{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IWG26CPX6BDKNRZFHU7DFRG3IF","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":"2ba4387a37eccbf45f0e7373bc5f4f03c883a4e8fab8aa9d9cc4cd3369eb7fd6","cross_cats_sorted":["cs.NA","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-14T05:14:23Z","title_canon_sha256":"1dfd117f69ae63d9baa65b99d51264a97fb76f4974b598dce846859120f05583"},"schema_version":"1.0","source":{"id":"1402.3365","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3365","created_at":"2026-06-04T14:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3365v2","created_at":"2026-06-04T14:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3365","created_at":"2026-06-04T14:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"IWG26CPX6BDK","created_at":"2026-06-04T14:09:25Z"},{"alias_kind":"pith_short_16","alias_value":"IWG26CPX6BDKNRZF","created_at":"2026-06-04T14:09:25Z"},{"alias_kind":"pith_short_8","alias_value":"IWG26CPX","created_at":"2026-06-04T14:09:25Z"}],"graph_snapshots":[{"event_id":"sha256:793d4305f5649a90a0e7e801fcc4f5a9f755204692de243b107865b6cfc06b1f","target":"graph","created_at":"2026-06-04T14:09:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1402.3365/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The $\\chi^2$-principle generalizes the Morozov discrepancy principle (MDP) to the augmented residual of the Tikhonov regularized least squares problem. Weighting of the data fidelity by a known Gaussian noise distribution on the measured data, when the regularization term is weighted by unknown inverse covariance information on the model parameters, the minimum of the Tikhonov functional is a random variable following a $\\chi^2$-distribution with $m+p-n$ degrees of freedom, model matrix $G:$ $m \\times n$ and regularizer $L:$ $p\\times n$. It is proved that the result holds also for $m<n$ when $","authors_text":"Rosemary A Renaut, Saeed Vatankhah, Vahid E Ardestani","cross_cats":["cs.NA","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-14T05:14:23Z","title":"Regularization Parameter Estimation for Underdetermined problems by the $\\chi^2$ principle with application to $2D$ focusing gravity inversion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3365","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":"sha256:95f6930db2bc84f3011d857340070ed3ada35b2c3246b47ba1ad5063902556a3","target":"record","created_at":"2026-06-04T14:09:25Z","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":"2ba4387a37eccbf45f0e7373bc5f4f03c883a4e8fab8aa9d9cc4cd3369eb7fd6","cross_cats_sorted":["cs.NA","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-14T05:14:23Z","title_canon_sha256":"1dfd117f69ae63d9baa65b99d51264a97fb76f4974b598dce846859120f05583"},"schema_version":"1.0","source":{"id":"1402.3365","kind":"arxiv","version":2}},"canonical_sha256":"458daf09f7f046a6c7253d3e32c4db415521ba1cc30664c2f2ad22ac89dca112","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"458daf09f7f046a6c7253d3e32c4db415521ba1cc30664c2f2ad22ac89dca112","first_computed_at":"2026-06-04T14:09:25.579110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T14:09:25.579110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zq/1IKSVkHkBrdhZhDPObyA6sRi/SEDimLQXloZXBomKzSKN2PA8EMmcswKTxHdt0RfG9lwQn9r/VgSn0dPbCQ==","signature_status":"signed_v1","signed_at":"2026-06-04T14:09:25.579688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.3365","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95f6930db2bc84f3011d857340070ed3ada35b2c3246b47ba1ad5063902556a3","sha256:793d4305f5649a90a0e7e801fcc4f5a9f755204692de243b107865b6cfc06b1f"],"state_sha256":"b2f06874fb25d6866c39ac5f88a580c78ec898996ad1e31b31274da3fbe9a1d2"}