{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:J6V3QJNZQO5V4LM55K7ZVWYRGR","short_pith_number":"pith:J6V3QJNZ","canonical_record":{"source":{"id":"0812.3063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2008-12-16T14:20:04Z","cross_cats_sorted":[],"title_canon_sha256":"a46c1f8cff8226112a3fd8738ac9afa81276355dfa7bdb5b37e230ce60223723","abstract_canon_sha256":"f432d179b80a70325198fd46d68627af0ec9e6312dbe0e42a093620be6e68393"},"schema_version":"1.0"},"canonical_sha256":"4fabb825b983bb5e2d9deabf9adb11346198cc7194ad6f33f708581f9222587c","source":{"kind":"arxiv","id":"0812.3063","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3063","created_at":"2026-07-04T15:33:53Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3063v1","created_at":"2026-07-04T15:33:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3063","created_at":"2026-07-04T15:33:53Z"},{"alias_kind":"pith_short_12","alias_value":"J6V3QJNZQO5V","created_at":"2026-07-04T15:33:53Z"},{"alias_kind":"pith_short_16","alias_value":"J6V3QJNZQO5V4LM5","created_at":"2026-07-04T15:33:53Z"},{"alias_kind":"pith_short_8","alias_value":"J6V3QJNZ","created_at":"2026-07-04T15:33:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:J6V3QJNZQO5V4LM55K7ZVWYRGR","target":"record","payload":{"canonical_record":{"source":{"id":"0812.3063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2008-12-16T14:20:04Z","cross_cats_sorted":[],"title_canon_sha256":"a46c1f8cff8226112a3fd8738ac9afa81276355dfa7bdb5b37e230ce60223723","abstract_canon_sha256":"f432d179b80a70325198fd46d68627af0ec9e6312dbe0e42a093620be6e68393"},"schema_version":"1.0"},"canonical_sha256":"4fabb825b983bb5e2d9deabf9adb11346198cc7194ad6f33f708581f9222587c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:33:53.391738Z","signature_b64":"N4JXGCrRlR+a3e+2k5PMT637kTfcnJDz+gs8FWZG8bfgb4F45Q5xjoodS3fwv4xyhHKtCFliObz43VYcSP0HBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fabb825b983bb5e2d9deabf9adb11346198cc7194ad6f33f708581f9222587c","last_reissued_at":"2026-07-04T15:33:53.391269Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:33:53.391269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.3063","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":"2026-07-04T15:33:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6SJz7pJ1oetCRQcL4ieFrhIgvAcUQ0XESweTyStIFFTASg3F9lfXURh+5iW7wmzrbjUAdTRnAEAISQBuBNbzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T00:20:35.494957Z"},"content_sha256":"1d4c6119885f6822d894c394317abeacef9e59eec10352a90754e835d17db656","schema_version":"1.0","event_id":"sha256:1d4c6119885f6822d894c394317abeacef9e59eec10352a90754e835d17db656"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:J6V3QJNZQO5V4LM55K7ZVWYRGR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher order minimum entropy approximations in radiative transfer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Martin Frank, Philipp Monreal","submitted_at":"2008-12-16T14:20:04Z","abstract_excerpt":"In this paper we approximate the radiative transfer equations by the method of moments, constructing mesoscopic approximations of arbitrary order of the otherwise microscopic system. To define the necessary closure a minimum entropy approach is utilized. While in radiative transfer, the minimum entropy closure for moment systems up to the first-order moment is well known, higher-order minimum entropy closures have not been implemented. This is probably due to the fact that the closure cannot be expressed in analytical form. Our focus thus lies in developing some general results about the minim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3063","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/0812.3063/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":"2026-07-04T15:33:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d9gZK4Kg1r/8iwhjjbP2V2wHjqUupV0BW990dkFZLbvGnyIelzG5XZf0R4nmd0lJfuZUu9rIYJN0d1QpTimOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T00:20:35.495532Z"},"content_sha256":"d11b34d7441b87470ba85f55abb37aa9c608c850183f06e59515461c54472595","schema_version":"1.0","event_id":"sha256:d11b34d7441b87470ba85f55abb37aa9c608c850183f06e59515461c54472595"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J6V3QJNZQO5V4LM55K7ZVWYRGR/bundle.json