{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CET7NMW53TUHJSG4FIV2XGBAYB","short_pith_number":"pith:CET7NMW5","canonical_record":{"source":{"id":"2509.05177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2025-09-05T15:24:42Z","cross_cats_sorted":[],"title_canon_sha256":"9f4d78ad825b41abc81b7e34524a1f286a4f01d6bbfc45642cee607d850ce5e3","abstract_canon_sha256":"856a54ac936798b2ef8d60fc13717197b3167b4e115a85a2f6acff13f99ba2ce"},"schema_version":"1.0"},"canonical_sha256":"1127f6b2dddce874c8dc2a2bab9820c0790369d91cdd96e45fa9c5c192919957","source":{"kind":"arxiv","id":"2509.05177","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.05177","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"2509.05177v1","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05177","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"CET7NMW53TUH","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"pith_short_16","alias_value":"CET7NMW53TUHJSG4","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"pith_short_8","alias_value":"CET7NMW5","created_at":"2026-07-05T12:05:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CET7NMW53TUHJSG4FIV2XGBAYB","target":"record","payload":{"canonical_record":{"source":{"id":"2509.05177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2025-09-05T15:24:42Z","cross_cats_sorted":[],"title_canon_sha256":"9f4d78ad825b41abc81b7e34524a1f286a4f01d6bbfc45642cee607d850ce5e3","abstract_canon_sha256":"856a54ac936798b2ef8d60fc13717197b3167b4e115a85a2f6acff13f99ba2ce"},"schema_version":"1.0"},"canonical_sha256":"1127f6b2dddce874c8dc2a2bab9820c0790369d91cdd96e45fa9c5c192919957","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:05:37.274532Z","signature_b64":"jAY5tkVpOEcSAu9P9gtEFa3H9vJoiCHnDSr7KkHgbqYogHcMU3WCj6wIfr8MJKr90JN6XP/hHEQp0DWm+LEJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1127f6b2dddce874c8dc2a2bab9820c0790369d91cdd96e45fa9c5c192919957","last_reissued_at":"2026-07-05T12:05:37.274129Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:05:37.274129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.05177","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"knpNg6zT+JSHpus2/hIDxVgdEyo2Km27lqMVBaAKQY5Aw0p+/J3qaAd7fa7FSdxTnGUN7IBitqiDv/eh9zmkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T05:41:17.743661Z"},"content_sha256":"b4ef598c69588c7a737eba821580e8cdf8af925173177d29dac8762cd429a9b5","schema_version":"1.0","event_id":"sha256:b4ef598c69588c7a737eba821580e8cdf8af925173177d29dac8762cd429a9b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CET7NMW53TUHJSG4FIV2XGBAYB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Treatment Effects of Multi-Valued Treatments in Hyper-Rectangle Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"econ.EM","authors_text":"Xunkang Tian","submitted_at":"2025-09-05T15:24:42Z","abstract_excerpt":"This study investigates the identification of marginal treatment responses within multi-valued treatment models. Extending the hyper-rectangle model introduced by Lee and Salanie (2018), this paper relaxes restrictive assumptions, including the requirement of known treatment selection thresholds and the dependence of treatments on all unobserved heterogeneity. By incorporating an additional ranked treatment assumption, this study demonstrates that the marginal treatment responses can be identified under a broader set of conditions, either point or set identification. The framework further enab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05177","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/2509.05177/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MGvshafmo1D/GL/Q7KxpskLA9BdOX3bbjERc+I3o7n7Xgi2YqNNbeM049usDNrlJ4CVyb4dV+jZZHQWpbvBbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T05:41:17.744298Z"},"content_sha256":"21c6572584a3c4ac9d7de353c9f969a6d74468216fd55d78645c065d792c31f8","schema_version":"1.0","event_id":"sha256:21c6572584a3c4ac9d7de353c9f969a6d74468216fd55d78645c065d792c31f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CET7NMW53TUHJSG4FIV2XGBAYB/bundle.json","state_url":"https://pith.science/pith/CET7NMW53TUHJSG4FIV2XGBAYB