{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EHY445SHN74D725OE64UGFWXX7","short_pith_number":"pith:EHY445SH","canonical_record":{"source":{"id":"1301.6234","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-26T11:03:19Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f304553331b6b4a05b71e30582c4e6d04a4d8b2bc195708a3f17be53eb8e301a","abstract_canon_sha256":"6e746d68eb4755ff02134e9f70ce4d60aff014daa9f39836f4c505e94cd62272"},"schema_version":"1.0"},"canonical_sha256":"21f1ce76476ff83febae27b94316d7bfcd7a12f6ec88f3458ff2286924de0bea","source":{"kind":"arxiv","id":"1301.6234","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6234","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6234v3","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6234","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"pith_short_12","alias_value":"EHY445SHN74D","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EHY445SHN74D725O","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EHY445SH","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EHY445SHN74D725OE64UGFWXX7","target":"record","payload":{"canonical_record":{"source":{"id":"1301.6234","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-26T11:03:19Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f304553331b6b4a05b71e30582c4e6d04a4d8b2bc195708a3f17be53eb8e301a","abstract_canon_sha256":"6e746d68eb4755ff02134e9f70ce4d60aff014daa9f39836f4c505e94cd62272"},"schema_version":"1.0"},"canonical_sha256":"21f1ce76476ff83febae27b94316d7bfcd7a12f6ec88f3458ff2286924de0bea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:42.005785Z","signature_b64":"xEitbZ4NKLLNRj0eF8+UxyVtCmtGMgsHvYLilgdYi8+m8m22d3IvPsJlmBmM5t+/kJmpFonhz9m19VKKsyy9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21f1ce76476ff83febae27b94316d7bfcd7a12f6ec88f3458ff2286924de0bea","last_reissued_at":"2026-05-18T03:28:42.005219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:42.005219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.6234","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"StfPVPJr+wPuIIVlLEUhs0l/Qodj+0ldpz59PSflnTew8PAyklXpklk2RazDCdrl2rwqQm34Up3rypEdc/VmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:24:03.631017Z"},"content_sha256":"1998e01aa27883d17549d82b25107ac52734c187aedc5c714da9b556ecfeb05a","schema_version":"1.0","event_id":"sha256:1998e01aa27883d17549d82b25107ac52734c187aedc5c714da9b556ecfeb05a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EHY445SHN74D725OE64UGFWXX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Note on Fractional Evolutionary Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Rainer Picard","submitted_at":"2013-01-26T11:03:19Z","abstract_excerpt":"A class of linear evolutionary equations with material laws involving fractional time-derivatives is considered. The main result is well-posedness and causality for this problem class. The approach is illustrated with two examples: a fractional Fokker-Planck type equation and a class of visco-elastic materials described via fractional derivatives. In conclusion the possibility of imposing initial conditions is discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6234","kind":"arxiv","version":3},"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":"2026-05-18T03:28:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cxkVvDRAAUR1QxLvk7t2sNiFVV/iZss30cGsFeJAK3+jaC/UGLjohmksLhrJp2Y4OWUoDuocOEX9Y+fgusZyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:24:03.631385Z"},"content_sha256":"4afb0d0e5a0c88ba2880c267369efe2fba8f05907783c7abd9e43f7c7c06b2e9","schema_version":"1.0","event_id":"sha256:4afb0d0e5a0c88ba2880c267369efe2fba8f05907783c7abd9e43f7c7c06b2e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EHY445SHN74D725OE64UGFWXX7/bundle.json","state_url":"https://pith.science/pith/EHY445SHN74D725OE64UGFWXX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EHY445SHN74D725OE64UGFWXX7/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":"2026-06-04T18:24:03Z","links":{"resolver":"https://pith.science/pith/EHY445SHN74D725OE64UGFWXX7","bundle":"https://pith.science/pith/EHY445SHN74D725OE64UGFWXX7/bundle.json","state":"https://pith.science/pith/EHY445SHN74D725OE64UGFWXX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EHY445SHN74D725OE64UGFWXX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EHY445SHN74D725OE64UGFWXX7","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":"6e746d68eb4755ff02134e9f70ce4d60aff014daa9f39836f4c505e94cd62272","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-26T11:03:19Z","title_canon_sha256":"f304553331b6b4a05b71e30582c4e6d04a4d8b2bc195708a3f17be53eb8e301a"},"schema_version":"1.0","source":{"id":"1301.6234","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6234","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6234v3","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6234","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"pith_short_12","alias_value":"EHY445SHN74D","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EHY445SHN74D725O","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EHY445SH","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:4afb0d0e5a0c88ba2880c267369efe2fba8f05907783c7abd9e43f7c7c06b2e9","target":"graph","created_at":"2026-05-18T03:28:42Z","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":"A class of linear evolutionary equations with material laws involving fractional time-derivatives is considered. The main result is well-posedness and causality for this problem class. The approach is illustrated with two examples: a fractional Fokker-Planck type equation and a class of visco-elastic materials described via fractional derivatives. In conclusion the possibility of imposing initial conditions is discussed.","authors_text":"Rainer Picard","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-26T11:03:19Z","title":"A Note on Fractional Evolutionary Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6234","kind":"arxiv","version":3},"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":"sha256:1998e01aa27883d17549d82b25107ac52734c187aedc5c714da9b556ecfeb05a","target":"record","created_at":"2026-05-18T03:28:42Z","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":"6e746d68eb4755ff02134e9f70ce4d60aff014daa9f39836f4c505e94cd62272","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-26T11:03:19Z","title_canon_sha256":"f304553331b6b4a05b71e30582c4e6d04a4d8b2bc195708a3f17be53eb8e301a"},"schema_version":"1.0","source":{"id":"1301.6234","kind":"arxiv","version":3}},"canonical_sha256":"21f1ce76476ff83febae27b94316d7bfcd7a12f6ec88f3458ff2286924de0bea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21f1ce76476ff83febae27b94316d7bfcd7a12f6ec88f3458ff2286924de0bea","first_computed_at":"2026-05-18T03:28:42.005219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:42.005219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xEitbZ4NKLLNRj0eF8+UxyVtCmtGMgsHvYLilgdYi8+m8m22d3IvPsJlmBmM5t+/kJmpFonhz9m19VKKsyy9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:42.005785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.6234","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1998e01aa27883d17549d82b25107ac52734c187aedc5c714da9b556ecfeb05a","sha256:4afb0d0e5a0c88ba2880c267369efe2fba8f05907783c7abd9e43f7c7c06b2e9"],"state_sha256":"097e28bd8b6c3ed6869084622ab68412a992d2f5fb365dc641817e4dd4a3d881"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZTeeR9XlzZLTJYP1EFDLoX/MlnrWhqs/sUsrDT7KZOiyniFe8AI4QH+JuyfPtBWqdvEkvUOTds3NjnZwHDU8Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T18:24:03.633404Z","bundle_sha256":"ada931848989fc6b56e9230c2b3551bdce4670ea48d53cfdc169177b8fdecacf"}}