{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2ZVURYA6WKLWAWZFLNK2TUTBUU","short_pith_number":"pith:2ZVURYA6","schema_version":"1.0","canonical_sha256":"d66b48e01eb297605b255b55a9d261a519e3747e06cead0568ea2c1dbb405380","source":{"kind":"arxiv","id":"2606.21840","version":1},"attestation_state":"computed","paper":{"title":"A Test for Treatment Heterogeneity under a Distributional Difference-in-Difference Framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.EM","math.ST","stat.AP","stat.TH"],"primary_cat":"stat.ME","authors_text":"Bing Li, Lingzhou Xue, Satarupa Bhattacharjee","submitted_at":"2026-06-20T02:15:54Z","abstract_excerpt":"We develop a novel distributional Difference-in-Differences (DiD) framework to capture treatment heterogeneity across outcome distributions. By leveraging optimal transport, we use the control group to estimate the untreated distributional drift from the pre- to post-treatment period and apply it to the treated group's pre-treatment baseline, constructing a counterfactual distribution under the assumption of no treatment effect. We frame the null hypothesis as a distributional equality between the transported counterfactual distribution and the observed treated post-treatment distribution, and"},"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":"2606.21840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-06-20T02:15:54Z","cross_cats_sorted":["econ.EM","math.ST","stat.AP","stat.TH"],"title_canon_sha256":"15d06e2c8b5b22a299e47cd0265d3528196636c000a68e31bbd143518fe5a240","abstract_canon_sha256":"6a7371ca76df5ae084061be8cc282bcea3690db789b1ff3349350ec1e5e53f43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:00.529828Z","signature_b64":"H6aVGFTBCnnXhGzHtwsOxxtMXvkZcgI2kFkw3Eu7lZ0lHNuukSNffRNRgOVaxNJgA3YblZu54Q2t+9ULNlW+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d66b48e01eb297605b255b55a9d261a519e3747e06cead0568ea2c1dbb405380","last_reissued_at":"2026-06-23T02:13:00.529428Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:00.529428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Test for Treatment Heterogeneity under a Distributional Difference-in-Difference Framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.EM","math.ST","stat.AP","stat.TH"],"primary_cat":"stat.ME","authors_text":"Bing Li, Lingzhou Xue, Satarupa Bhattacharjee","submitted_at":"2026-06-20T02:15:54Z","abstract_excerpt":"We develop a novel distributional Difference-in-Differences (DiD) framework to capture treatment heterogeneity across outcome distributions. By leveraging optimal transport, we use the control group to estimate the untreated distributional drift from the pre- to post-treatment period and apply it to the treated group's pre-treatment baseline, constructing a counterfactual distribution under the assumption of no treatment effect. We frame the null hypothesis as a distributional equality between the transported counterfactual distribution and the observed treated post-treatment distribution, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21840","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/2606.21840/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":"2606.21840","created_at":"2026-06-23T02:13:00.529486+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.21840v1","created_at":"2026-06-23T02:13:00.529486+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.21840","created_at":"2026-06-23T02:13:00.529486+00:00"},{"alias_kind":"pith_short_12","alias_value":"2ZVURYA6WKLW","created_at":"2026-06-23T02:13:00.529486+00:00"},{"alias_kind":"pith_short_16","alias_value":"2ZVURYA6WKLWAWZF","created_at":"2026-06-23T02:13:00.529486+00:00"},{"alias_kind":"pith_short_8","alias_value":"2ZVURYA6","created_at":"2026-06-23T02:13:00.529486+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/2ZVURYA6WKLWAWZFLNK2TUTBUU","json":"https://pith.science/pith/2ZVURYA6WKLWAWZFLNK2TUTBUU.json","graph_json":"https://pith.science/api/pith-number/2ZVURYA6WKLWAWZFLNK2TUTBUU/graph.json","events_json":"https://pith.science/api/pith-number/2ZVURYA6WKLWAWZFLNK2TUTBUU/events.json","paper":"https://pith.science/paper/2ZVURYA6"},"agent_actions":{"view_html":"https://pith.science/pith/2ZVURYA6WKLWAWZFLNK2TUTBUU","download_json":"https://pith.science/pith/2ZVURYA6WKLWAWZFLNK2TUTBUU.json","view_paper":"https://pith.science/paper/2ZVURYA6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.21840&json=true","fetch_graph":"https://pith.science/api/pith-number/2ZVURYA6WKLWAWZFLNK2TUTBUU/graph.json","fetch_events":"https://pith.science/api/pith-number/2ZVURYA6WKLWAWZFLNK2TUTBUU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2ZVURYA6WKLWAWZFLNK2TUTBUU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2ZVURYA6WKLWAWZFLNK2TUTBUU/action/storage_attestation","attest_author":"https://pith.science/pith/2ZVURYA6WKLWAWZFLNK2TUTBUU/action/author_attestation","sign_citation":"https://pith.science/pith/2ZVURYA6WKLWAWZFLNK2TUTBUU/action/citation_signature","submit_replication":"https://pith.science/pith/2ZVURYA6WKLWAWZFLNK2TUTBUU/action/replication_record"}},"created_at":"2026-06-23T02:13:00.529486+00:00","updated_at":"2026-06-23T02:13:00.529486+00:00"}