{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IRC3DXOFDC3EC257YIGTWWBBNR","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":"75d840408178b052c991cdd0c56781475d7ceaae9325c5baeca3506987a39c68","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-17T12:00:34Z","title_canon_sha256":"062b7af53e33a286aa6dd4ddef090f9ab340a1582d753f80e65ff2e2ac6517e6"},"schema_version":"1.0","source":{"id":"1602.05382","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05382","created_at":"2026-05-18T00:49:19Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05382v3","created_at":"2026-05-18T00:49:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05382","created_at":"2026-05-18T00:49:19Z"},{"alias_kind":"pith_short_12","alias_value":"IRC3DXOFDC3E","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IRC3DXOFDC3EC257","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IRC3DXOF","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:d8970bc380717c07a8e59370fd829c4eee1b727ca4ca90d4ecd2dd57f9967f70","target":"graph","created_at":"2026-05-18T00:49:19Z","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 consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.","authors_text":"Manabu Machida","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-17T12:00:34Z","title":"The time-fractional radiative transport equation -- Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05382","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":"sha256:17242cee95068e696c9d96c666b7607878798650bfc3787f2b6b6169fe34cad3","target":"record","created_at":"2026-05-18T00:49:19Z","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":"75d840408178b052c991cdd0c56781475d7ceaae9325c5baeca3506987a39c68","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-17T12:00:34Z","title_canon_sha256":"062b7af53e33a286aa6dd4ddef090f9ab340a1582d753f80e65ff2e2ac6517e6"},"schema_version":"1.0","source":{"id":"1602.05382","kind":"arxiv","version":3}},"canonical_sha256":"4445b1ddc518b6416bbfc20d3b58216c4655076837322aac57808ab0864e99be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4445b1ddc518b6416bbfc20d3b58216c4655076837322aac57808ab0864e99be","first_computed_at":"2026-05-18T00:49:19.184275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:19.184275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QmFT8ds0yN08ohUUEtN/p/WRc5CszFo5RtRsBYAqRStN2pYP4dGWSICqpmVKa5leL4dL3nwglLsiwpU7OTlwCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:19.184704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05382","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17242cee95068e696c9d96c666b7607878798650bfc3787f2b6b6169fe34cad3","sha256:d8970bc380717c07a8e59370fd829c4eee1b727ca4ca90d4ecd2dd57f9967f70"],"state_sha256":"430a4d8f921c1328375054f101a9773b320436b06b347d8eb6c3f04f3d0576f1"}