{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NX3D3XYSSWLCU7OCLA74ZOBMKH","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":"52817999ebc3c091c908b631c8feec4914a9cab818aa0367452f53d589e6b4fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2009-07-13T07:04:06Z","title_canon_sha256":"abd51fe19e7899867d9e9fc2617d09cb26fbbc8e059ff18d35c9d90bbf071609"},"schema_version":"1.0","source":{"id":"0907.2099","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2099","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2099v1","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2099","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"pith_short_12","alias_value":"NX3D3XYSSWLC","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"NX3D3XYSSWLCU7OC","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"NX3D3XYS","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:b8ecb4a075f53eb7bb1193eadc9c601adbb36c73f38504ebf7ae13bc584daaaa","target":"graph","created_at":"2026-05-18T03:56:24Z","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 investigate moment methods from a general point of view using an operator notation. This theoretical approach lets us explore the moment closure problem in more detail. This gives rise to a new idea, proposed in [Levermore2005, Levermore2009], of how to improve the well-known Pn approximations. We systematically develop a diffusive correction to the Pn equations from the operator formulation - the so-called Dn approximation. We validate the new approach with numerical examples in one and two dimensions.","authors_text":"C. David Levermore, Martin Frank, Matthias Schaefer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2009-07-13T07:04:06Z","title":"Diffusive Corrections to Pn Approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2099","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:e51755c931e574f7c8c7873f4797eef87978b6d31dbed6333ddd1ca0cbf578e4","target":"record","created_at":"2026-05-18T03:56:24Z","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":"52817999ebc3c091c908b631c8feec4914a9cab818aa0367452f53d589e6b4fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2009-07-13T07:04:06Z","title_canon_sha256":"abd51fe19e7899867d9e9fc2617d09cb26fbbc8e059ff18d35c9d90bbf071609"},"schema_version":"1.0","source":{"id":"0907.2099","kind":"arxiv","version":1}},"canonical_sha256":"6df63ddf1295962a7dc2583fccb82c51d04e72afa0daf6cb7dc7a1cef7c0661c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6df63ddf1295962a7dc2583fccb82c51d04e72afa0daf6cb7dc7a1cef7c0661c","first_computed_at":"2026-05-18T03:56:24.564775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:24.564775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HG5vCOED742HGMpaPKLAEuGlTy54UDpE+Rm8sv7W9Qv2Zh6F7m0SksZCfD0gskXlkxYDLwEhFWcL8/6ib2DDCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:24.565354Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.2099","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e51755c931e574f7c8c7873f4797eef87978b6d31dbed6333ddd1ca0cbf578e4","sha256:b8ecb4a075f53eb7bb1193eadc9c601adbb36c73f38504ebf7ae13bc584daaaa"],"state_sha256":"ef744ef75c84cdd5d32d536e8c8866b52c7aeb19b92c76ba8a32349bdfa72914"}