","state_url":"https://pith.science/pith/J6V3QJNZQO5V4LM55K7ZVWYRGR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J6V3QJNZQO5V4LM55K7ZVWYRGR/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":"2026-08-15T00:20:35Z","links":{"resolver":"https://pith.science/pith/J6V3QJNZQO5V4LM55K7ZVWYRGR","bundle":"https://pith.science/pith/J6V3QJNZQO5V4LM55K7ZVWYRGR/bundle.json","state":"https://pith.science/pith/J6V3QJNZQO5V4LM55K7ZVWYRGR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J6V3QJNZQO5V4LM55K7ZVWYRGR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:J6V3QJNZQO5V4LM55K7ZVWYRGR","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":"f432d179b80a70325198fd46d68627af0ec9e6312dbe0e42a093620be6e68393","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2008-12-16T14:20:04Z","title_canon_sha256":"a46c1f8cff8226112a3fd8738ac9afa81276355dfa7bdb5b37e230ce60223723"},"schema_version":"1.0","source":{"id":"0812.3063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3063","created_at":"2026-07-04T15:33:53Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3063v1","created_at":"2026-07-04T15:33:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3063","created_at":"2026-07-04T15:33:53Z"},{"alias_kind":"pith_short_12","alias_value":"J6V3QJNZQO5V","created_at":"2026-07-04T15:33:53Z"},{"alias_kind":"pith_short_16","alias_value":"J6V3QJNZQO5V4LM5","created_at":"2026-07-04T15:33:53Z"},{"alias_kind":"pith_short_8","alias_value":"J6V3QJNZ","created_at":"2026-07-04T15:33:53Z"}],"graph_snapshots":[{"event_id":"sha256:d11b34d7441b87470ba85f55abb37aa9c608c850183f06e59515461c54472595","target":"graph","created_at":"2026-07-04T15:33:53Z","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/0812.3063/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we approximate the radiative transfer equations by the method of moments, constructing mesoscopic approximations of arbitrary order of the otherwise microscopic system. To define the necessary closure a minimum entropy approach is utilized. While in radiative transfer, the minimum entropy closure for moment systems up to the first-order moment is well known, higher-order minimum entropy closures have not been implemented. This is probably due to the fact that the closure cannot be expressed in analytical form. Our focus thus lies in developing some general results about the minim","authors_text":"Martin Frank, Philipp Monreal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2008-12-16T14:20:04Z","title":"Higher order minimum entropy approximations in radiative transfer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3063","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":"sha256:1d4c6119885f6822d894c394317abeacef9e59eec10352a90754e835d17db656","target":"record","created_at":"2026-07-04T15:33:53Z","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":"f432d179b80a70325198fd46d68627af0ec9e6312dbe0e42a093620be6e68393","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2008-12-16T14:20:04Z","title_canon_sha256":"a46c1f8cff8226112a3fd8738ac9afa81276355dfa7bdb5b37e230ce60223723"},"schema_version":"1.0","source":{"id":"0812.3063","kind":"arxiv","version":1}},"canonical_sha256":"4fabb825b983bb5e2d9deabf9adb11346198cc7194ad6f33f708581f9222587c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fabb825b983bb5e2d9deabf9adb11346198cc7194ad6f33f708581f9222587c","first_computed_at":"2026-07-04T15:33:53.391269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:33:53.391269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N4JXGCrRlR+a3e+2k5PMT637kTfcnJDz+gs8FWZG8bfgb4F45Q5xjoodS3fwv4xyhHKtCFliObz43VYcSP0HBA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:33:53.391738Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d4c6119885f6822d894c394317abeacef9e59eec10352a90754e835d17db656","sha256:d11b34d7441b87470ba85f55abb37aa9c608c850183f06e59515461c54472595"],"state_sha256":"db813560d5b10e9a5e5a47663727964024be0e55e8b80ec55ec2b646f3433903"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ypWGZlt1BYysEdPPK1ZdOucAFh4IGGm3nSBFBuhHWm+9bunPNOvs6e6fKYAvCeQoNhHztGl7V9rn868xrsS7CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T00:20:35.499570Z","bundle_sha256":"dca64315abef07c980b82ece8219c43abef6146acb662e7c051c3bd96c317af2"}}