{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BDKLBSMYAZ7YKJCNRFFGLZC3B7","short_pith_number":"pith:BDKLBSMY","canonical_record":{"source":{"id":"1606.01311","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-04T00:33:41Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"9082cf0d4e032dc0999c6adde99a06adc5ededda64765aa1fefd7c00d44fe561","abstract_canon_sha256":"890f771003ed07fc27e97d902ca35e3e04eb7c3c38510b84b40ee8f1332a94cc"},"schema_version":"1.0"},"canonical_sha256":"08d4b0c998067f85244d894a65e45b0ff65544fe8b6d57811e808a7857263311","source":{"kind":"arxiv","id":"1606.01311","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01311","created_at":"2026-05-18T00:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01311v3","created_at":"2026-05-18T00:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01311","created_at":"2026-05-18T00:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"BDKLBSMYAZ7Y","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BDKLBSMYAZ7YKJCN","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BDKLBSMY","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BDKLBSMYAZ7YKJCNRFFGLZC3B7","target":"record","payload":{"canonical_record":{"source":{"id":"1606.01311","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-04T00:33:41Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"9082cf0d4e032dc0999c6adde99a06adc5ededda64765aa1fefd7c00d44fe561","abstract_canon_sha256":"890f771003ed07fc27e97d902ca35e3e04eb7c3c38510b84b40ee8f1332a94cc"},"schema_version":"1.0"},"canonical_sha256":"08d4b0c998067f85244d894a65e45b0ff65544fe8b6d57811e808a7857263311","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:48.733625Z","signature_b64":"UqTzxofpI3ReyIc4n/TFdC8Z2iBkrONKsZcTnJF3ea9+xfP6QSxvlmS0TAZ/FDbQ1ey/ICLi9fnvki6uE52QCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08d4b0c998067f85244d894a65e45b0ff65544fe8b6d57811e808a7857263311","last_reissued_at":"2026-05-18T00:51:48.732908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:48.732908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.01311","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SiKqPKJCsGW26wi5PJJEkGrHD0xDBdzQ6PNT5wMDUYWtJUhqYVSkAF9Cc5ALnrA9SCqhQX4PmAV2IqM/h5gVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:57:05.592533Z"},"content_sha256":"e9c8df4004f5b50d9031345f4a6bf4ca8e132cf5d624769ae03cc2f7c5abe7f7","schema_version":"1.0","event_id":"sha256:e9c8df4004f5b50d9031345f4a6bf4ca8e132cf5d624769ae03cc2f7c5abe7f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BDKLBSMYAZ7YKJCNRFFGLZC3B7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Validity and regularization of classical half-space equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Jianfeng Lu, Qin Li, Weiran Sun","submitted_at":"2016-06-04T00:33:41Z","abstract_excerpt":"Recent result [Wu and Guo, Comm. Math. Phys., 2015] has shown that over the 2D unit disk, the classical half-space equation (CHS) for the neutron transport does not capture the correct boundary layer behaviour as long believed. In this paper we develop a regularization technique for CHS to any arbitrary order and use its first-order regularization to show that in the case of the 2D unit disk, although CHS misrepresents the boundary layer behaviour, it does give the correct boundary condition for the interior macroscopic (Laplace) equation. Therefore CHS is still a valid equation to recover the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01311","kind":"arxiv","version":3},"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":"2026-05-18T00:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D6iPkpjR+br48oliIdc9x4IgYnc1EA9xpRnA2JOYgXoINFEa9rWEPeg0jv7PO0H6PY9USaRrg7z0vv+uHHivAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:57:05.593250Z"},"content_sha256":"678a6f06a1252ecab2411ff24823cb6c66ba20722e6d1f3710c84da43bfedb25","schema_version":"1.0","event_id":"sha256:678a6f06a1252ecab2411ff24823cb6c66ba20722e6d1f3710c84da43bfedb25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDKLBSMYAZ7YKJCNRFFGLZC3B7/bundle.json","state_url":"https://pith.science/pith/BDKLBSMYAZ7YKJCNRFFGLZC3B