{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:IYSMWOAX5TTGBA5TNUGUTSWYEH","short_pith_number":"pith:IYSMWOAX","schema_version":"1.0","canonical_sha256":"4624cb3817ece66083b36d0d49cad821ed453e78550111e70c721f6c98668173","source":{"kind":"arxiv","id":"1408.0712","version":1},"attestation_state":"computed","paper":{"title":"Application of the $\\chi^2$ principle and unbiased predictive risk estimator for determining the regularization parameter in 3D focusing gravity inversion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Rosemary A. Renaut, Saeed Vatankhah, Vahid E. Ardestani","submitted_at":"2014-08-04T15:40:47Z","abstract_excerpt":"The $\\chi^2$ principle and the unbiased predictive risk estimator are used to determine optimal regularization parameters in the context of 3D focusing gravity inversion with the minimum support stabilizer. At each iteration of the focusing inversion the minimum support stabilizer is determined and then the fidelity term is updated using the standard form transformation. Solution of the resulting Tikhonov functional is found efficiently using the singular value decomposition of the transformed model matrix, which also provides for efficient determination of the updated regularization parameter"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.0712","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-04T15:40:47Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"07710262fe54028b8c8ddbedd70634dac079d377f7c8f4de6af1e9e7cf1f3975","abstract_canon_sha256":"f2859ffd8ea238472bf8998ca35dcfc438aae14df205dc1260f8fc0f46a25e50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T16:08:41.629371Z","signature_b64":"pceFJDVcC1Sy/JuZo4Lv+f3+NulVtIp8IOlOMTwF1BnyeZQZXK/Q5ExROAasiMQMXZ376fgTr2+oKJH0vQlBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4624cb3817ece66083b36d0d49cad821ed453e78550111e70c721f6c98668173","last_reissued_at":"2026-06-04T16:08:41.628793Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T16:08:41.628793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Application of the $\\chi^2$ principle and unbiased predictive risk estimator for determining the regularization parameter in 3D focusing gravity inversion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Rosemary A. Renaut, Saeed Vatankhah, Vahid E. Ardestani","submitted_at":"2014-08-04T15:40:47Z","abstract_excerpt":"The $\\chi^2$ principle and the unbiased predictive risk estimator are used to determine optimal regularization parameters in the context of 3D focusing gravity inversion with the minimum support stabilizer. At each iteration of the focusing inversion the minimum support stabilizer is determined and then the fidelity term is updated using the standard form transformation. Solution of the resulting Tikhonov functional is found efficiently using the singular value decomposition of the transformed model matrix, which also provides for efficient determination of the updated regularization parameter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0712","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1408.0712/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.0712","created_at":"2026-06-04T16:08:41.628853+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0712v1","created_at":"2026-06-04T16:08:41.628853+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0712","created_at":"2026-06-04T16:08:41.628853+00:00"},{"alias_kind":"pith_short_12","alias_value":"IYSMWOAX5TTG","created_at":"2026-06-04T16:08:41.628853+00:00"},{"alias_kind":"pith_short_16","alias_value":"IYSMWOAX5TTGBA5T","created_at":"2026-06-04T16:08:41.628853+00:00"},{"alias_kind":"pith_short_8","alias_value":"IYSMWOAX","created_at":"2026-06-04T16:08:41.628853+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IYSMWOAX5TTGBA5TNUGUTSWYEH","json":"https://pith.science/pith/IYSMWOAX5TTGBA5TNUGUTSWYEH.json","graph_json":"https://pith.science/api/pith-number/IYSMWOAX5TTGBA5TNUGUTSWYEH/graph.json","events_json":"https://pith.science/api/pith-number/IYSMWOAX5TTGBA5TNUGUTSWYEH/events.json","paper":"https://pith.science/paper/IYSMWOAX"},"agent_actions":{"view_html":"https://pith.science/pith/IYSMWOAX5TTGBA5TNUGUTSWYEH","download_json":"https://pith.science/pith/IYSMWOAX5TTGBA5TNUGUTSWYEH.json","view_paper":"https://pith.science/paper/IYSMWOAX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0712&json=true","fetch_graph":"https://pith.science/api/pith-number/IYSMWOAX5TTGBA5TNUGUTSWYEH/graph.json","fetch_events":"https://pith.science/api/pith-number/IYSMWOAX5TTGBA5TNUGUTSWYEH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IYSMWOAX5TTGBA5TNUGUTSWYEH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IYSMWOAX5TTGBA5TNUGUTSWYEH/action/storage_attestation","attest_author":"https://pith.science/pith/IYSMWOAX5TTGBA5TNUGUTSWYEH/action/author_attestation","sign_citation":"https://pith.science/pith/IYSMWOAX5TTGBA5TNUGUTSWYEH/action/citation_signature","submit_replication":"https://pith.science/pith/IYSMWOAX5TTGBA5TNUGUTSWYEH/action/replication_record"}},"created_at":"2026-06-04T16:08:41.628853+00:00","updated_at":"2026-06-04T16:08:41.628853+00:00"}