{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FOOHI7OMHIP2GEQBIVPBIHJH5M","short_pith_number":"pith:FOOHI7OM","canonical_record":{"source":{"id":"2410.19396","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.HE","submitted_at":"2024-10-25T08:55:16Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"19f53961f3cc31a12d0dc73ea1214cc35d39493eaa31b0cc4df8665c9e895e34","abstract_canon_sha256":"438d244822339a25e0721d00d20ddf6e7e800ca024463aee22c9a46f74ead13b"},"schema_version":"1.0"},"canonical_sha256":"2b9c747dcc3a1fa31201455e141d27eb023bd1044a1d2d571eac5ba1b37a830d","source":{"kind":"arxiv","id":"2410.19396","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.19396","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"2410.19396v1","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.19396","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"FOOHI7OMHIP2","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"FOOHI7OMHIP2GEQB","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"FOOHI7OM","created_at":"2026-07-05T11:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FOOHI7OMHIP2GEQBIVPBIHJH5M","target":"record","payload":{"canonical_record":{"source":{"id":"2410.19396","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.HE","submitted_at":"2024-10-25T08:55:16Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"19f53961f3cc31a12d0dc73ea1214cc35d39493eaa31b0cc4df8665c9e895e34","abstract_canon_sha256":"438d244822339a25e0721d00d20ddf6e7e800ca024463aee22c9a46f74ead13b"},"schema_version":"1.0"},"canonical_sha256":"2b9c747dcc3a1fa31201455e141d27eb023bd1044a1d2d571eac5ba1b37a830d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:26:01.307268Z","signature_b64":"Z5q05dx8K774CjSSWXZ7vebW+N5IQMfDluDh/lPelGQ96sUKBYtYj2b1MmLpEyoiIOokivpMrT7PpuY3PWisDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b9c747dcc3a1fa31201455e141d27eb023bd1044a1d2d571eac5ba1b37a830d","last_reissued_at":"2026-07-05T11:26:01.306803Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:26:01.306803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.19396","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":"2026-07-05T11:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tZPE2+m5TyU8vxuDLGKkbtigxRy6yCSWfCuRsWIZYyOQF4/5Qml9VEBHVxgoHe2UMc5Ax+phsUGIwOq0zFrLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T22:22:23.061823Z"},"content_sha256":"c3ec62914985958f08341fa78972b201f5ede6e5a0b02d77f2fd13924d677dc8","schema_version":"1.0","event_id":"sha256:c3ec62914985958f08341fa78972b201f5ede6e5a0b02d77f2fd13924d677dc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FOOHI7OMHIP2GEQBIVPBIHJH5M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A rigorous solution to the superluminal issue in the diffusion equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"astro-ph.HE","authors_text":"Kun Fang, Meng-Jie Zhao, Peng-fei Yin, Xiao-Jun Bi, Xing-Jian Lv","submitted_at":"2024-10-25T08:55:16Z","abstract_excerpt":"Superluminal propagation is an intrinsic problem in the diffusion equation and has not been effectively addressed for a long time. In this work, a rigorous solution to this issue is obtained under the assumption that particles undergo a random flight process, where they move isotropically at a constant speed while experiencing random scatterings. We validate this solution by comparing it with comprehensive simulations of the random flight process and find that it significantly deviates from the solution derived from the J\\\"{u}ttner propagator. This solution is broadly applicable to various dif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.19396","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.19396/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WI00XF4fsmgzrBRfXs7Nxq5G8GO5cMKeGq29D9QeTFlrWgCH56okV1P6W8MGwElE9UTxWRAtlAGBe8PwKN/8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T22:22:23.062697Z"},"content_sha256":"b05b7abea935d7a2c6ec34022e38d474c0b49cc3b6af032ff69ea8226a04e5cd","schema_version":"1.0","event_id":"sha256:b05b7abea935d7a2c6ec34022e38d474c0b49cc3b6af032ff69ea8226a04e5cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FOOHI7OMHIP2GEQBIVPBIHJH5M/bundle.json","state_url":"https://pith.science/pith/FOOHI7OMHIP2GEQBIVPBIHJH5M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