e0e42b53e898a632f16317","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-11T21:12:28Z","title_canon_sha256":"907336cbffc11edb9c54a642642541598328e8c124d65bfa1b808d90f4ac0be6"},"schema_version":"1.0","source":{"id":"1601.06121","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06121","created_at":"2026-05-18T01:16:43Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06121v1","created_at":"2026-05-18T01:16:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06121","created_at":"2026-05-18T01:16:43Z"},{"alias_kind":"pith_short_12","alias_value":"ABGUF5EIVJUS","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ABGUF5EIVJUS6M6Y","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ABGUF5EI","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:1b9b079cf1bbc2b861485289fb9ce2b1c8f9abb6d52851025573a0edd2bae6ff","target":"graph","created_at":"2026-05-18T01:16:43Z","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 manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on fractals subset of real-line lies in the fact that they are used for better modelling of processes with memory effect.","authors_text":"Alireza Khalili Golmankhaneh, Dumitru Baleanu","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-11T21:12:28Z","title":"New Derivatives on Fractal Subset of Real-line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06121","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:a4a1281eb8cdfec50cfc1bc81b6fb3d6839c15216ee5b8d4e01a9416edc4ae3d","target":"record","created_at":"2026-05-18T01:16:43Z","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":"20ea032fc7e78d73c08a97af779d21fbc67053db92e0e42b53e898a632f16317","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-11T21:12:28Z","title_canon_sha256":"907336cbffc11edb9c54a642642541598328e8c124d65bfa1b808d90f4ac0be6"},"schema_version":"1.0","source":{"id":"1601.06121","kind":"arxiv","version":1}},"canonical_sha256":"004d42f488aa692f33d8cf43e132760f377b619a511125969e9d379d1356c350","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"004d42f488aa692f33d8cf43e132760f377b619a511125969e9d379d1356c350","first_computed_at":"2026-05-18T01:16:43.221839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:43.221839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C/FX5YqQpAaWgpAhiPJy2V4Uowqt/M6aVJ4e5OmWNTI5TffLA8euXp03grEoWqxyvlQCnuPdWQ0TYesQlVAqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:43.222332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06121","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4a1281eb8cdfec50cfc1bc81b6fb3d6839c15216ee5b8d4e01a9416edc4ae3d","sha256:1b9b079cf1bbc2b861485289fb9ce2b1c8f9abb6d52851025573a0edd2bae6ff"],"state_sha256":"67852fe7232c6642c5e937446acb5a568288d61e4f0ed2f391e1c37d8f1f2f1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"evnQmx6UKCanOWtFw/qKNuTV+wA0zp5+ue+Fpr0H6I5GKv5WYRpJ3Yd4orJov+dee+z5V9FR311UdCx+s7VvCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T11:25:21.410942Z","bundle_sha256":"303c51d8b5d50bb8419eabde796a445d200cc9b1d4a76d346a20d1a9f0754d43"}}