{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6J6RCS6MXFGREHWJNJIZYCS3WO","short_pith_number":"pith:6J6RCS6M","canonical_record":{"source":{"id":"2406.07868","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2024-06-12T04:49:11Z","cross_cats_sorted":[],"title_canon_sha256":"44616f2a4f95aea843c9ee2f1f8ce7bfedfa9d2f194b4dd0910fa88dbdf00b5b","abstract_canon_sha256":"014e525ea3339c455873afd8db493d3620ba8d21cd04d8571170ac923e7bfddc"},"schema_version":"1.0"},"canonical_sha256":"f27d114bccb94d121ec96a519c0a5bb3ae574596ccb172da3d6b80d3da6bdabf","source":{"kind":"arxiv","id":"2406.07868","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.07868","created_at":"2026-07-05T09:06:42Z"},{"alias_kind":"arxiv_version","alias_value":"2406.07868v2","created_at":"2026-07-05T09:06:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.07868","created_at":"2026-07-05T09:06:42Z"},{"alias_kind":"pith_short_12","alias_value":"6J6RCS6MXFGR","created_at":"2026-07-05T09:06:42Z"},{"alias_kind":"pith_short_16","alias_value":"6J6RCS6MXFGREHWJ","created_at":"2026-07-05T09:06:42Z"},{"alias_kind":"pith_short_8","alias_value":"6J6RCS6M","created_at":"2026-07-05T09:06:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6J6RCS6MXFGREHWJNJIZYCS3WO","target":"record","payload":{"canonical_record":{"source":{"id":"2406.07868","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2024-06-12T04:49:11Z","cross_cats_sorted":[],"title_canon_sha256":"44616f2a4f95aea843c9ee2f1f8ce7bfedfa9d2f194b4dd0910fa88dbdf00b5b","abstract_canon_sha256":"014e525ea3339c455873afd8db493d3620ba8d21cd04d8571170ac923e7bfddc"},"schema_version":"1.0"},"canonical_sha256":"f27d114bccb94d121ec96a519c0a5bb3ae574596ccb172da3d6b80d3da6bdabf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:06:42.155536Z","signature_b64":"5ngTSlVlGSgwgIFYPd2u5Sqip3FW7SRa+jXhw+FoJ2EYmibBhWzORcNadSjStMFSiJ23DbZ/x3KBhW1UnNrlCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f27d114bccb94d121ec96a519c0a5bb3ae574596ccb172da3d6b80d3da6bdabf","last_reissued_at":"2026-07-05T09:06:42.154996Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:06:42.154996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.07868","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:06:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TH+owMcP/Iwo0CpzdRRoPNVyPrWRxp3UIL5WCOz+qUauLYoqKeWezcM2T3BWBMUkMwK61XfjqpA2Pcw7klgGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:25:01.163544Z"},"content_sha256":"fad23482b3eb844a21e54c0c688b70e83e9b1e56cc80daa7f5b1bfd71ec0ea2f","schema_version":"1.0","event_id":"sha256:fad23482b3eb844a21e54c0c688b70e83e9b1e56cc80daa7f5b1bfd71ec0ea2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6J6RCS6MXFGREHWJNJIZYCS3WO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bridging multiple worlds: multi-marginal optimal transport for causal partial-identification problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Jian Qian, Shu Ge, Zijun Gao","submitted_at":"2024-06-12T04:49:11Z","abstract_excerpt":"Under the prevalent potential outcome model in causal inference, each unit is associated with multiple potential outcomes but at most one of which is observed, leading to many causal quantities being only partially identified. The inherent missing data issue echoes the multi-marginal optimal transport (MOT) problem, where marginal distributions are known, but how the marginals couple to form the joint distribution is unavailable. In this paper, we cast the causal partial identification problem in the framework of MOT with $K$ margins and $d$-dimensional outcomes and obtain the exact partial id"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.07868","kind":"arxiv","version":2},"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/2406.07868/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":"2026-07-05T09:06:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"imhU/YS9zTtHJo1SM226g6sXY4RLAgsf0hQgXb8VGVpaGe3klalZUIV9H5zMAIbeegK21gSqKabsPBbdYykrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:25:01.163925Z"},"content_sha256":"ddd013c5a6c87272b5246f739e68d4faf3fa6b38a19dcb3855560d4a0451829b","schema_version":"1.0","event_id":"sha256:ddd013c5a6c87272b5246f739e68d4faf3fa6b38a19dcb3855560d4a0451829b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6J6RCS6MXFGREHWJNJIZYCS3WO/bundle.json","state_url":"https://pith.science