{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DHIY2U6DYGYAHX4EX4A5ZQT3Y6","short_pith_number":"pith:DHIY2U6D","canonical_record":{"source":{"id":"1701.01479","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T21:16:42Z","cross_cats_sorted":[],"title_canon_sha256":"c5662203792f0f90c3cac8ddb9bf6857b2f3e660edfd4edecbfeb2546ca5ebb0","abstract_canon_sha256":"24c22343c08f06c720209d7fe1644c11b446118bb4bb241005a1590bc779b848"},"schema_version":"1.0"},"canonical_sha256":"19d18d53c3c1b003df84bf01dcc27bc7a1a652a7238c88a4c8212eb7f0177b45","source":{"kind":"arxiv","id":"1701.01479","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01479","created_at":"2026-05-18T00:53:16Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01479v1","created_at":"2026-05-18T00:53:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01479","created_at":"2026-05-18T00:53:16Z"},{"alias_kind":"pith_short_12","alias_value":"DHIY2U6DYGYA","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DHIY2U6DYGYAHX4E","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DHIY2U6D","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DHIY2U6DYGYAHX4EX4A5ZQT3Y6","target":"record","payload":{"canonical_record":{"source":{"id":"1701.01479","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T21:16:42Z","cross_cats_sorted":[],"title_canon_sha256":"c5662203792f0f90c3cac8ddb9bf6857b2f3e660edfd4edecbfeb2546ca5ebb0","abstract_canon_sha256":"24c22343c08f06c720209d7fe1644c11b446118bb4bb241005a1590bc779b848"},"schema_version":"1.0"},"canonical_sha256":"19d18d53c3c1b003df84bf01dcc27bc7a1a652a7238c88a4c8212eb7f0177b45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:16.730777Z","signature_b64":"IxaiybWvv/22reyz+NTgtPe/bIFdsF+Pq5V6+ajrSTca57mcKYmQFoKK08MA5jFKl5RQJ5jCr0YpHcdQzwoKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19d18d53c3c1b003df84bf01dcc27bc7a1a652a7238c88a4c8212eb7f0177b45","last_reissued_at":"2026-05-18T00:53:16.730380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:16.730380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.01479","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":"2026-05-18T00:53:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KIHgvJ9pXZ52myDN+V02ja8/LOsLLNsAGCXTXwgrgA7beg4wa9tefj3a+CKDbyjgl6IYmr0nvpnckNIPMxW9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:18:04.026847Z"},"content_sha256":"32193508034a68fa2cecd04ad49fc0b798d06ee8bc0710fd34cc1eb21eec10cd","schema_version":"1.0","event_id":"sha256:32193508034a68fa2cecd04ad49fc0b798d06ee8bc0710fd34cc1eb21eec10cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DHIY2U6DYGYAHX4EX4A5ZQT3Y6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parabolic problem with fractional time derivative with nonlocal and nonsingular Mittag-Leffler kernel","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Atangana, I. Area, J.D Djida","submitted_at":"2017-01-05T21:16:42Z","abstract_excerpt":"We prove H\\\"older regularity results for a class of nonlinear parabolic problem with fractional-time derivative with nonlocal and Mittag-Leffler nonsingular kernel. Existence of weak solutions via approximating solutions is proved. Moreover, the H\\\"{o}lder continuity of viscosity solutions is obtained. We get the similar results as those obtained by Allen (see {\\url{https://arxiv.org/abs/1610.10073}})"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01479","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":"2026-05-18T00:53:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DpyXyEv83JBIkb1bMMq2iUXMLir0KGnifB1NF7pT+yV3zMXw47lg1awMvI3oUk2n9ATAv4y6OuaGgrZk/EwXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:18:04.027193Z"},"content_sha256":"d418cc74191f27b5cb5ce0b10e864947e326745a8a2c095ce5d50b89797e070f","schema_version":"1.0","event_id":"sha256:d418cc74191f27b5cb5ce0b10e864947e326745a8a2c095ce5d50b89797e070f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DHIY2U6DYGYAHX4EX4A5ZQT3Y6/bundle.json","state_url":"https://pith.science/