{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:VVXTSAWPNKQR7XJXGN6L5LZKS2","short_pith_number":"pith:VVXTSAWP","schema_version":"1.0","canonical_sha256":"ad6f3902cf6aa11fdd37337cbeaf2a96806e7060709858b35073cb0b8b84210c","source":{"kind":"arxiv","id":"2607.10926","version":1},"attestation_state":"computed","paper":{"title":"The Spectral Structure of Latent Treatment Effects","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Bijan Mazaheri, Hamza Virk, Yihren Wu","submitted_at":"2026-07-12T21:23:13Z","abstract_excerpt":"Identifying heterogeneous treatment effects under unobserved confounding is central in observational causal inference. In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) [Mazaheri-Squires-Uhler '25] recover the mixture of treatment effects through recursively constructed scalar moments. We show that this sequence is one projection of a more fundamental object. Under the same population factorization assumptions, there is an exact compressed observable operator: after projecting onto the shared proxy signal subspace, the difference of two treatment-arm q"},"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":"2607.10926","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-12T21:23:13Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"f8cead2978d74fe358a700e1434067385bac14885a624ca5ac117c4e17bb6d8c","abstract_canon_sha256":"c4fbfd3728fb35f48cb1b66503f626f991cbf741604a4b95cdf69d56e32c504f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:21:48.077224Z","signature_b64":"iXCpfsnRJOhqV2N4UPdTyoVQESOiq0qUXlExfboMTxeA7C8tkYgcQgB0r4m4GeKsWV9Q0LavgcqLHHShAAdeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad6f3902cf6aa11fdd37337cbeaf2a96806e7060709858b35073cb0b8b84210c","last_reissued_at":"2026-07-14T01:21:48.076276Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:21:48.076276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Spectral Structure of Latent Treatment Effects","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Bijan Mazaheri, Hamza Virk, Yihren Wu","submitted_at":"2026-07-12T21:23:13Z","abstract_excerpt":"Identifying heterogeneous treatment effects under unobserved confounding is central in observational causal inference. In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) [Mazaheri-Squires-Uhler '25] recover the mixture of treatment effects through recursively constructed scalar moments. We show that this sequence is one projection of a more fundamental object. Under the same population factorization assumptions, there is an exact compressed observable operator: after projecting onto the shared proxy signal subspace, the difference of two treatment-arm q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10926","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/2607.10926/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":"2607.10926","created_at":"2026-07-14T01:21:48.076760+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.10926v1","created_at":"2026-07-14T01:21:48.076760+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10926","created_at":"2026-07-14T01:21:48.076760+00:00"},{"alias_kind":"pith_short_12","alias_value":"VVXTSAWPNKQR","created_at":"2026-07-14T01:21:48.076760+00:00"},{"alias_kind":"pith_short_16","alias_value":"VVXTSAWPNKQR7XJX","created_at":"2026-07-14T01:21:48.076760+00:00"},{"alias_kind":"pith_short_8","alias_value":"VVXTSAWP","created_at":"2026-07-14T01:21:48.076760+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/VVXTSAWPNKQR7XJXGN6L5LZKS2","json":"https://pith.science/pith/VVXTSAWPNKQR7XJXGN6L5LZKS2.json","graph_json":"https://pith.science/api/pith-number/VVXTSAWPNKQR7XJXGN6L5LZKS2/graph.json","events_json":"https://pith.science/api/pith-number/VVXTSAWPNKQR7XJXGN6L5LZKS2/events.json","paper":"https://pith.science/paper/VVXTSAWP"},"agent_actions":{"view_html":"https://pith.science/pith/VVXTSAWPNKQR7XJXGN6L5LZKS2","download_json":"https://pith.science/pith/VVXTSAWPNKQR7XJXGN6L5LZKS2.json","view_paper":"https://pith.science/paper/VVXTSAWP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.10926&json=true","fetch_graph":"https://pith.science/api/pith-number/VVXTSAWPNKQR7XJXGN6L5LZKS2/graph.json","fetch_events":"https://pith.science/api/pith-number/VVXTSAWPNKQR7XJXGN6L5LZKS2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VVXTSAWPNKQR7XJXGN6L5LZKS2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VVXTSAWPNKQR7XJXGN6L5LZKS2/action/storage_attestation","attest_author":"https://pith.science/pith/VVXTSAWPNKQR7XJXGN6L5LZKS2/action/author_attestation","sign_citation":"https://pith.science/pith/VVXTSAWPNKQR7XJXGN6L5LZKS2/action/citation_signature","submit_replication":"https://pith.science/pith/VVXTSAWPNKQR7XJXGN6L5LZKS2/action/replication_record"}},"created_at":"2026-07-14T01:21:48.076760+00:00","updated_at":"2026-07-14T01:21:48.076760+00:00"}