{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BAFFLP4PTVWMR7YFPQAFLTB7HU","short_pith_number":"pith:BAFFLP4P","canonical_record":{"source":{"id":"1808.03241","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-08-09T17:21:18Z","cross_cats_sorted":[],"title_canon_sha256":"28e5b568fd61d2d732e7d6f5bc43a054d229777ad14d57bcf5ea5a1de8415cb6","abstract_canon_sha256":"ba4f5482b879f3f7f393210c838497ae7ba82480454975a7a57730fe76e0179e"},"schema_version":"1.0"},"canonical_sha256":"080a55bf8f9d6cc8ff057c0055cc3f3d112d156ebebcc2b473cc9ec02bb1ef97","source":{"kind":"arxiv","id":"1808.03241","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03241","created_at":"2026-05-18T00:07:39Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03241v3","created_at":"2026-05-18T00:07:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03241","created_at":"2026-05-18T00:07:39Z"},{"alias_kind":"pith_short_12","alias_value":"BAFFLP4PTVWM","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"BAFFLP4PTVWMR7YF","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"BAFFLP4P","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BAFFLP4PTVWMR7YFPQAFLTB7HU","target":"record","payload":{"canonical_record":{"source":{"id":"1808.03241","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-08-09T17:21:18Z","cross_cats_sorted":[],"title_canon_sha256":"28e5b568fd61d2d732e7d6f5bc43a054d229777ad14d57bcf5ea5a1de8415cb6","abstract_canon_sha256":"ba4f5482b879f3f7f393210c838497ae7ba82480454975a7a57730fe76e0179e"},"schema_version":"1.0"},"canonical_sha256":"080a55bf8f9d6cc8ff057c0055cc3f3d112d156ebebcc2b473cc9ec02bb1ef97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:39.942138Z","signature_b64":"GTekC4fmA6whaZeAvNTDMds4vTKxLebTgzw8dwAXW9TOjf9BheXFT91dNkEj1Np6rg5QdguHH3R8xShZvNi1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"080a55bf8f9d6cc8ff057c0055cc3f3d112d156ebebcc2b473cc9ec02bb1ef97","last_reissued_at":"2026-05-18T00:07:39.941408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:39.941408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.03241","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":"2026-05-18T00:07:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NWfS/UycBDwJig9CIU91I2J5VOKNQUt1BGZZsd/gcRtK/Xyw80HzL496Fd5Ek9eqxiBMCG917HwhwwLenDuPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:38:02.436364Z"},"content_sha256":"6ccdb9297af03c423970792d67ada24918ffc9be9e520590748787555853a44e","schema_version":"1.0","event_id":"sha256:6ccdb9297af03c423970792d67ada24918ffc9be9e520590748787555853a44e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BAFFLP4PTVWMR7YFPQAFLTB7HU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Generalization of Higher-Order Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"E. C. Aifantis, K. Parisis","submitted_at":"2018-08-09T17:21:18Z","abstract_excerpt":"A fractional generalization of the second author's higher-order diffusion theory is given and fundamental solutions are obtained. The extension from the integer to the fractional case involves a proper treatment of the fractional Laplacian of Riesz type. This is done with analogy to an earlier treatment in extending the second author's gradient elasticity model from the integer to the fractional case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03241","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":"2026-05-18T00:07:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JureJRGsGi7R6swTf2q8okMKN/KgEAtTPU5Zg0p5bQCyFPralAZgg7vuXCDQdfDswmVFtefkfekNjc6oy271DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:38:02.436697Z"},"content_sha256":"40702a448d694cb6b0951c8d1af7fa4394c50322803d5b11756a625924118ec8","schema_version":"1.0","event_id":"sha256:40702a448d694cb6b0951c8d1af7fa4394c50322803d5b11756a625924118ec8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BAFFLP4PTVWMR7YFPQAFLTB7HU/bundle.json","state_url":"https://pith.science/pith/BAFFLP4PTVWMR7YFPQAFLTB7HU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BAFFLP4PTVWMR7YFPQAFLTB7HU/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":"2026-06-10T21:38:02Z","links":{"resolver":"https://pith.science/pith/BAFFLP4PTVWMR7YFPQAFLTB7HU","bundle":"https://pith.science/pith/BAFFLP4PTVWMR7YFPQAFLTB7HU/bundle.json","state":"https://pith.science/pith/BAFFLP4PTVWMR7YFPQAFLTB7HU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BAFFLP4PTVWMR7YFPQAFLTB7HU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BAFFLP4PTVWMR7YFPQAFLTB7HU","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":"ba4f5482b879f3f7f393210c838497ae7ba82480454975a7a57730fe76e0179e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-08-09T17:21:18Z","title_canon_sha256":"28e5b568fd61d2d732e7d6f5bc43a054d229777ad14d57bcf5ea5a1de8415cb6"},"schema_version":"1.0","source":{"id":"1808.03241","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03241","created_at":"2026-05-18T00:07:39Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03241v3","created_at":"2026-05-18T00:07:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03241","created_at":"2026-05-18T00:07:39Z"},{"alias_kind":"pith_short_12","alias_value":"BAFFLP4PTVWM","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"BAFFLP4PTVWMR7YF","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"BAFFLP4P","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:40702a448d694cb6b0951c8d1af7fa4394c50322803d5b11756a625924118ec8","target":"graph","created_at":"2026-05-18T00:07:39Z","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 fractional generalization of the second author's higher-order diffusion theory is given and fundamental solutions are obtained. The extension from the integer to the fractional case involves a proper treatment of the fractional Laplacian of Riesz type. This is done with analogy to an earlier treatment in extending the second author's gradient elasticity model from the integer to the fractional case.","authors_text":"E. C. Aifantis, K. Parisis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-08-09T17:21:18Z","title":"Fractional Generalization of Higher-Order Diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03241","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":"sha256:6ccdb9297af03c423970792d67ada24918ffc9be9e520590748787555853a44e","target":"record","created_at":"2026-05-18T00:07:39Z","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":"ba4f5482b879f3f7f393210c838497ae7ba82480454975a7a57730fe76e0179e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-08-09T17:21:18Z","title_canon_sha256":"28e5b568fd61d2d732e7d6f5bc43a054d229777ad14d57bcf5ea5a1de8415cb6"},"schema_version":"1.0","source":{"id":"1808.03241","kind":"arxiv","version":3}},"canonical_sha256":"080a55bf8f9d6cc8ff057c0055cc3f3d112d156ebebcc2b473cc9ec02bb1ef97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"080a55bf8f9d6cc8ff057c0055cc3f3d112d156ebebcc2b473cc9ec02bb1ef97","first_computed_at":"2026-05-18T00:07:39.941408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:39.941408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GTekC4fmA6whaZeAvNTDMds4vTKxLebTgzw8dwAXW9TOjf9BheXFT91dNkEj1Np6rg5QdguHH3R8xShZvNi1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:39.942138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.03241","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ccdb9297af03c423970792d67ada24918ffc9be9e520590748787555853a44e","sha256:40702a448d694cb6b0951c8d1af7fa4394c50322803d5b11756a625924118ec8"],"state_sha256":"8f6d6bd20c16f9f37db0835a2d87e9dc5e1b84c4ecf91e471b87544c40d55029"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HjraUsBBSmvBS1xcUUb5NC2Qk3hdjbOBDfCWiS0xrj9f1ymwXxNSZfJ2JzG6yiixr4STnXUm35f9j9b2m4DNDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:38:02.438462Z","bundle_sha256":"c08b91ea07a88b3f782419cdc284c34965f3a352daa6539da726ec47c07cf95b"}}