FOOHI7OMHIP2GEQBIVPBIHJH5M/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":"2026-08-10T22:22:23Z","links":{"resolver":"https://pith.science/pith/FOOHI7OMHIP2GEQBIVPBIHJH5M","bundle":"https://pith.science/pith/FOOHI7OMHIP2GEQBIVPBIHJH5M/bundle.json","state":"https://pith.science/pith/FOOHI7OMHIP2GEQBIVPBIHJH5M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FOOHI7OMHIP2GEQBIVPBIHJH5M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FOOHI7OMHIP2GEQBIVPBIHJH5M","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":"438d244822339a25e0721d00d20ddf6e7e800ca024463aee22c9a46f74ead13b","cross_cats_sorted":["hep-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.HE","submitted_at":"2024-10-25T08:55:16Z","title_canon_sha256":"19f53961f3cc31a12d0dc73ea1214cc35d39493eaa31b0cc4df8665c9e895e34"},"schema_version":"1.0","source":{"id":"2410.19396","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.19396","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"2410.19396v1","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.19396","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"FOOHI7OMHIP2","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"FOOHI7OMHIP2GEQB","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"FOOHI7OM","created_at":"2026-07-05T11:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:b05b7abea935d7a2c6ec34022e38d474c0b49cc3b6af032ff69ea8226a04e5cd","target":"graph","created_at":"2026-07-05T11:26:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.19396/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Superluminal propagation is an intrinsic problem in the diffusion equation and has not been effectively addressed for a long time. In this work, a rigorous solution to this issue is obtained under the assumption that particles undergo a random flight process, where they move isotropically at a constant speed while experiencing random scatterings. We validate this solution by comparing it with comprehensive simulations of the random flight process and find that it significantly deviates from the solution derived from the J\\\"{u}ttner propagator. This solution is broadly applicable to various dif","authors_text":"Kun Fang, Meng-Jie Zhao, Peng-fei Yin, Xiao-Jun Bi, Xing-Jian Lv","cross_cats":["hep-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.HE","submitted_at":"2024-10-25T08:55:16Z","title":"A rigorous solution to the superluminal issue in the diffusion equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.19396","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:c3ec62914985958f08341fa78972b201f5ede6e5a0b02d77f2fd13924d677dc8","target":"record","created_at":"2026-07-05T11:26:01Z","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":"438d244822339a25e0721d00d20ddf6e7e800ca024463aee22c9a46f74ead13b","cross_cats_sorted":["hep-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.HE","submitted_at":"2024-10-25T08:55:16Z","title_canon_sha256":"19f53961f3cc31a12d0dc73ea1214cc35d39493eaa31b0cc4df8665c9e895e34"},"schema_version":"1.0","source":{"id":"2410.19396","kind":"arxiv","version":1}},"canonical_sha256":"2b9c747dcc3a1fa31201455e141d27eb023bd1044a1d2d571eac5ba1b37a830d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b9c747dcc3a1fa31201455e141d27eb023bd1044a1d2d571eac5ba1b37a830d","first_computed_at":"2026-07-05T11:26:01.306803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:26:01.306803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z5q05dx8K774CjSSWXZ7vebW+N5IQMfDluDh/lPelGQ96sUKBYtYj2b1MmLpEyoiIOokivpMrT7PpuY3PWisDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:26:01.307268Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.19396","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3ec62914985958f08341fa78972b201f5ede6e5a0b02d77f2fd13924d677dc8","sha256:b05b7abea935d7a2c6ec34022e38d474c0b49cc3b6af032ff69ea8226a04e5cd"],"state_sha256":"36460d0811e029c1930674a1a202e74550ff5fc266f0a54c458b9bb8d8bc4dc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"53pfScJZ9BJIuS93pzsmTMKB4Kp4qdEV3qSt0SAyjQ5Fm9oqbKHQ4Z4D3mnowldV1skO35THeYTU9Zh7tn3JCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T22:22:23.068666Z","bundle_sha256":"674f5dd0a90599ea0aefd23f00b3170d153fc1fd25a124f7166c9899785e87af"}}