{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WHISEZIZFAU6MQYIMWJLOBOXFJ","short_pith_number":"pith:WHISEZIZ","canonical_record":{"source":{"id":"1808.02071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-06T19:06:47Z","cross_cats_sorted":[],"title_canon_sha256":"6a5ee78f27bfbd87de9895c985a2db324e88012d11bfa93ab5574c6067e2b8c2","abstract_canon_sha256":"7b438a8b3d5282b35c35bcc2d0c51e5e2d9735b21b517ab6a50cfd39fa7ea661"},"schema_version":"1.0"},"canonical_sha256":"b1d12265192829e643086592b705d72a4ad70bbf3e62568ae8395927fcaf9bc6","source":{"kind":"arxiv","id":"1808.02071","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02071","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02071v1","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02071","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"pith_short_12","alias_value":"WHISEZIZFAU6","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WHISEZIZFAU6MQYI","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WHISEZIZ","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WHISEZIZFAU6MQYIMWJLOBOXFJ","target":"record","payload":{"canonical_record":{"source":{"id":"1808.02071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-06T19:06:47Z","cross_cats_sorted":[],"title_canon_sha256":"6a5ee78f27bfbd87de9895c985a2db324e88012d11bfa93ab5574c6067e2b8c2","abstract_canon_sha256":"7b438a8b3d5282b35c35bcc2d0c51e5e2d9735b21b517ab6a50cfd39fa7ea661"},"schema_version":"1.0"},"canonical_sha256":"b1d12265192829e643086592b705d72a4ad70bbf3e62568ae8395927fcaf9bc6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:47.717591Z","signature_b64":"9kTUNqjQ2hTLRNEj72r1iqC/XcCTlyp9Kf4lImKwIcNpTEzmKOF2UGysFXF3Giku3s0pYS3q7AufYRSnROQMCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1d12265192829e643086592b705d72a4ad70bbf3e62568ae8395927fcaf9bc6","last_reissued_at":"2026-05-18T00:08:47.716950Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:47.716950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.02071","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":"2026-05-18T00:08:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vb4Sms6L8OqyGq66Hi4oicxkYhDyCEgGLItmSRS0ACpw9oFhEUqEQvtK1xMOI0TUGdzvWU4/qCpOwXyFXYe8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:19:32.143759Z"},"content_sha256":"0fe0e90815cb40a7355eff853cb7f661b6a69e2d6276c2c8962f68cb777d6540","schema_version":"1.0","event_id":"sha256:0fe0e90815cb40a7355eff853cb7f661b6a69e2d6276c2c8962f68cb777d6540"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WHISEZIZFAU6MQYIMWJLOBOXFJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverse problems for the stationary transport equation in the diffusion scaling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gunther Uhlmann, Qin Li, Ru-Yu Lai","submitted_at":"2018-08-06T19:06:47Z","abstract_excerpt":"We consider the inverse problem of reconstructing the optical parameters of the radiative transfer equation (RTE) from boundary measurements in the diffusion limit. In the diffusive regime (the Knudsen number $\\mathsf{Kn}\\ll 1$), the forward problem for the stationary RTE is well approximated by an elliptic equation. However, the connection between the inverse problem for the RTE and the inverse problem for the elliptic equation has not been fully developed. This problem is particularly interesting because the former one is mildly ill-posed , with a Lipschitz type stability estimate, while the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02071","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":"2026-05-18T00:08:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qDzk6TGtsXu5xPdEKPRUuX7m8ovscYOcByQ4mGrKipfcNbXUhU9JfK3Vuh9OVPHB8wvkDoE1ZrlPwch4epG1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:19:32.144188Z"},"content_sha256":"6a0b2527159698bea1c4c6886f98a0c1fbb7df4f65ecf7c95b3239051f90bfb9","schema_version":"1.0","event_id":"sha256:6a0b2527159698bea1c4c6886f98a0c1fbb7df4f65ecf7c95b3239051f90bfb9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WHISEZIZFAU6MQYIMWJLOBOXFJ/bundle.json","state