{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RLY3JINRCKNWDYLNX3SXET4LOM","short_pith_number":"pith:RLY3JINR","canonical_record":{"source":{"id":"1612.01219","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-05T01:58:29Z","cross_cats_sorted":[],"title_canon_sha256":"f5c35770959cd158c4627d1a7a88e226158fe8aab5682036c3730a057a71d62e","abstract_canon_sha256":"681562cbea29de6f5371fecc29edf4d9e5683f7cc927b225cc67ab6aeef731d6"},"schema_version":"1.0"},"canonical_sha256":"8af1b4a1b1129b61e16dbee5724f8b733e99c1fbddf5e870b9715acec5f2ad33","source":{"kind":"arxiv","id":"1612.01219","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01219","created_at":"2026-05-18T00:46:44Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01219v2","created_at":"2026-05-18T00:46:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01219","created_at":"2026-05-18T00:46:44Z"},{"alias_kind":"pith_short_12","alias_value":"RLY3JINRCKNW","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RLY3JINRCKNWDYLN","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RLY3JINR","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RLY3JINRCKNWDYLNX3SXET4LOM","target":"record","payload":{"canonical_record":{"source":{"id":"1612.01219","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-05T01:58:29Z","cross_cats_sorted":[],"title_canon_sha256":"f5c35770959cd158c4627d1a7a88e226158fe8aab5682036c3730a057a71d62e","abstract_canon_sha256":"681562cbea29de6f5371fecc29edf4d9e5683f7cc927b225cc67ab6aeef731d6"},"schema_version":"1.0"},"canonical_sha256":"8af1b4a1b1129b61e16dbee5724f8b733e99c1fbddf5e870b9715acec5f2ad33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:44.011247Z","signature_b64":"+jEGtpM7Ktn8Z60o+WXuW4zgXNKFAjCXqF7YUouibVNHi/KCXKELZC5hXdhJJNfHuCW0z29/7DyRAyg0cUclAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8af1b4a1b1129b61e16dbee5724f8b733e99c1fbddf5e870b9715acec5f2ad33","last_reissued_at":"2026-05-18T00:46:44.010566Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:44.010566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.01219","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":"2026-05-18T00:46:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXuSiF959XSTosP+TVHW0pWijFFRMdXrYw+yacqjUym9bt35N6vVyFKtpoiwAbxxcmU/8Do4VRmf6IRQAM8BAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:36:15.080973Z"},"content_sha256":"71e2281f72ec3710e9c9a667615b2014af41abda553d8e2d7eb031fa21d9dd70","schema_version":"1.0","event_id":"sha256:71e2281f72ec3710e9c9a667615b2014af41abda553d8e2d7eb031fa21d9dd70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RLY3JINRCKNWDYLNX3SXET4LOM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform regularity for linear kinetic equations with random input based on hypocoercivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Li Wang, Qin Li","submitted_at":"2016-12-05T01:58:29Z","abstract_excerpt":"In this paper we study the effect of randomness in kinetic equations that preserve mass. Our focus is in proving the analyticity of the solution with respect to the randomness, which naturally leads to the convergence of numerical methods. The analysis is carried out in a general setting, with the regularity result not depending on the specific form of the collision term, the probability distribution of the random variables, or the regime the system is in, and thereby termed \"uniform\". Applications include the linear Boltzmann equation, BGK model, Carlemann model, among many others; and the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01219","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":""},"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":"2026-05-18T00:46:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4o1xi+Knmhcgw0OSEdXtzxnK3WiPRouvdndw3otO2jUVD8p5iRyiu4sUGrsAYhT7LPrMa3B06xTp/79prKGJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:36:15.081658Z"},"content_sha256":"d9be40c502cf15d6e64b55469ede54451b8c73cc4f2ab95b963e2dd2ca7ffcda","schema_version":"1.0","event_id":"sha256:d9be40c502cf15d6e64b55469ede54451b8c73cc4f2ab95b963e2dd2ca7ffcda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RLY3JINRCKNWDYLNX3SXET4LOM/bundle