{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7BGXLP23K6GFGKEISVNKJTOBDJ","short_pith_number":"pith:7BGXLP23","canonical_record":{"source":{"id":"1208.0772","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2012-08-03T15:34:04Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"878546379031945ef353dd01c80c6d4724fa0215673416a0a6a0726838ac1371","abstract_canon_sha256":"38e528b3dd6353bd98a476089fb868f7460118463abf2a782b0d1eff357258a8"},"schema_version":"1.0"},"canonical_sha256":"f84d75bf5b578c532888955aa4cdc11a4fba7bfed72dad7ee320bbcb2749c109","source":{"kind":"arxiv","id":"1208.0772","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0772","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0772v1","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0772","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"7BGXLP23K6GF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7BGXLP23K6GFGKEI","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7BGXLP23","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7BGXLP23K6GFGKEISVNKJTOBDJ","target":"record","payload":{"canonical_record":{"source":{"id":"1208.0772","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2012-08-03T15:34:04Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"878546379031945ef353dd01c80c6d4724fa0215673416a0a6a0726838ac1371","abstract_canon_sha256":"38e528b3dd6353bd98a476089fb868f7460118463abf2a782b0d1eff357258a8"},"schema_version":"1.0"},"canonical_sha256":"f84d75bf5b578c532888955aa4cdc11a4fba7bfed72dad7ee320bbcb2749c109","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:22.841429Z","signature_b64":"5rMafLo0wJjnPuJX4NCTdNPwL8zXZJFrXGvQRTUGa69AcSRbVTGCwfYSPoh1uA6aa3qyaOhevdpRclW4natiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f84d75bf5b578c532888955aa4cdc11a4fba7bfed72dad7ee320bbcb2749c109","last_reissued_at":"2026-05-18T03:49:22.840792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:22.840792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.0772","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":"2026-05-18T03:49:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qkfsS0INLxd6tdsP/A0gMpErQ+e9cj0zHHEJ/g1u0j1CDGEDy8P3O3V0xzdRir7XoCnDHrgaV1/F1nZWdeUSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T08:12:43.287022Z"},"content_sha256":"93dff7d4a69c2cea19519b6b753a9bf09fbba9475a9112493b62df696dc55fd9","schema_version":"1.0","event_id":"sha256:93dff7d4a69c2cea19519b6b753a9bf09fbba9475a9112493b62df696dc55fd9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7BGXLP23K6GFGKEISVNKJTOBDJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbed, Entropy-Based Closure for Radiative Transfer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"physics.comp-ph","authors_text":"Cory D. Hauck, Edgar Olbrant, Martin Frank","submitted_at":"2012-08-03T15:34:04Z","abstract_excerpt":"We derive a hierarchy of closures based on perturbations of well-known entropy-based closures; we therefore refer to them as perturbed entropy-based models. Our derivation reveals final equations containing an additional convective and diffusive term which are added to the flux term of the standard closure. We present numerical simulations for the simplest member of the hierarchy, the perturbed M1 or PM1 model, in one spatial dimension. Simulations are performed using a Runge-Kutta discontinuous Galerkin method with special limiters that guarantee the realizability of the moment variables and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0772","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":""},"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":"2026-05-18T03:49:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JCX9Kags3HXa/uVlFKeILO9I1z9hYHG7y6cS3DRk/wopqYge1DnqePieqQoDY255ZOw8tSZZ3UCnoFY5BzNcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T08:12:43.287382Z"},"content_sha256":"f19caaf9c487d6a35a5dde7f3784241b9fcf864147ceef4cf472f250eb8328fb","schema_version":"1.0","event_id":"sha256:f19caaf9c487d6a35a5dde7f3784241b9fcf864147ceef4cf472f250eb8328fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7BGXLP23K6GFGKEISVNKJTOBDJ/bundle.json","state_url":"https://pith.science/pith/7BGXLP23K6GFGKEISVNKJTOBDJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7BGXLP23K6GFGKEISVNKJTOBDJ/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":"2026-05-21T08:12:43Z","links":{"resolver":"https://pith.science/pith/7BGXLP23K6GFGKEISVNKJTOBDJ","bundle":"https://pith.science/pith/7BGXLP23K6GFGKEISVNKJTOBDJ/bundle.json","state":"https://pith.science/pith/7BGXLP23K6GFGKEISVNKJTOBDJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7BGXLP23K6GFGKEISVNKJTOBDJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7BGXLP23K6GFGKEISVNKJTOBDJ","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":"38e528b3dd6353bd98a476089fb868f7460118463abf2a782b0d1eff357258a8","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2012-08-03T15:34:04Z","title_canon_sha256":"878546379031945ef353dd01c80c6d4724fa0215673416a0a6a0726838ac1371"},"schema_version":"1.0","source":{"id":"1208.0772","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0772","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0772v1","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0772","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"7BGXLP23K6GF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7BGXLP23K6GFGKEI","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7BGXLP23","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:f19caaf9c487d6a35a5dde7f3784241b9fcf864147ceef4cf472f250eb8328fb","target":"graph","created_at":"2026-05-18T03:49:22Z","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 derive a hierarchy of closures based on perturbations of well-known entropy-based closures; we therefore refer to them as perturbed entropy-based models. Our derivation reveals final equations containing an additional convective and diffusive term which are added to the flux term of the standard closure. We present numerical simulations for the simplest member of the hierarchy, the perturbed M1 or PM1 model, in one spatial dimension. Simulations are performed using a Runge-Kutta discontinuous Galerkin method with special limiters that guarantee the realizability of the moment variables and ","authors_text":"Cory D. Hauck, Edgar Olbrant, Martin Frank","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2012-08-03T15:34:04Z","title":"Perturbed, Entropy-Based Closure for Radiative Transfer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0772","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":"sha256:93dff7d4a69c2cea19519b6b753a9bf09fbba9475a9112493b62df696dc55fd9","target":"record","created_at":"2026-05-18T03:49:22Z","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":"38e528b3dd6353bd98a476089fb868f7460118463abf2a782b0d1eff357258a8","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2012-08-03T15:34:04Z","title_canon_sha256":"878546379031945ef353dd01c80c6d4724fa0215673416a0a6a0726838ac1371"},"schema_version":"1.0","source":{"id":"1208.0772","kind":"arxiv","version":1}},"canonical_sha256":"f84d75bf5b578c532888955aa4cdc11a4fba7bfed72dad7ee320bbcb2749c109","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f84d75bf5b578c532888955aa4cdc11a4fba7bfed72dad7ee320bbcb2749c109","first_computed_at":"2026-05-18T03:49:22.840792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:22.840792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5rMafLo0wJjnPuJX4NCTdNPwL8zXZJFrXGvQRTUGa69AcSRbVTGCwfYSPoh1uA6aa3qyaOhevdpRclW4natiDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:22.841429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.0772","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93dff7d4a69c2cea19519b6b753a9bf09fbba9475a9112493b62df696dc55fd9","sha256:f19caaf9c487d6a35a5dde7f3784241b9fcf864147ceef4cf472f250eb8328fb"],"state_sha256":"74d8782ee35f5e52034753a055cfdb2c381f9cf5a52bfec2c0a60246e9ae4457"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A5IzhqZxUi1FBXVyRcNGSpNOXw4EB/Gj1Q8lW1pGCwEmidsw1THPXdQLe2R9xK8Mc4J2K2C+lgHFklWynS6sCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T08:12:43.289512Z","bundle_sha256":"6e484ba2bbdec68bd1544bde255009527fe1bbd569a777d8a5ce52a3f4071f9b"}}