{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VBJKBBTW2Y6YIBF4GC6IBLIKW4","short_pith_number":"pith:VBJKBBTW","canonical_record":{"source":{"id":"1901.01865","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2019-01-04T10:35:55Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"462354828a6647119095edadc6547a8b6a3f8baa129622c217dd772303deffa4","abstract_canon_sha256":"f16841452bea25924a11ceddb4f2ef96e461c7c279f266e564ab4dd4f2b54a2e"},"schema_version":"1.0"},"canonical_sha256":"a852a08676d63d8404bc30bc80ad0ab727ed621c7920c447f7b86fe6559cdf3a","source":{"kind":"arxiv","id":"1901.01865","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.01865","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"arxiv_version","alias_value":"1901.01865v1","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01865","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"pith_short_12","alias_value":"VBJKBBTW2Y6Y","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VBJKBBTW2Y6YIBF4","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VBJKBBTW","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VBJKBBTW2Y6YIBF4GC6IBLIKW4","target":"record","payload":{"canonical_record":{"source":{"id":"1901.01865","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2019-01-04T10:35:55Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"462354828a6647119095edadc6547a8b6a3f8baa129622c217dd772303deffa4","abstract_canon_sha256":"f16841452bea25924a11ceddb4f2ef96e461c7c279f266e564ab4dd4f2b54a2e"},"schema_version":"1.0"},"canonical_sha256":"a852a08676d63d8404bc30bc80ad0ab727ed621c7920c447f7b86fe6559cdf3a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:49.459619Z","signature_b64":"jko2YLyJlXOCuz+jzkBFncUtSfAIBBERMPCazB89VZ2KOdtnjmXJW0biJb7uaijEoLx5iB7GwzRsSm7iKNJQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a852a08676d63d8404bc30bc80ad0ab727ed621c7920c447f7b86fe6559cdf3a","last_reissued_at":"2026-05-17T23:56:49.459174Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:49.459174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.01865","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":"2026-05-17T23:56:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U4lG6yGb+GF8mKqtNO30gGVL7q5c4ZM4PVFH8Ai9Kn/ml23bG9zfwDrD7F1QCjFPn0g99SpnBO4ifPweUGqsBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:23:18.346066Z"},"content_sha256":"6dcfc48071fa22d4ca8f8c4b02c9f155c2704974ee92e3d5b360831d85c1aabb","schema_version":"1.0","event_id":"sha256:6dcfc48071fa22d4ca8f8c4b02c9f155c2704974ee92e3d5b360831d85c1aabb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VBJKBBTW2Y6YIBF4GC6IBLIKW4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Implicit Discontinuous Galerkin Method for the Boltzmann Equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"physics.comp-ph","authors_text":"Lei Wu, Peng Wang, Wei Su, Yonghao Zhang","submitted_at":"2019-01-04T10:35:55Z","abstract_excerpt":"An implicit high-order discontinuous Galerkin (DG) method is developed to find steady-state solution of rarefied gas flow described by the Boltzmann equation with full collision operator. In the physical space, velocity distribution function is approximated by the piecewise polynomials of degree up to 4, while in the velocity space the fast spectral method is incorporated into the DG to evaluate the collision operator. A specific polynomial approximation for the collision operator is proposed to reduce the computational complexity of the fast spectral method by $K$ times, where for two-dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01865","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":"2026-05-17T23:56:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6lqwgQ5Tsp7rZ+8Kjw0WHyTrXSuGFJm/V6uVv+aqMjMFy57BfoqLWw2Xy623HPm4IGjX34xPnySkbTsXe9dTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:23:18.346438Z"},"content_sha256":"1c151ceca7d302a33ac7078905b4f0d64241bfa807df8e237f6cf8259bde0615","schema_version":"1.0","event_id":"sha256:1c151ceca7d302a33ac7078905b4f0d64241bfa807df8e237f6cf8259bde0615"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VBJKBBTW2Y6YIBF4GC6IBLIKW4/bundle.json","state_url":"https://pith.science/pith/VBJKBBTW2Y6YIBF4GC6IBLIKW4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VBJKBBTW2Y6YIBF4GC6IBLIKW4/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":"2026-05-30T09:23:18Z","links":{"resolver":"https://pith.science/pith/VBJKBBTW2Y6YIBF4GC6IBLIKW4","bundle":"https://pith.science/pith/VBJKBBTW2Y6YIBF4GC6IBLIKW4/bundle.json","state":"https://pith.science/pith/VBJKBBTW2Y6YIBF4GC6IBLIKW4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VBJKBBTW2Y6YIBF4GC6IBLIKW4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VBJKBBTW2Y6YIBF4GC6IBLIKW4","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":"f16841452bea25924a11ceddb4f2ef96e461c7c279f266e564ab4dd4f2b54a2e","cross_cats_sorted":["physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2019-01-04T10:35:55Z","title_canon_sha256":"462354828a6647119095edadc6547a8b6a3f8baa129622c217dd772303deffa4"},"schema_version":"1.0","source":{"id":"1901.01865","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.01865","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"arxiv_version","alias_value":"1901.01865v1","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01865","created_at":"2026-05-17T23:56:49Z"},{"alias_kind":"pith_short_12","alias_value":"VBJKBBTW2Y6Y","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VBJKBBTW2Y6YIBF4","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VBJKBBTW","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:1c151ceca7d302a33ac7078905b4f0d64241bfa807df8e237f6cf8259bde0615","target":"graph","created_at":"2026-05-17T23:56:49Z","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":"An implicit high-order discontinuous Galerkin (DG) method is developed to find steady-state solution of rarefied gas flow described by the Boltzmann equation with full collision operator. In the physical space, velocity distribution function is approximated by the piecewise polynomials of degree up to 4, while in the velocity space the fast spectral method is incorporated into the DG to evaluate the collision operator. A specific polynomial approximation for the collision operator is proposed to reduce the computational complexity of the fast spectral method by $K$ times, where for two-dimensi","authors_text":"Lei Wu, Peng Wang, Wei Su, Yonghao Zhang","cross_cats":["physics.flu-dyn"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2019-01-04T10:35:55Z","title":"Implicit Discontinuous Galerkin Method for the Boltzmann Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01865","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":"sha256:6dcfc48071fa22d4ca8f8c4b02c9f155c2704974ee92e3d5b360831d85c1aabb","target":"record","created_at":"2026-05-17T23:56:49Z","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":"f16841452bea25924a11ceddb4f2ef96e461c7c279f266e564ab4dd4f2b54a2e","cross_cats_sorted":["physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2019-01-04T10:35:55Z","title_canon_sha256":"462354828a6647119095edadc6547a8b6a3f8baa129622c217dd772303deffa4"},"schema_version":"1.0","source":{"id":"1901.01865","kind":"arxiv","version":1}},"canonical_sha256":"a852a08676d63d8404bc30bc80ad0ab727ed621c7920c447f7b86fe6559cdf3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a852a08676d63d8404bc30bc80ad0ab727ed621c7920c447f7b86fe6559cdf3a","first_computed_at":"2026-05-17T23:56:49.459174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:49.459174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jko2YLyJlXOCuz+jzkBFncUtSfAIBBERMPCazB89VZ2KOdtnjmXJW0biJb7uaijEoLx5iB7GwzRsSm7iKNJQBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:49.459619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.01865","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dcfc48071fa22d4ca8f8c4b02c9f155c2704974ee92e3d5b360831d85c1aabb","sha256:1c151ceca7d302a33ac7078905b4f0d64241bfa807df8e237f6cf8259bde0615"],"state_sha256":"f84b98c24fc4d62f84f037aa0c999a3acb3028a99a07a5bc1b90d56a3445605c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kgAgQCEmo0eOnTiVcqCu2EbdPFK0iG7+J2uZpKLvkMW02nJ/agFNCG/XP/EjgItHX1+B+lhyhLn7WhqiscuhBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:23:18.348440Z","bundle_sha256":"e7fb550df438cb800a531106cce39a4ebaa91909da9fd1b7363bfc8685fd91ad"}}