{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XH7JWQ3DHSZSG3MKLQXWNPD2BV","short_pith_number":"pith:XH7JWQ3D","canonical_record":{"source":{"id":"1207.5141","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-21T13:53:23Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"289812e70d2a22fab9ce9148ec7863b39af4c67145eb4889f86e2c6c31976db3","abstract_canon_sha256":"909dfdec9dc3c230ba4606f29dd4e81fa724e199511ad9f0dd0644e551a49513"},"schema_version":"1.0"},"canonical_sha256":"b9fe9b43633cb3236d8a5c2f66bc7a0d5d52371128e287211baefeb78773f716","source":{"kind":"arxiv","id":"1207.5141","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5141","created_at":"2026-05-18T03:25:05Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5141v2","created_at":"2026-05-18T03:25:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5141","created_at":"2026-05-18T03:25:05Z"},{"alias_kind":"pith_short_12","alias_value":"XH7JWQ3DHSZS","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XH7JWQ3DHSZSG3MK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XH7JWQ3D","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XH7JWQ3DHSZSG3MKLQXWNPD2BV","target":"record","payload":{"canonical_record":{"source":{"id":"1207.5141","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-21T13:53:23Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"289812e70d2a22fab9ce9148ec7863b39af4c67145eb4889f86e2c6c31976db3","abstract_canon_sha256":"909dfdec9dc3c230ba4606f29dd4e81fa724e199511ad9f0dd0644e551a49513"},"schema_version":"1.0"},"canonical_sha256":"b9fe9b43633cb3236d8a5c2f66bc7a0d5d52371128e287211baefeb78773f716","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:05.942836Z","signature_b64":"fk9J3pEcQKDSJ0jcQ4XlLt+/bYaNaQ5csPXffviEkFrrluDaDow8eiRDCa1hD0i/kfpYNZ+lGSv58XsBdda1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9fe9b43633cb3236d8a5c2f66bc7a0d5d52371128e287211baefeb78773f716","last_reissued_at":"2026-05-18T03:25:05.942282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:05.942282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.5141","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":"2026-05-18T03:25:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zoq2jJn7XQuX5NF/o7cJTGHhNJgsSWc5YPB6cFPc10ynpZNR9LLygMfzka9RjCMPK/THEFvS0IEnx23U3folAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:07:35.197187Z"},"content_sha256":"3db049af1ec02a53b4890d564d6ce287d3baf5ceea57803fefc3f0ba6ea50a8f","schema_version":"1.0","event_id":"sha256:3db049af1ec02a53b4890d564d6ce287d3baf5ceea57803fefc3f0ba6ea50a8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XH7JWQ3DHSZSG3MKLQXWNPD2BV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Recovery of Source Singularities via the Radiative Transfer Equation with Partial Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Mark Hubenthal","submitted_at":"2012-07-21T13:53:23Z","abstract_excerpt":"The inverse source problem for the radiative transfer equation is considered, with partial data. Here we demonstrate numerical computation of the normal operator $X_{V}^{*}X_{V}$ where $X_{V}$ is the partial data solution operator to the radiative transfer equation. The numerical scheme is based in part on a forward solver designed by F. Monard and G. Bal. We will see that one can detect quite well the visible singularities of an internal optical source $f$ for generic anisotropic $k$ and $\\sigma$, with or without noise added to the accessible data $X_{V}f$. In particular, we use a truncated