{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:2U2LZQXATMWK7SZVHA6GKY6TGS","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":"3a3442767fabbbd08b714880bc4f67611088c07346c089ab28fb67de9cf7ae09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-09-29T16:41:05Z","title_canon_sha256":"2f816ceeeba019cc4905c8465f96aea8be28bd7b2bf1cd945844d0a171c21a19"},"schema_version":"1.0","source":{"id":"2109.14544","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.14544","created_at":"2026-07-05T05:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"2109.14544v4","created_at":"2026-07-05T05:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.14544","created_at":"2026-07-05T05:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"2U2LZQXATMWK","created_at":"2026-07-05T05:47:43Z"},{"alias_kind":"pith_short_16","alias_value":"2U2LZQXATMWK7SZV","created_at":"2026-07-05T05:47:43Z"},{"alias_kind":"pith_short_8","alias_value":"2U2LZQXA","created_at":"2026-07-05T05:47:43Z"}],"graph_snapshots":[{"event_id":"sha256:51fa2919d428b9a341eb8c4070bb919a618275c11cdf5864e326ed56d39de75c","target":"graph","created_at":"2026-07-05T05:47:43Z","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/2109.14544/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is potentially present. We develop a method and discuss its capability to distinguish between covariates that are confounded with the response by latent variables and those that are not. Thus, we provide a test and methodology for partial goodness of fit. The test is based on comparing a novel higher-order least squares principle with ordinary least squares. In spite of","authors_text":"Christoph Schultheiss, Ming Yuan, Peter B\\\"uhlmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-09-29T16:41:05Z","title":"Higher-order least squares: assessing partial goodness of fit of linear causal models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.14544","kind":"arxiv","version":4},"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:fa7879ef88cf100792eb5ca4aae0921698a575a201cef196a8bd7fc87bac270d","target":"record","created_at":"2026-07-05T05:47:43Z","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":"3a3442767fabbbd08b714880bc4f67611088c07346c089ab28fb67de9cf7ae09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-09-29T16:41:05Z","title_canon_sha256":"2f816ceeeba019cc4905c8465f96aea8be28bd7b2bf1cd945844d0a171c21a19"},"schema_version":"1.0","source":{"id":"2109.14544","kind":"arxiv","version":4}},"canonical_sha256":"d534bcc2e09b2cafcb35383c6563d334913729b10b6236249d81366515fda165","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d534bcc2e09b2cafcb35383c6563d334913729b10b6236249d81366515fda165","first_computed_at":"2026-07-05T05:47:43.964811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:47:43.964811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TkD4shtFayiKOkzdU+BPH5D0KtqqNMnq6d8AgswjGIZn18oJyKdKM6TgRlzuF0HMaLmRl5venCF+RJnughmMCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:47:43.965213Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.14544","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa7879ef88cf100792eb5ca4aae0921698a575a201cef196a8bd7fc87bac270d","sha256:51fa2919d428b9a341eb8c4070bb919a618275c11cdf5864e326ed56d39de75c"],"state_sha256":"d1bfd4c4efa7099a2a9ffce24f5a5ec71218e8cdfbee269e4c982655d74b2000"}