7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDKLBSMYAZ7YKJCNRFFGLZC3B7/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":"2026-05-26T09:57:05Z","links":{"resolver":"https://pith.science/pith/BDKLBSMYAZ7YKJCNRFFGLZC3B7","bundle":"https://pith.science/pith/BDKLBSMYAZ7YKJCNRFFGLZC3B7/bundle.json","state":"https://pith.science/pith/BDKLBSMYAZ7YKJCNRFFGLZC3B7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDKLBSMYAZ7YKJCNRFFGLZC3B7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BDKLBSMYAZ7YKJCNRFFGLZC3B7","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":"890f771003ed07fc27e97d902ca35e3e04eb7c3c38510b84b40ee8f1332a94cc","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-04T00:33:41Z","title_canon_sha256":"9082cf0d4e032dc0999c6adde99a06adc5ededda64765aa1fefd7c00d44fe561"},"schema_version":"1.0","source":{"id":"1606.01311","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01311","created_at":"2026-05-18T00:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01311v3","created_at":"2026-05-18T00:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01311","created_at":"2026-05-18T00:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"BDKLBSMYAZ7Y","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BDKLBSMYAZ7YKJCN","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BDKLBSMY","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:678a6f06a1252ecab2411ff24823cb6c66ba20722e6d1f3710c84da43bfedb25","target":"graph","created_at":"2026-05-18T00:51:48Z","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":"Recent result [Wu and Guo, Comm. Math. Phys., 2015] has shown that over the 2D unit disk, the classical half-space equation (CHS) for the neutron transport does not capture the correct boundary layer behaviour as long believed. In this paper we develop a regularization technique for CHS to any arbitrary order and use its first-order regularization to show that in the case of the 2D unit disk, although CHS misrepresents the boundary layer behaviour, it does give the correct boundary condition for the interior macroscopic (Laplace) equation. Therefore CHS is still a valid equation to recover the","authors_text":"Jianfeng Lu, Qin Li, Weiran Sun","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-04T00:33:41Z","title":"Validity and regularization of classical half-space equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01311","kind":"arxiv","version":3},"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:e9c8df4004f5b50d9031345f4a6bf4ca8e132cf5d624769ae03cc2f7c5abe7f7","target":"record","created_at":"2026-05-18T00:51:48Z","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":"890f771003ed07fc27e97d902ca35e3e04eb7c3c38510b84b40ee8f1332a94cc","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-04T00:33:41Z","title_canon_sha256":"9082cf0d4e032dc0999c6adde99a06adc5ededda64765aa1fefd7c00d44fe561"},"schema_version":"1.0","source":{"id":"1606.01311","kind":"arxiv","version":3}},"canonical_sha256":"08d4b0c998067f85244d894a65e45b0ff65544fe8b6d57811e808a7857263311","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08d4b0c998067f85244d894a65e45b0ff65544fe8b6d57811e808a7857263311","first_computed_at":"2026-05-18T00:51:48.732908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:48.732908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UqTzxofpI3ReyIc4n/TFdC8Z2iBkrONKsZcTnJF3ea9+xfP6QSxvlmS0TAZ/FDbQ1ey/ICLi9fnvki6uE52QCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:48.733625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.01311","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9c8df4004f5b50d9031345f4a6bf4ca8e132cf5d624769ae03cc2f7c5abe7f7","sha256:678a6f06a1252ecab2411ff24823cb6c66ba20722e6d1f3710c84da43bfedb25"],"state_sha256":"447e7c7bd2fe1a172333af35c944b023e83b785a00ea587a603c12c76d50879a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbbdJJ/AcjSv54EBFLreLVRxyTMSIAiDGi6ae5wNuEDo0vCm5k9z+VhoHV8z0xKVMgSNZ4L+mGGX8BTlbmsNAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:57:05.597405Z","bundle_sha256":"5ff16b4a9181709bff9cffbd61013a70d5526e34fdabe5225af4f3bfb8d8e600"}}