{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WCCTK2HQSHKQR357B4A3CQXBZQ","short_pith_number":"pith:WCCTK2HQ","canonical_record":{"source":{"id":"1409.0476","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-29T01:53:19Z","cross_cats_sorted":[],"title_canon_sha256":"39127932b1f49ac167c319890814448886b19e7f8c2d8f99f42f747557f464f2","abstract_canon_sha256":"53f6ba3632779290f305e0ade6f034cb8ddaca8afcc2ab7c657b032ab827bec0"},"schema_version":"1.0"},"canonical_sha256":"b0853568f091d508efbf0f01b142e1cc2b4d13d032fd807f30fd6021f65c781a","source":{"kind":"arxiv","id":"1409.0476","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0476","created_at":"2026-05-18T02:09:41Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0476v3","created_at":"2026-05-18T02:09:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0476","created_at":"2026-05-18T02:09:41Z"},{"alias_kind":"pith_short_12","alias_value":"WCCTK2HQSHKQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WCCTK2HQSHKQR357","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WCCTK2HQ","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WCCTK2HQSHKQR357B4A3CQXBZQ","target":"record","payload":{"canonical_record":{"source":{"id":"1409.0476","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-29T01:53:19Z","cross_cats_sorted":[],"title_canon_sha256":"39127932b1f49ac167c319890814448886b19e7f8c2d8f99f42f747557f464f2","abstract_canon_sha256":"53f6ba3632779290f305e0ade6f034cb8ddaca8afcc2ab7c657b032ab827bec0"},"schema_version":"1.0"},"canonical_sha256":"b0853568f091d508efbf0f01b142e1cc2b4d13d032fd807f30fd6021f65c781a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:41.687472Z","signature_b64":"OR6EDmHHvq+kp+I+YIW5fySMXYaPd09lK+i1nTUwoG/OiVDOfR2JludKxIBepk+Ry/iUzRu5OAgkGEODOh1aBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0853568f091d508efbf0f01b142e1cc2b4d13d032fd807f30fd6021f65c781a","last_reissued_at":"2026-05-18T02:09:41.686586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:41.686586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.0476","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":"2026-05-18T02:09:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m+PLC/eWj9hxxUzHw3+HBpNzc8mAlgdtTpwrj6YYL/urjfiA3oq8T92KyeLijYIJze8eGzD66oQmkwvsT7qsDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:01:25.148005Z"},"content_sha256":"4b44a5594ffeba5fb11d2076361d21638230712b93c319e8d8a6d0baa6a8650d","schema_version":"1.0","event_id":"sha256:4b44a5594ffeba5fb11d2076361d21638230712b93c319e8d8a6d0baa6a8650d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WCCTK2HQSHKQR357B4A3CQXBZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusion approximations and domain decomposition method of linear transport equations: asymptotics and numerics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jianfeng Lu, Qin Li, Weiran Sun","submitted_at":"2014-08-29T01:53:19Z","abstract_excerpt":"In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist. The diffusion equations and their data are derived from asymptotic and layer analysis which allows general scattering kernels and general data. We apply the half-space solver in [20] to resolve the boundary layer equation and obtain the boundary data for the diffusion equation. The algorithms are validated by numerical experiments and also by error analysis fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0476","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":"2026-05-18T02:09:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QmmC8DyqoNvhQ4DNHEqra/RaSMpuJhFZc6elUWWXG0jNQeVK3Md2coNzMU0XNxtiuHXrUEwYm/Pq+b5uLFn6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:01:25.148731Z"},"content_sha256":"00438e3fa9ba3de19fa564a8384c8ebb1a6b754dae989163858dec2666bf938e","schema_version":"1.0","event_id":"sha256:00438e3fa9ba3de19fa564a8384c8ebb1a6b754dae989163858dec2666bf938e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WCCTK2HQSHKQR357B4A3CQXBZQ/bundle.json","state_url":"https://pith.science/pith/WCCTK2HQSHKQR357B4A3CQXBZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WCCTK2HQSHKQR357B4A3CQXBZQ/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":"2026-05-26T22:01:25Z","links":{"resolver":"https://pith.science/pith/WCCTK2HQSHKQR357B4A3CQXBZQ","bundle":"https://pith.science/pith/WCCTK2HQSHKQR357B4A3CQXBZQ/bundle.json","state":"https://pith.science/pith/WCCTK2HQSHKQR357B4A3CQXBZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WCCTK2HQSHKQR357B4A3CQXBZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WCCTK2HQSHKQR357B4A3CQXBZQ","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":"53f6ba3632779290f305e0ade6f034cb8ddaca8afcc2ab7c657b032ab827bec0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-29T01:53:19Z","title_canon_sha256":"39127932b1f49ac167c319890814448886b19e7f8c2d8f99f42f747557f464f2"},"schema_version":"1.0","source":{"id":"1409.0476","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0476","created_at":"2026-05-18T02:09:41Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0476v3","created_at":"2026-05-18T02:09:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0476","created_at":"2026-05-18T02:09:41Z"},{"alias_kind":"pith_short_12","alias_value":"WCCTK2HQSHKQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WCCTK2HQSHKQR357","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WCCTK2HQ","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:00438e3fa9ba3de19fa564a8384c8ebb1a6b754dae989163858dec2666bf938e","target":"graph","created_at":"2026-05-18T02:09:41Z","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":"In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist. The diffusion equations and their data are derived from asymptotic and layer analysis which allows general scattering kernels and general data. We apply the half-space solver in [20] to resolve the boundary layer equation and obtain the boundary data for the diffusion equation. The algorithms are validated by numerical experiments and also by error analysis fo","authors_text":"Jianfeng Lu, Qin Li, Weiran Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-29T01:53:19Z","title":"Diffusion approximations and domain decomposition method of linear transport equations: asymptotics and numerics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0476","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":"sha256:4b44a5594ffeba5fb11d2076361d21638230712b93c319e8d8a6d0baa6a8650d","target":"record","created_at":"2026-05-18T02:09:41Z","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":"53f6ba3632779290f305e0ade6f034cb8ddaca8afcc2ab7c657b032ab827bec0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-29T01:53:19Z","title_canon_sha256":"39127932b1f49ac167c319890814448886b19e7f8c2d8f99f42f747557f464f2"},"schema_version":"1.0","source":{"id":"1409.0476","kind":"arxiv","version":3}},"canonical_sha256":"b0853568f091d508efbf0f01b142e1cc2b4d13d032fd807f30fd6021f65c781a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0853568f091d508efbf0f01b142e1cc2b4d13d032fd807f30fd6021f65c781a","first_computed_at":"2026-05-18T02:09:41.686586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:41.686586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OR6EDmHHvq+kp+I+YIW5fySMXYaPd09lK+i1nTUwoG/OiVDOfR2JludKxIBepk+Ry/iUzRu5OAgkGEODOh1aBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:41.687472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0476","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b44a5594ffeba5fb11d2076361d21638230712b93c319e8d8a6d0baa6a8650d","sha256:00438e3fa9ba3de19fa564a8384c8ebb1a6b754dae989163858dec2666bf938e"],"state_sha256":"6da43de95caf1782b81ae51d6e7d83d25cb0984d223d1d65f2bcc609c8adfd60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VQmodGEsTkotL2B8ThBZHRd0PuKe5Yx9C0hhG4ZGn704aNmLuOpV2FWb4+Ufv4aMKjGBK1BTUMjH0r8ga/LbDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:01:25.153221Z","bundle_sha256":"7f0d2b95489a3bbd9dcd6015cfaec6042c83df3fc5bbf0c6b748c7ae8465aed8"}}