{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XKQUP2E6UWCOBSMB4T75JABI7L","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":"da93cae042c08f697d7790bd103dbd6072913b1ca08cc682943e69a50a89c6f0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-24T09:17:19Z","title_canon_sha256":"902956df1cd3c475f2c2f094d501389348dbc56359000377da70d33e3814760d"},"schema_version":"1.0","source":{"id":"1203.5397","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5397","created_at":"2026-05-18T01:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5397v1","created_at":"2026-05-18T01:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5397","created_at":"2026-05-18T01:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"XKQUP2E6UWCO","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XKQUP2E6UWCOBSMB","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XKQUP2E6","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:457cdb91b71b420ef57dd12bee2ac5f0943f6396cf436f1ee76d5d6adbccb8c1","target":"graph","created_at":"2026-05-18T01:58:02Z","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":"This paper provides a mathematical framework for Fisher information analysis for inverse problems based on Gaussian noise on infinite-dimensional Hilbert space. The covariance operator for the Gaussian noise is assumed to be trace class, and the Jacobian of the forward operator Hilbert-Schmidt. We show that the appropriate space for defining the Fisher information is given by the Cameron-Martin space. This is mainly because the range space of the covariance operator always is strictly smaller than the Hilbert space. For the Fisher information to be well-defined, it is furthermore required that","authors_text":"Andrei Khrennikov, B\\\"o rje Nilsson, Joachim Toft, Mats Gustafsson, Sven Nordebo","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-24T09:17:19Z","title":"Fisher Information for Inverse Problems and Trace Class Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5397","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:f0561d76f4a93c82794a65df2c872fbae19c67947bdf7adbda67ce4d8197eebb","target":"record","created_at":"2026-05-18T01:58:02Z","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":"da93cae042c08f697d7790bd103dbd6072913b1ca08cc682943e69a50a89c6f0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-24T09:17:19Z","title_canon_sha256":"902956df1cd3c475f2c2f094d501389348dbc56359000377da70d33e3814760d"},"schema_version":"1.0","source":{"id":"1203.5397","kind":"arxiv","version":1}},"canonical_sha256":"baa147e89ea584e0c981e4ffd48028fae8ef3675d80406c798a9691c89971624","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"baa147e89ea584e0c981e4ffd48028fae8ef3675d80406c798a9691c89971624","first_computed_at":"2026-05-18T01:58:02.235081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:02.235081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x+ImUZAi1kg7j/S+jH7q59d8x5jt/40RiRh0SQsXEnHS4hrFQmg1akCqW721bqoVIQBfDovTZdXokGDtBxFFCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:02.235620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.5397","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0561d76f4a93c82794a65df2c872fbae19c67947bdf7adbda67ce4d8197eebb","sha256:457cdb91b71b420ef57dd12bee2ac5f0943f6396cf436f1ee76d5d6adbccb8c1"],"state_sha256":"8062c9576d28a558f19ee6f50b3bbc3344e21ac3a3e316bbac187833462427cd"}