_url":"https://pith.science/pith/WHISEZIZFAU6MQYIMWJLOBOXFJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WHISEZIZFAU6MQYIMWJLOBOXFJ/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":"2026-06-09T16:19:32Z","links":{"resolver":"https://pith.science/pith/WHISEZIZFAU6MQYIMWJLOBOXFJ","bundle":"https://pith.science/pith/WHISEZIZFAU6MQYIMWJLOBOXFJ/bundle.json","state":"https://pith.science/pith/WHISEZIZFAU6MQYIMWJLOBOXFJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WHISEZIZFAU6MQYIMWJLOBOXFJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WHISEZIZFAU6MQYIMWJLOBOXFJ","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":"7b438a8b3d5282b35c35bcc2d0c51e5e2d9735b21b517ab6a50cfd39fa7ea661","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-06T19:06:47Z","title_canon_sha256":"6a5ee78f27bfbd87de9895c985a2db324e88012d11bfa93ab5574c6067e2b8c2"},"schema_version":"1.0","source":{"id":"1808.02071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02071","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02071v1","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02071","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"pith_short_12","alias_value":"WHISEZIZFAU6","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WHISEZIZFAU6MQYI","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WHISEZIZ","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:6a0b2527159698bea1c4c6886f98a0c1fbb7df4f65ecf7c95b3239051f90bfb9","target":"graph","created_at":"2026-05-18T00:08:47Z","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":"We consider the inverse problem of reconstructing the optical parameters of the radiative transfer equation (RTE) from boundary measurements in the diffusion limit. In the diffusive regime (the Knudsen number $\\mathsf{Kn}\\ll 1$), the forward problem for the stationary RTE is well approximated by an elliptic equation. However, the connection between the inverse problem for the RTE and the inverse problem for the elliptic equation has not been fully developed. This problem is particularly interesting because the former one is mildly ill-posed , with a Lipschitz type stability estimate, while the","authors_text":"Gunther Uhlmann, Qin Li, Ru-Yu Lai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-06T19:06:47Z","title":"Inverse problems for the stationary transport equation in the diffusion scaling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02071","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":"sha256:0fe0e90815cb40a7355eff853cb7f661b6a69e2d6276c2c8962f68cb777d6540","target":"record","created_at":"2026-05-18T00:08:47Z","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":"7b438a8b3d5282b35c35bcc2d0c51e5e2d9735b21b517ab6a50cfd39fa7ea661","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-06T19:06:47Z","title_canon_sha256":"6a5ee78f27bfbd87de9895c985a2db324e88012d11bfa93ab5574c6067e2b8c2"},"schema_version":"1.0","source":{"id":"1808.02071","kind":"arxiv","version":1}},"canonical_sha256":"b1d12265192829e643086592b705d72a4ad70bbf3e62568ae8395927fcaf9bc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1d12265192829e643086592b705d72a4ad70bbf3e62568ae8395927fcaf9bc6","first_computed_at":"2026-05-18T00:08:47.716950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:47.716950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9kTUNqjQ2hTLRNEj72r1iqC/XcCTlyp9Kf4lImKwIcNpTEzmKOF2UGysFXF3Giku3s0pYS3q7AufYRSnROQMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:47.717591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fe0e90815cb40a7355eff853cb7f661b6a69e2d6276c2c8962f68cb777d6540","sha256:6a0b2527159698bea1c4c6886f98a0c1fbb7df4f65ecf7c95b3239051f90bfb9"],"state_sha256":"2eefc6535b1e41358996b96a8a2a1dbcffa36b75a65b6d8e9db7e5585b169e82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e2VSYGA+P+07MJnKcdr3P3Zl+nv5CXE6L2tq+82nJcSP/6ZDsEehSlgw9KsoXGmjoIJcoamXdjS+Sjri2Z+xCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:19:32.146434Z","bundle_sha256":"25c1be7a595b8061095c60911bfac560fc622f57fff07706b03745e444d069ee"}}