{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LYHX3MS642ZLHSBNYAJKTWAOOK","short_pith_number":"pith:LYHX3MS6","canonical_record":{"source":{"id":"1105.1577","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-09T04:05:48Z","cross_cats_sorted":[],"title_canon_sha256":"be89ef303faf59387bf6d2725a9ae583ba0ac3a486b5b85ade3f49278e20e918","abstract_canon_sha256":"fefa5d31bcc98591dd72452406392ccffa3a11857eebdae61b478048a80453bd"},"schema_version":"1.0"},"canonical_sha256":"5e0f7db25ee6b2b3c82dc012a9d80e7294a870969c646796fbe385012b3493db","source":{"kind":"arxiv","id":"1105.1577","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1577","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1577v3","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1577","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"LYHX3MS642ZL","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LYHX3MS642ZLHSBN","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LYHX3MS6","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LYHX3MS642ZLHSBNYAJKTWAOOK","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1577","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-09T04:05:48Z","cross_cats_sorted":[],"title_canon_sha256":"be89ef303faf59387bf6d2725a9ae583ba0ac3a486b5b85ade3f49278e20e918","abstract_canon_sha256":"fefa5d31bcc98591dd72452406392ccffa3a11857eebdae61b478048a80453bd"},"schema_version":"1.0"},"canonical_sha256":"5e0f7db25ee6b2b3c82dc012a9d80e7294a870969c646796fbe385012b3493db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:02.684312Z","signature_b64":"jqfmMM3EkRdWGVGaQo4NH4aqrFPWsG1duM/4XF4AjsJkrgafEbZX7y5a2Fc8L7LTcTQQwQURRX6em7hdYbXADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e0f7db25ee6b2b3c82dc012a9d80e7294a870969c646796fbe385012b3493db","last_reissued_at":"2026-05-18T02:02:02.683705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:02.683705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1577","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":"2026-05-18T02:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L9UstpTN85ew6FOZy0RgIdnJCGsQcYJ0V+ok+jZbrvtxMQOs4BpHLbhGwXzpmb2vJ2LGYZ3e+Jvx3DqaAS4TAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:28:41.975123Z"},"content_sha256":"292ff108b31745e8598d2bf70594ec6e8b2e22326b92e0cced180a7a342a5539","schema_version":"1.0","event_id":"sha256:292ff108b31745e8598d2bf70594ec6e8b2e22326b92e0cced180a7a342a5539"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LYHX3MS642ZLHSBNYAJKTWAOOK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Inverse Source Problem in Radiative Transfer with Partial Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mark Hubenthal","submitted_at":"2011-05-09T04:05:48Z","abstract_excerpt":"The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a certain subset of the domain, which we call the visible set. Furthermore, it is shown for an open dense set of $C^{\\infty}$ absorption and scattering coefficients that one can recover the part of the wave front set of the source that is supported in the microlocally visible set, modulo a function in the Sobolev space $H^{k}$ for $k$ arbitrarily large. This "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1577","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":"2026-05-18T02:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+/NCaKoIUSrtl6MFYJwFN3PpgmcvG5j8ItVDJgqdxvYuUfQe9N1jYaYqmjwT4GMH8DlmvJLLYp5oB3Pty/mDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:28:41.975827Z"},"content_sha256":"1e4d41e9a62669fc43f30371dc9328e03971835d0419ad2be55b43120ad64751","schema_version":"1.0","event_id":"sha256:1e4d41e9a62669fc43f30371dc9328e03971835d0419ad2be55b43120ad64751"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LYHX3MS642ZLHSBNYAJKTWAOOK/bundle.json","state_url":"https://pith.science/pith/LYHX3MS642ZLHSBNYAJKTWAOOK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LYHX3MS642ZLHSBNYAJKTWAOOK/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":"2026-05-27T09:28:41Z","links":{"resolver":"https://pith.science/pith/LYHX3MS642ZLHSBNYAJKTWAOOK","bundle":"https://pith.science/pith/LYHX3MS642ZLHSBNYAJKTWAOOK/bundle.json","state":"https://pith.science/pith/LYHX3MS642ZLHSBNYAJKTWAOOK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LYHX3MS642ZLHSBNYAJKTWAOOK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LYHX3MS642ZLHSBNYAJKTWAOOK","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":"fefa5d31bcc98591dd72452406392ccffa3a11857eebdae61b478048a80453bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-09T04:05:48Z","title_canon_sha256":"be89ef303faf59387bf6d2725a9ae583ba0ac3a486b5b85ade3f49278e20e918"},"schema_version":"1.0","source":{"id":"1105.1577","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1577","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1577v3","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1577","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"LYHX3MS642ZL","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LYHX3MS642ZLHSBN","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LYHX3MS6","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:1e4d41e9a62669fc43f30371dc9328e03971835d0419ad2be55b43120ad64751","target":"graph","created_at":"2026-05-18T02:02:02Z","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":"The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a certain subset of the domain, which we call the visible set. Furthermore, it is shown for an open dense set of $C^{\\infty}$ absorption and scattering coefficients that one can recover the part of the wave front set of the source that is supported in the microlocally visible set, modulo a function in the Sobolev space $H^{k}$ for $k$ arbitrarily large. This ","authors_text":"Mark Hubenthal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-09T04:05:48Z","title":"An Inverse Source Problem in Radiative Transfer with Partial Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1577","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":"sha256:292ff108b31745e8598d2bf70594ec6e8b2e22326b92e0cced180a7a342a5539","target":"record","created_at":"2026-05-18T02:02:02Z","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":"fefa5d31bcc98591dd72452406392ccffa3a11857eebdae61b478048a80453bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-09T04:05:48Z","title_canon_sha256":"be89ef303faf59387bf6d2725a9ae583ba0ac3a486b5b85ade3f49278e20e918"},"schema_version":"1.0","source":{"id":"1105.1577","kind":"arxiv","version":3}},"canonical_sha256":"5e0f7db25ee6b2b3c82dc012a9d80e7294a870969c646796fbe385012b3493db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e0f7db25ee6b2b3c82dc012a9d80e7294a870969c646796fbe385012b3493db","first_computed_at":"2026-05-18T02:02:02.683705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:02.683705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jqfmMM3EkRdWGVGaQo4NH4aqrFPWsG1duM/4XF4AjsJkrgafEbZX7y5a2Fc8L7LTcTQQwQURRX6em7hdYbXADg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:02.684312Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1577","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:292ff108b31745e8598d2bf70594ec6e8b2e22326b92e0cced180a7a342a5539","sha256:1e4d41e9a62669fc43f30371dc9328e03971835d0419ad2be55b43120ad64751"],"state_sha256":"588499b72dabed54ee9657ee8c4569f25f0c97f16edba39f67ec8619d1d23d56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5UEheeAeIRKyCVvz2nqPJkwXQL8Unmnrj/TpN/021CUxL2qfJCFMaKj+wZJwE6iOZRAqQr44OD6JI9fkifzCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:28:41.979371Z","bundle_sha256":"c67193bdb826ba345cd7b7b75ab81bb47dc364aea8fcf85011602cc5552de95a"}}