{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:XCVM7SRMDRG5ZXJJZYVX7G7PC5","short_pith_number":"pith:XCVM7SRM","canonical_record":{"source":{"id":"2102.13021","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-02-25T17:25:12Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"133e165b954c3e0bbc9bbeff52214f0ea7cfcbe208bece5ffc014d922023b588","abstract_canon_sha256":"f6ba894e7407dace57ff55a427d9a0373da3aaa278ceefb78603f268967b9575"},"schema_version":"1.0"},"canonical_sha256":"b8aacfca2c1c4ddcdd29ce2b7f9bef177010eb0208d0ec44f53718d54842519a","source":{"kind":"arxiv","id":"2102.13021","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.13021","created_at":"2026-07-05T03:29:28Z"},{"alias_kind":"arxiv_version","alias_value":"2102.13021v2","created_at":"2026-07-05T03:29:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.13021","created_at":"2026-07-05T03:29:28Z"},{"alias_kind":"pith_short_12","alias_value":"XCVM7SRMDRG5","created_at":"2026-07-05T03:29:28Z"},{"alias_kind":"pith_short_16","alias_value":"XCVM7SRMDRG5ZXJJ","created_at":"2026-07-05T03:29:28Z"},{"alias_kind":"pith_short_8","alias_value":"XCVM7SRM","created_at":"2026-07-05T03:29:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:XCVM7SRMDRG5ZXJJZYVX7G7PC5","target":"record","payload":{"canonical_record":{"source":{"id":"2102.13021","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-02-25T17:25:12Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"133e165b954c3e0bbc9bbeff52214f0ea7cfcbe208bece5ffc014d922023b588","abstract_canon_sha256":"f6ba894e7407dace57ff55a427d9a0373da3aaa278ceefb78603f268967b9575"},"schema_version":"1.0"},"canonical_sha256":"b8aacfca2c1c4ddcdd29ce2b7f9bef177010eb0208d0ec44f53718d54842519a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:29:28.201977Z","signature_b64":"gM6CtmDw+LY3jpvw3MJDJaUOQ+ZXvHdkXmgtoA30jDcTJKig7LqgtWVnKI45B2W7UXJ7u2J3rr04hiIbalENAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8aacfca2c1c4ddcdd29ce2b7f9bef177010eb0208d0ec44f53718d54842519a","last_reissued_at":"2026-07-05T03:29:28.201377Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:29:28.201377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.13021","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:29:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gbgCrmxoIQxWnZTfRTe0MZa9bEGDy4Qp7/ceZihEA/MWyHTgBxoOPnt6Q+rBTWmdhRo+kynPX96Y397GLMY6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:12:19.072892Z"},"content_sha256":"aee9de90ad6dcec5e26b3a7de9d1db1b940bcd381406fc1ecbfd69f2147bf71d","schema_version":"1.0","event_id":"sha256:aee9de90ad6dcec5e26b3a7de9d1db1b940bcd381406fc1ecbfd69f2147bf71d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:XCVM7SRMDRG5ZXJJZYVX7G7PC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semi-implicit Hybrid Discrete $\\left(\\text{H}^T_N\\right)$ Approximation of Thermal Radiative Transfer","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"James A. Rossmanith, Minwoo Shin, Ryan G. McClarren","submitted_at":"2021-02-25T17:25:12Z","abstract_excerpt":"The thermal radiative transfer (TRT) equations form an integro-differential system that describes the propagation and collisional interactions of photons. Computing accurate and efficient numerical solutions TRT are challenging for several reasons, the first of which is that TRT is defined on a high-dimensional phase. In order to reduce the dimensionality of the phase space, classical approaches such as the P$_N$ (spherical harmonics) or the S$_N$ (discrete ordinates) ansatz are often used in the literature. In this work, we introduce a novel approach: the hybrid discrete (H$^T_N$) approximati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.13021","kind":"arxiv","version":2},"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/2102.13021/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":"2026-07-05T03:29:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ae/xUiDWj6Gh8YDq+RE3QiNBgydi5AiEWol+dHGQOByXiTne5CQEqAiRjvxkTVFVdgp8l3YUwENuGJdHIWNDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:12:19.073275Z"},"content_sha256":"a9cf6e8b8d20ac8d49e9aa12fc71afc331dc30332f507d06e3f604967135e594","schema_version":"1.0","event_id":"sha256:a9cf6e8b8d20ac8d49e9aa12fc71afc331dc30332f507d06e3f604967135e594"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XCVM7SRMDRG5ZXJJZYVX7G7PC5/bundle.json","state_url":"https://pith.science