N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5141","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":"2026-05-18T03:25:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T5FeVbBTIxmtLY3nvD9LXSh9TVVAHaju0Pj7dD2dS+xbnfmLBaVayLfmVjF1O91eLUspneStbs5KtTFDC72mCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:07:35.197547Z"},"content_sha256":"00e6c40d479c7b51d3d08aa38410a4ed968f4af7875848595bfc565a6316fe85","schema_version":"1.0","event_id":"sha256:00e6c40d479c7b51d3d08aa38410a4ed968f4af7875848595bfc565a6316fe85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XH7JWQ3DHSZSG3MKLQXWNPD2BV/bundle.json","state_url":"https://pith.science/pith/XH7JWQ3DHSZSG3MKLQXWNPD2BV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XH7JWQ3DHSZSG3MKLQXWNPD2BV/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":"2026-05-27T05:07:35Z","links":{"resolver":"https://pith.science/pith/XH7JWQ3DHSZSG3MKLQXWNPD2BV","bundle":"https://pith.science/pith/XH7JWQ3DHSZSG3MKLQXWNPD2BV/bundle.json","state":"https://pith.science/pith/XH7JWQ3DHSZSG3MKLQXWNPD2BV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XH7JWQ3DHSZSG3MKLQXWNPD2BV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XH7JWQ3DHSZSG3MKLQXWNPD2BV","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":"909dfdec9dc3c230ba4606f29dd4e81fa724e199511ad9f0dd0644e551a49513","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-21T13:53:23Z","title_canon_sha256":"289812e70d2a22fab9ce9148ec7863b39af4c67145eb4889f86e2c6c31976db3"},"schema_version":"1.0","source":{"id":"1207.5141","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5141","created_at":"2026-05-18T03:25:05Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5141v2","created_at":"2026-05-18T03:25:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5141","created_at":"2026-05-18T03:25:05Z"},{"alias_kind":"pith_short_12","alias_value":"XH7JWQ3DHSZS","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XH7JWQ3DHSZSG3MK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XH7JWQ3D","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:00e6c40d479c7b51d3d08aa38410a4ed968f4af7875848595bfc565a6316fe85","target":"graph","created_at":"2026-05-18T03:25:05Z","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 we demonstrate numerical computation of the normal operator $X_{V}^{*}X_{V}$ where $X_{V}$ is the partial data solution operator to the radiative transfer equation. The numerical scheme is based in part on a forward solver designed by F. Monard and G. Bal. We will see that one can detect quite well the visible singularities of an internal optical source $f$ for generic anisotropic $k$ and $\\sigma$, with or without noise added to the accessible data $X_{V}f$. In particular, we use a truncated N","authors_text":"Mark Hubenthal","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-21T13:53:23Z","title":"Numerical Recovery of Source Singularities via the Radiative Transfer Equation with Partial Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5141","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":"sha256:3db049af1ec02a53b4890d564d6ce287d3baf5ceea57803fefc3f0ba6ea50a8f","target":"record","created_at":"2026-05-18T03:25:05Z","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":"909dfdec9dc3c230ba4606f29dd4e81fa724e199511ad9f0dd0644e551a49513","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-21T13:53:23Z","title_canon_sha256":"289812e70d2a22fab9ce9148ec7863b39af4c67145eb4889f86e2c6c31976db3"},"schema_version":"1.0","source":{"id":"1207.5141","kind":"arxiv","version":2}},"canonical_sha256":"b9fe9b43633cb3236d8a5c2f66bc7a0d5d52371128e287211baefeb78773f716","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9fe9b43633cb3236d8a5c2f66bc7a0d5d52371128e287211baefeb78773f716","first_computed_at":"2026-05-18T03:25:05.942282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:05.942282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fk9J3pEcQKDSJ0jcQ4XlLt+/bYaNaQ5csPXffviEkFrrluDaDow8eiRDCa1hD0i/kfpYNZ+lGSv58XsBdda1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:05.942836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5141","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3db049af1ec02a53b4890d564d6ce287d3baf5ceea57803fefc3f0ba6ea50a8f","sha256:00e6c40d479c7b51d3d08aa38410a4ed968f4af7875848595bfc565a6316fe85"],"state_sha256":"80b8580f23ed3217fa95785aa82481761fa80d40223102cd9332d69469821ab2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u8OafmVdVz2C5Gts80UHNeoIqDhhRVdMMO1niB9GDWQsxn8ocPiXE11yDTT9Jo0uIzubeDg2DFF3eyyiuhWyAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:07:35.199626Z","bundle_sha256":"6b0018727f0c3873d003fbbfa31cdef51971142efe3a419e3a3f71a122cb25aa"}}