/pith/6J6RCS6MXFGREHWJNJIZYCS3WO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6J6RCS6MXFGREHWJNJIZYCS3WO/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":"2026-07-06T20:25:01Z","links":{"resolver":"https://pith.science/pith/6J6RCS6MXFGREHWJNJIZYCS3WO","bundle":"https://pith.science/pith/6J6RCS6MXFGREHWJNJIZYCS3WO/bundle.json","state":"https://pith.science/pith/6J6RCS6MXFGREHWJNJIZYCS3WO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6J6RCS6MXFGREHWJNJIZYCS3WO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6J6RCS6MXFGREHWJNJIZYCS3WO","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":"014e525ea3339c455873afd8db493d3620ba8d21cd04d8571170ac923e7bfddc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2024-06-12T04:49:11Z","title_canon_sha256":"44616f2a4f95aea843c9ee2f1f8ce7bfedfa9d2f194b4dd0910fa88dbdf00b5b"},"schema_version":"1.0","source":{"id":"2406.07868","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.07868","created_at":"2026-07-05T09:06:42Z"},{"alias_kind":"arxiv_version","alias_value":"2406.07868v2","created_at":"2026-07-05T09:06:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.07868","created_at":"2026-07-05T09:06:42Z"},{"alias_kind":"pith_short_12","alias_value":"6J6RCS6MXFGR","created_at":"2026-07-05T09:06:42Z"},{"alias_kind":"pith_short_16","alias_value":"6J6RCS6MXFGREHWJ","created_at":"2026-07-05T09:06:42Z"},{"alias_kind":"pith_short_8","alias_value":"6J6RCS6M","created_at":"2026-07-05T09:06:42Z"}],"graph_snapshots":[{"event_id":"sha256:ddd013c5a6c87272b5246f739e68d4faf3fa6b38a19dcb3855560d4a0451829b","target":"graph","created_at":"2026-07-05T09:06:42Z","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/2406.07868/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Under the prevalent potential outcome model in causal inference, each unit is associated with multiple potential outcomes but at most one of which is observed, leading to many causal quantities being only partially identified. The inherent missing data issue echoes the multi-marginal optimal transport (MOT) problem, where marginal distributions are known, but how the marginals couple to form the joint distribution is unavailable. In this paper, we cast the causal partial identification problem in the framework of MOT with $K$ margins and $d$-dimensional outcomes and obtain the exact partial id","authors_text":"Jian Qian, Shu Ge, Zijun Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2024-06-12T04:49:11Z","title":"Bridging multiple worlds: multi-marginal optimal transport for causal partial-identification problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.07868","kind":"arxiv","version":2},"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:fad23482b3eb844a21e54c0c688b70e83e9b1e56cc80daa7f5b1bfd71ec0ea2f","target":"record","created_at":"2026-07-05T09:06:42Z","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":"014e525ea3339c455873afd8db493d3620ba8d21cd04d8571170ac923e7bfddc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2024-06-12T04:49:11Z","title_canon_sha256":"44616f2a4f95aea843c9ee2f1f8ce7bfedfa9d2f194b4dd0910fa88dbdf00b5b"},"schema_version":"1.0","source":{"id":"2406.07868","kind":"arxiv","version":2}},"canonical_sha256":"f27d114bccb94d121ec96a519c0a5bb3ae574596ccb172da3d6b80d3da6bdabf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f27d114bccb94d121ec96a519c0a5bb3ae574596ccb172da3d6b80d3da6bdabf","first_computed_at":"2026-07-05T09:06:42.154996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:06:42.154996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5ngTSlVlGSgwgIFYPd2u5Sqip3FW7SRa+jXhw+FoJ2EYmibBhWzORcNadSjStMFSiJ23DbZ/x3KBhW1UnNrlCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:06:42.155536Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.07868","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fad23482b3eb844a21e54c0c688b70e83e9b1e56cc80daa7f5b1bfd71ec0ea2f","sha256:ddd013c5a6c87272b5246f739e68d4faf3fa6b38a19dcb3855560d4a0451829b"],"state_sha256":"f4e5d9261fd7a7e59622438b4ba4b725582178f6079f85679e06b2f8b867fa8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6f/N12UyR9Jn8KUL0JJWVTIbqg3Jo8IksfkPYDQI/dfuJ8tRKx4Tgpz3gLiRd1riVRXhkB89dYiU2ZISZVJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T20:25:01.166309Z","bundle_sha256":"379cf2ec6e85f4f11d17105a03688a825767065309de4f53b4b1ddbc5f342447"}}