pith/DHIY2U6DYGYAHX4EX4A5ZQT3Y6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DHIY2U6DYGYAHX4EX4A5ZQT3Y6/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":"2026-06-03T15:18:04Z","links":{"resolver":"https://pith.science/pith/DHIY2U6DYGYAHX4EX4A5ZQT3Y6","bundle":"https://pith.science/pith/DHIY2U6DYGYAHX4EX4A5ZQT3Y6/bundle.json","state":"https://pith.science/pith/DHIY2U6DYGYAHX4EX4A5ZQT3Y6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DHIY2U6DYGYAHX4EX4A5ZQT3Y6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DHIY2U6DYGYAHX4EX4A5ZQT3Y6","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":"24c22343c08f06c720209d7fe1644c11b446118bb4bb241005a1590bc779b848","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T21:16:42Z","title_canon_sha256":"c5662203792f0f90c3cac8ddb9bf6857b2f3e660edfd4edecbfeb2546ca5ebb0"},"schema_version":"1.0","source":{"id":"1701.01479","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01479","created_at":"2026-05-18T00:53:16Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01479v1","created_at":"2026-05-18T00:53:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01479","created_at":"2026-05-18T00:53:16Z"},{"alias_kind":"pith_short_12","alias_value":"DHIY2U6DYGYA","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DHIY2U6DYGYAHX4E","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DHIY2U6D","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:d418cc74191f27b5cb5ce0b10e864947e326745a8a2c095ce5d50b89797e070f","target":"graph","created_at":"2026-05-18T00:53:16Z","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 prove H\\\"older regularity results for a class of nonlinear parabolic problem with fractional-time derivative with nonlocal and Mittag-Leffler nonsingular kernel. Existence of weak solutions via approximating solutions is proved. Moreover, the H\\\"{o}lder continuity of viscosity solutions is obtained. We get the similar results as those obtained by Allen (see {\\url{https://arxiv.org/abs/1610.10073}})","authors_text":"A. Atangana, I. Area, J.D Djida","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T21:16:42Z","title":"Parabolic problem with fractional time derivative with nonlocal and nonsingular Mittag-Leffler kernel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01479","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":"sha256:32193508034a68fa2cecd04ad49fc0b798d06ee8bc0710fd34cc1eb21eec10cd","target":"record","created_at":"2026-05-18T00:53:16Z","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":"24c22343c08f06c720209d7fe1644c11b446118bb4bb241005a1590bc779b848","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T21:16:42Z","title_canon_sha256":"c5662203792f0f90c3cac8ddb9bf6857b2f3e660edfd4edecbfeb2546ca5ebb0"},"schema_version":"1.0","source":{"id":"1701.01479","kind":"arxiv","version":1}},"canonical_sha256":"19d18d53c3c1b003df84bf01dcc27bc7a1a652a7238c88a4c8212eb7f0177b45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19d18d53c3c1b003df84bf01dcc27bc7a1a652a7238c88a4c8212eb7f0177b45","first_computed_at":"2026-05-18T00:53:16.730380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:16.730380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IxaiybWvv/22reyz+NTgtPe/bIFdsF+Pq5V6+ajrSTca57mcKYmQFoKK08MA5jFKl5RQJ5jCr0YpHcdQzwoKAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:16.730777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01479","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32193508034a68fa2cecd04ad49fc0b798d06ee8bc0710fd34cc1eb21eec10cd","sha256:d418cc74191f27b5cb5ce0b10e864947e326745a8a2c095ce5d50b89797e070f"],"state_sha256":"b4a159ccb63a81d2352ad5b36795613d13619c7e2aca5162d8f506e4d2506271"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zuX0c0k+0mB5dDujDskDwKrei6r7aKakxIj4204G6067+JRJFYDnGlaoUsVAnSx66g7A3sZExCsY2WSt5W8ZBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:18:04.029143Z","bundle_sha256":"a9e78e6b35dab4d31e6f62194dc4ee12e10d7e5d2b80ae01bfc5a2f5a1d2b6ec"}}