.json","state_url":"https://pith.science/pith/RLY3JINRCKNWDYLNX3SXET4LOM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RLY3JINRCKNWDYLNX3SXET4LOM/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":"2026-06-07T21:36:15Z","links":{"resolver":"https://pith.science/pith/RLY3JINRCKNWDYLNX3SXET4LOM","bundle":"https://pith.science/pith/RLY3JINRCKNWDYLNX3SXET4LOM/bundle.json","state":"https://pith.science/pith/RLY3JINRCKNWDYLNX3SXET4LOM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RLY3JINRCKNWDYLNX3SXET4LOM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RLY3JINRCKNWDYLNX3SXET4LOM","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":"681562cbea29de6f5371fecc29edf4d9e5683f7cc927b225cc67ab6aeef731d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-05T01:58:29Z","title_canon_sha256":"f5c35770959cd158c4627d1a7a88e226158fe8aab5682036c3730a057a71d62e"},"schema_version":"1.0","source":{"id":"1612.01219","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01219","created_at":"2026-05-18T00:46:44Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01219v2","created_at":"2026-05-18T00:46:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01219","created_at":"2026-05-18T00:46:44Z"},{"alias_kind":"pith_short_12","alias_value":"RLY3JINRCKNW","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RLY3JINRCKNWDYLN","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RLY3JINR","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:d9be40c502cf15d6e64b55469ede54451b8c73cc4f2ab95b963e2dd2ca7ffcda","target":"graph","created_at":"2026-05-18T00:46:44Z","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 study the effect of randomness in kinetic equations that preserve mass. Our focus is in proving the analyticity of the solution with respect to the randomness, which naturally leads to the convergence of numerical methods. The analysis is carried out in a general setting, with the regularity result not depending on the specific form of the collision term, the probability distribution of the random variables, or the regime the system is in, and thereby termed \"uniform\". Applications include the linear Boltzmann equation, BGK model, Carlemann model, among many others; and the re","authors_text":"Li Wang, Qin Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-05T01:58:29Z","title":"Uniform regularity for linear kinetic equations with random input based on hypocoercivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01219","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":"sha256:71e2281f72ec3710e9c9a667615b2014af41abda553d8e2d7eb031fa21d9dd70","target":"record","created_at":"2026-05-18T00:46:44Z","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":"681562cbea29de6f5371fecc29edf4d9e5683f7cc927b225cc67ab6aeef731d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-05T01:58:29Z","title_canon_sha256":"f5c35770959cd158c4627d1a7a88e226158fe8aab5682036c3730a057a71d62e"},"schema_version":"1.0","source":{"id":"1612.01219","kind":"arxiv","version":2}},"canonical_sha256":"8af1b4a1b1129b61e16dbee5724f8b733e99c1fbddf5e870b9715acec5f2ad33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8af1b4a1b1129b61e16dbee5724f8b733e99c1fbddf5e870b9715acec5f2ad33","first_computed_at":"2026-05-18T00:46:44.010566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:44.010566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+jEGtpM7Ktn8Z60o+WXuW4zgXNKFAjCXqF7YUouibVNHi/KCXKELZC5hXdhJJNfHuCW0z29/7DyRAyg0cUclAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:44.011247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01219","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71e2281f72ec3710e9c9a667615b2014af41abda553d8e2d7eb031fa21d9dd70","sha256:d9be40c502cf15d6e64b55469ede54451b8c73cc4f2ab95b963e2dd2ca7ffcda"],"state_sha256":"3d59ac337c92655c859f63ff6c2790c30e1d5e3d605b5b85ce605fff1aa61cf3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vAqUolv1rCRj+eqWUfAriHjCfSfMgulmQaxDzl9HlAM6uekFL0p5OtffDESal562vEYhXq8fMlrWrT1f9FJNBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:36:15.085412Z","bundle_sha256":"3816b6a185b279d93071562493176cfa3db3768fe7b7863c0eebd2921247de04"}}