/pith/XCVM7SRMDRG5ZXJJZYVX7G7PC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XCVM7SRMDRG5ZXJJZYVX7G7PC5/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":"2026-07-07T12:12:19Z","links":{"resolver":"https://pith.science/pith/XCVM7SRMDRG5ZXJJZYVX7G7PC5","bundle":"https://pith.science/pith/XCVM7SRMDRG5ZXJJZYVX7G7PC5/bundle.json","state":"https://pith.science/pith/XCVM7SRMDRG5ZXJJZYVX7G7PC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XCVM7SRMDRG5ZXJJZYVX7G7PC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XCVM7SRMDRG5ZXJJZYVX7G7PC5","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":"f6ba894e7407dace57ff55a427d9a0373da3aaa278ceefb78603f268967b9575","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-02-25T17:25:12Z","title_canon_sha256":"133e165b954c3e0bbc9bbeff52214f0ea7cfcbe208bece5ffc014d922023b588"},"schema_version":"1.0","source":{"id":"2102.13021","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.13021","created_at":"2026-07-05T03:29:28Z"},{"alias_kind":"arxiv_version","alias_value":"2102.13021v2","created_at":"2026-07-05T03:29:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.13021","created_at":"2026-07-05T03:29:28Z"},{"alias_kind":"pith_short_12","alias_value":"XCVM7SRMDRG5","created_at":"2026-07-05T03:29:28Z"},{"alias_kind":"pith_short_16","alias_value":"XCVM7SRMDRG5ZXJJ","created_at":"2026-07-05T03:29:28Z"},{"alias_kind":"pith_short_8","alias_value":"XCVM7SRM","created_at":"2026-07-05T03:29:28Z"}],"graph_snapshots":[{"event_id":"sha256:a9cf6e8b8d20ac8d49e9aa12fc71afc331dc30332f507d06e3f604967135e594","target":"graph","created_at":"2026-07-05T03:29:28Z","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/2102.13021/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The thermal radiative transfer (TRT) equations form an integro-differential system that describes the propagation and collisional interactions of photons. Computing accurate and efficient numerical solutions TRT are challenging for several reasons, the first of which is that TRT is defined on a high-dimensional phase. In order to reduce the dimensionality of the phase space, classical approaches such as the P$_N$ (spherical harmonics) or the S$_N$ (discrete ordinates) ansatz are often used in the literature. In this work, we introduce a novel approach: the hybrid discrete (H$^T_N$) approximati","authors_text":"James A. Rossmanith, Minwoo Shin, Ryan G. McClarren","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-02-25T17:25:12Z","title":"Semi-implicit Hybrid Discrete $\\left(\\text{H}^T_N\\right)$ Approximation of Thermal Radiative Transfer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.13021","kind":"arxiv","version":2},"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:aee9de90ad6dcec5e26b3a7de9d1db1b940bcd381406fc1ecbfd69f2147bf71d","target":"record","created_at":"2026-07-05T03:29:28Z","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":"f6ba894e7407dace57ff55a427d9a0373da3aaa278ceefb78603f268967b9575","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-02-25T17:25:12Z","title_canon_sha256":"133e165b954c3e0bbc9bbeff52214f0ea7cfcbe208bece5ffc014d922023b588"},"schema_version":"1.0","source":{"id":"2102.13021","kind":"arxiv","version":2}},"canonical_sha256":"b8aacfca2c1c4ddcdd29ce2b7f9bef177010eb0208d0ec44f53718d54842519a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8aacfca2c1c4ddcdd29ce2b7f9bef177010eb0208d0ec44f53718d54842519a","first_computed_at":"2026-07-05T03:29:28.201377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:29:28.201377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gM6CtmDw+LY3jpvw3MJDJaUOQ+ZXvHdkXmgtoA30jDcTJKig7LqgtWVnKI45B2W7UXJ7u2J3rr04hiIbalENAw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:29:28.201977Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.13021","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aee9de90ad6dcec5e26b3a7de9d1db1b940bcd381406fc1ecbfd69f2147bf71d","sha256:a9cf6e8b8d20ac8d49e9aa12fc71afc331dc30332f507d06e3f604967135e594"],"state_sha256":"7724f592cb03c1317907e230255f3a9214ae84a68f44699a8a97f615e4061297"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HVkWJeZfZGxPUF/bGbJOku7E2pVPymgnP1m7bGzsc3OF3rqDdJeYjfaJCJ4rFeWT9HWPcT7bHBeWM3lbeSrBBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T12:12:19.075284Z","bundle_sha256":"06b8d4a5033c3fdf18d806e081bb3c6985f67e747630a602f0d96aa31eb6f024"}}