{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SC5UBVGGJUMC4BLZ7BDT7YILV2","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":"2dace716f5147513e0de52c9b20de7c4561d69690fcbfda76ad65fcf69365d05","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-08T02:04:36Z","title_canon_sha256":"83100162605134a00d5ea24e837b29b4c32cfd779e7eb616733035d3c9b9e147"},"schema_version":"1.0","source":{"id":"2607.06912","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06912","created_at":"2026-07-09T00:19:39Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06912v1","created_at":"2026-07-09T00:19:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06912","created_at":"2026-07-09T00:19:39Z"},{"alias_kind":"pith_short_12","alias_value":"SC5UBVGGJUMC","created_at":"2026-07-09T00:19:39Z"},{"alias_kind":"pith_short_16","alias_value":"SC5UBVGGJUMC4BLZ","created_at":"2026-07-09T00:19:39Z"},{"alias_kind":"pith_short_8","alias_value":"SC5UBVGG","created_at":"2026-07-09T00:19:39Z"}],"graph_snapshots":[{"event_id":"sha256:955943a4560382c941b9179a3eff1b503f31dbee93cb6837147aaa00370c4996","target":"graph","created_at":"2026-07-09T00:19:39Z","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/2607.06912/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a framework for causal inference in behavioral health case studies -- and observational N=1 settings more generally -- under unmeasured confounding. The framework rests on a class of causal estimands, termed $\\Omega$ estimands, defined as contrasts of functions of an outcome variable's support rather than its distribution. Because such estimands do not depend on how probability is distributed over supports, they are insensitive to the confounding that limits other methods. We prove that, in a structural causal model, the observational and interventional supports of an outcome coinci","authors_text":"Shane Sparkes","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-08T02:04:36Z","title":"Causal Inference for Case Studies in Behavioral Health"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06912","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:add706893c335115bea3029d7040c8566ebaca01abca71b58929657790225eca","target":"record","created_at":"2026-07-09T00:19:39Z","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":"2dace716f5147513e0de52c9b20de7c4561d69690fcbfda76ad65fcf69365d05","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-08T02:04:36Z","title_canon_sha256":"83100162605134a00d5ea24e837b29b4c32cfd779e7eb616733035d3c9b9e147"},"schema_version":"1.0","source":{"id":"2607.06912","kind":"arxiv","version":1}},"canonical_sha256":"90bb40d4c64d182e0579f8473fe10bae8b2a4b03dbb27cf774777c89d1344fb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90bb40d4c64d182e0579f8473fe10bae8b2a4b03dbb27cf774777c89d1344fb2","first_computed_at":"2026-07-09T00:19:39.331640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T00:19:39.331640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rw20ZhocNI1hZg5/lwlVHUb9/obev0adgbGOn8DA6nX7YQjfXA6NpGhGM4Cg88RSTRZfN7gNXtwaMRDYZEXkBg==","signature_status":"signed_v1","signed_at":"2026-07-09T00:19:39.332073Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06912","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:add706893c335115bea3029d7040c8566ebaca01abca71b58929657790225eca","sha256:955943a4560382c941b9179a3eff1b503f31dbee93cb6837147aaa00370c4996"],"state_sha256":"a3a426f544b0ecb87891a4850124171cfa52dfc3b867ba0382e2ad69582d19d4"}