{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7TMRQXAZE3U3W7AVZTG3IDDSTC","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":"7bc23928dfe2981dacf66e5e5a8de6423dcc884ee7724968fba3a9b19941597c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-02-03T00:58:49Z","title_canon_sha256":"57f1c222ddb3ae3d3f21b91771c21572ab5cdff35fde5b32c57116a07c8691d6"},"schema_version":"1.0","source":{"id":"1302.0441","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0441","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0441v2","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0441","created_at":"2026-05-18T01:51:51Z"},{"alias_kind":"pith_short_12","alias_value":"7TMRQXAZE3U3","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7TMRQXAZE3U3W7AV","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7TMRQXAZ","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:05aa867f37181adbb0010446ef507ee7164fb8f3be645b0083a25bc6b7d8fd41","target":"graph","created_at":"2026-05-18T01:51:51Z","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":"In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the transformation itself depends on additional unknown parameters and we wish to determine both sets of parameters simultaneously. When separable problems are solved by optimization, convergence can often be accelerated by elimination of the linear variables, a strategy which appears most prominently in the variable projection methods due to Golub, Pereyra, and Kau","authors_text":"Anna C. Gilbert, Paul Shearer","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-02-03T00:58:49Z","title":"A generalization of variable elimination for separable inverse problems beyond least squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0441","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":"sha256:461b4594459ffe8a21f858e28afe680eebef9e161d39c1980ecccc8931c9e5e8","target":"record","created_at":"2026-05-18T01:51:51Z","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":"7bc23928dfe2981dacf66e5e5a8de6423dcc884ee7724968fba3a9b19941597c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-02-03T00:58:49Z","title_canon_sha256":"57f1c222ddb3ae3d3f21b91771c21572ab5cdff35fde5b32c57116a07c8691d6"},"schema_version":"1.0","source":{"id":"1302.0441","kind":"arxiv","version":2}},"canonical_sha256":"fcd9185c1926e9bb7c15cccdb40c7298b9573f9f55a22a232424da1af774d475","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcd9185c1926e9bb7c15cccdb40c7298b9573f9f55a22a232424da1af774d475","first_computed_at":"2026-05-18T01:51:51.088835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:51:51.088835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TZPSxdFJdHjAilQQDUhYQHnZK5iY6ejDn0JrsnmX1RoQDfPpXZDM4WfF71kxUHqdUIfinfQxbCgBxafV7s+ODA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:51:51.089217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0441","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:461b4594459ffe8a21f858e28afe680eebef9e161d39c1980ecccc8931c9e5e8","sha256:05aa867f37181adbb0010446ef507ee7164fb8f3be645b0083a25bc6b7d8fd41"],"state_sha256":"1cf44c30570981684066a7b65d36b3db13c21fa7852b5a1a65771042ef8381b0"}