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CET7NMW53TUHJSG4FIV2XGBAYB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-07T05:41:17Z","links":{"resolver":"https://pith.science/pith/CET7NMW53TUHJSG4FIV2XGBAYB","bundle":"https://pith.science/pith/CET7NMW53TUHJSG4FIV2XGBAYB/bundle.json","state":"https://pith.science/pith/CET7NMW53TUHJSG4FIV2XGBAYB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CET7NMW53TUHJSG4FIV2XGBAYB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CET7NMW53TUHJSG4FIV2XGBAYB","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":"856a54ac936798b2ef8d60fc13717197b3167b4e115a85a2f6acff13f99ba2ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2025-09-05T15:24:42Z","title_canon_sha256":"9f4d78ad825b41abc81b7e34524a1f286a4f01d6bbfc45642cee607d850ce5e3"},"schema_version":"1.0","source":{"id":"2509.05177","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.05177","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"2509.05177v1","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05177","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"CET7NMW53TUH","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"pith_short_16","alias_value":"CET7NMW53TUHJSG4","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"pith_short_8","alias_value":"CET7NMW5","created_at":"2026-07-05T12:05:37Z"}],"graph_snapshots":[{"event_id":"sha256:21c6572584a3c4ac9d7de353c9f969a6d74468216fd55d78645c065d792c31f8","target":"graph","created_at":"2026-07-05T12:05:37Z","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/2509.05177/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This study investigates the identification of marginal treatment responses within multi-valued treatment models. Extending the hyper-rectangle model introduced by Lee and Salanie (2018), this paper relaxes restrictive assumptions, including the requirement of known treatment selection thresholds and the dependence of treatments on all unobserved heterogeneity. By incorporating an additional ranked treatment assumption, this study demonstrates that the marginal treatment responses can be identified under a broader set of conditions, either point or set identification. The framework further enab","authors_text":"Xunkang Tian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2025-09-05T15:24:42Z","title":"Treatment Effects of Multi-Valued Treatments in Hyper-Rectangle Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05177","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:b4ef598c69588c7a737eba821580e8cdf8af925173177d29dac8762cd429a9b5","target":"record","created_at":"2026-07-05T12:05:37Z","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":"856a54ac936798b2ef8d60fc13717197b3167b4e115a85a2f6acff13f99ba2ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2025-09-05T15:24:42Z","title_canon_sha256":"9f4d78ad825b41abc81b7e34524a1f286a4f01d6bbfc45642cee607d850ce5e3"},"schema_version":"1.0","source":{"id":"2509.05177","kind":"arxiv","version":1}},"canonical_sha256":"1127f6b2dddce874c8dc2a2bab9820c0790369d91cdd96e45fa9c5c192919957","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1127f6b2dddce874c8dc2a2bab9820c0790369d91cdd96e45fa9c5c192919957","first_computed_at":"2026-07-05T12:05:37.274129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:05:37.274129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jAY5tkVpOEcSAu9P9gtEFa3H9vJoiCHnDSr7KkHgbqYogHcMU3WCj6wIfr8MJKr90JN6XP/hHEQp0DWm+LEJAw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:05:37.274532Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.05177","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4ef598c69588c7a737eba821580e8cdf8af925173177d29dac8762cd429a9b5","sha256:21c6572584a3c4ac9d7de353c9f969a6d74468216fd55d78645c065d792c31f8"],"state_sha256":"2b4eff2bb3d86c7040fcc3ecf4734f5e9bb283e0c8ddcf817b60b3d358353ef3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uJzZAt9DSs+0ibbB3VlJLHVY7Anlg6gUkZ2cYep8lc/kr/MltqlAO758Ialt7QBQ52mwTLRu1ilRq01hBW7cAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T05:41:17.748536Z","bundle_sha256":"7ed81e7435382fe7b3f748f20c97e74fff6b2d4d2467104a39d1e4076952df46"}}