{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KUYS7PY3DVP5DL5GKJHVI272YN","short_pith_number":"pith:KUYS7PY3","canonical_record":{"source":{"id":"1502.06127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-21T18:34:24Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"5871b41f2d271b5410e6ecdd19442042d01a4765d2203d2bca58ba34217faab4","abstract_canon_sha256":"9cb14768777462ca21d17de49853fb18d69fc199ab9b6ed74ad19a1bc1cfffdf"},"schema_version":"1.0"},"canonical_sha256":"55312fbf1b1d5fd1afa6524f546bfac353eb17d8236dd7144d55f5213b9c6873","source":{"kind":"arxiv","id":"1502.06127","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06127","created_at":"2026-05-18T01:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06127v1","created_at":"2026-05-18T01:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06127","created_at":"2026-05-18T01:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"KUYS7PY3DVP5","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KUYS7PY3DVP5DL5G","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KUYS7PY3","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KUYS7PY3DVP5DL5GKJHVI272YN","target":"record","payload":{"canonical_record":{"source":{"id":"1502.06127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-21T18:34:24Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"5871b41f2d271b5410e6ecdd19442042d01a4765d2203d2bca58ba34217faab4","abstract_canon_sha256":"9cb14768777462ca21d17de49853fb18d69fc199ab9b6ed74ad19a1bc1cfffdf"},"schema_version":"1.0"},"canonical_sha256":"55312fbf1b1d5fd1afa6524f546bfac353eb17d8236dd7144d55f5213b9c6873","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:01.749431Z","signature_b64":"jEC8J/Ock/3mNvCklmF3Q8rr14W65mrPQkeZ1KHhiv8SV+7EHXJe9hKtOK+vEiH+663Eflpl2gzmjbcattMfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55312fbf1b1d5fd1afa6524f546bfac353eb17d8236dd7144d55f5213b9c6873","last_reissued_at":"2026-05-18T01:01:01.748723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:01.748723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.06127","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":"2026-05-18T01:01:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hFO+SrDO9/O9PMNIBn/hOVVQD/pKsXKaiuU1PSM3IYsiZz/6onVwnsgrO0LZ4VKcTmZadQHMRfouwDKqUfpfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:46:10.730054Z"},"content_sha256":"07441aa1d53a63213f6a63247a2e0031c4bf26fbdfa1a99d3ad386a039814724","schema_version":"1.0","event_id":"sha256:07441aa1d53a63213f6a63247a2e0031c4bf26fbdfa1a99d3ad386a039814724"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KUYS7PY3DVP5DL5GKJHVI272YN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computable Solutions of Fractional Reaction-Diffusion Equations Associated with Generalized Riemann-Liouville Fractional Derivatives of Fractional Order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.M. Mathai, H.J. Haubold, R.K. Saxena","submitted_at":"2015-02-21T18:34:24Z","abstract_excerpt":"This paper is in continuation of the authors' recently published paper (Journal of Mathematical Physics 55(2014)083519) in which computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative as space derivative is derived. In the present paper, computable solutions of distributed order fractional reaction-diffusion equations associated with generalized Riemann-Liouville derivatives of fractional orders as the time-derivative and Riesz-Feller fractional derivative as the space derivati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06127","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":"2026-05-18T01:01:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sl71FIxhoAPCfXSqmURh4FQpQAKS9WLxGDdAykI2NLmtOA++IRWXYCZfyuLUk3IfymNjFScjXUFwaBAx3goyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:46:10.730403Z"},"content_sha256":"60da2970f8485f370ebcd032eea92c11ac106aa1d2301410ad36e28ce6a63280","schema_version":"1.0","event_id":"sha256:60da2970f8485f370ebcd032eea92c11ac106aa1d2301410ad36e28ce6a63280"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KUYS7PY3DVP5DL5GKJHVI272YN/bundle.json","state_url":"https://pith.science/pith/KUYS7PY3DVP5DL5GKJHVI272YN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KUYS7PY3DVP5DL5GKJHVI272YN/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":"2026-05-30T22:46:10Z","links":{"resolver":"https://pith.science/pith/KUYS7PY3DVP5DL5GKJHVI272YN","bundle":"https://pith.science/pith/KUYS7PY3DVP5DL5GKJHVI272YN/bundle.json","state":"https://pith.science/pith/KUYS7PY3DVP5DL5GKJHVI272YN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KUYS7PY3DVP5DL5GKJHVI272YN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KUYS7PY3DVP5DL5GKJHVI272YN","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":"9cb14768777462ca21d17de49853fb18d69fc199ab9b6ed74ad19a1bc1cfffdf","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-21T18:34:24Z","title_canon_sha256":"5871b41f2d271b5410e6ecdd19442042d01a4765d2203d2bca58ba34217faab4"},"schema_version":"1.0","source":{"id":"1502.06127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06127","created_at":"2026-05-18T01:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06127v1","created_at":"2026-05-18T01:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06127","created_at":"2026-05-18T01:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"KUYS7PY3DVP5","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KUYS7PY3DVP5DL5G","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KUYS7PY3","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:60da2970f8485f370ebcd032eea92c11ac106aa1d2301410ad36e28ce6a63280","target":"graph","created_at":"2026-05-18T01:01:01Z","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":"This paper is in continuation of the authors' recently published paper (Journal of Mathematical Physics 55(2014)083519) in which computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative as space derivative is derived. In the present paper, computable solutions of distributed order fractional reaction-diffusion equations associated with generalized Riemann-Liouville derivatives of fractional orders as the time-derivative and Riesz-Feller fractional derivative as the space derivati","authors_text":"A.M. Mathai, H.J. Haubold, R.K. Saxena","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-21T18:34:24Z","title":"Computable Solutions of Fractional Reaction-Diffusion Equations Associated with Generalized Riemann-Liouville Fractional Derivatives of Fractional Order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06127","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":"sha256:07441aa1d53a63213f6a63247a2e0031c4bf26fbdfa1a99d3ad386a039814724","target":"record","created_at":"2026-05-18T01:01:01Z","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":"9cb14768777462ca21d17de49853fb18d69fc199ab9b6ed74ad19a1bc1cfffdf","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-21T18:34:24Z","title_canon_sha256":"5871b41f2d271b5410e6ecdd19442042d01a4765d2203d2bca58ba34217faab4"},"schema_version":"1.0","source":{"id":"1502.06127","kind":"arxiv","version":1}},"canonical_sha256":"55312fbf1b1d5fd1afa6524f546bfac353eb17d8236dd7144d55f5213b9c6873","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55312fbf1b1d5fd1afa6524f546bfac353eb17d8236dd7144d55f5213b9c6873","first_computed_at":"2026-05-18T01:01:01.748723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:01.748723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jEC8J/Ock/3mNvCklmF3Q8rr14W65mrPQkeZ1KHhiv8SV+7EHXJe9hKtOK+vEiH+663Eflpl2gzmjbcattMfCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:01.749431Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07441aa1d53a63213f6a63247a2e0031c4bf26fbdfa1a99d3ad386a039814724","sha256:60da2970f8485f370ebcd032eea92c11ac106aa1d2301410ad36e28ce6a63280"],"state_sha256":"0bef717fca9c228ef6416e1924c2bf5f5469d19df5bceceb32f9086be2c0fdc2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TCBWLHEmz64CAPy4TaWVdEB/0ZdcmIytMTD9xLD6UwKAaDEYUCO3JFym2E1RwOrIGZNckUEaTB6pfVjLOC08DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:46:10.732218Z","bundle_sha256":"fae4344452a9cafcbeeee8629a85aa802bf3684f3dd0fd70836280dc1c87afb9"}}