{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2W25QJQE7ZVK5J5DE6ICLUBKW5","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":"870f0728962f8585ee715177d6ac9c4815269cf64630ee1096e57ff60a3da19c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-28T16:57:38Z","title_canon_sha256":"3393095cfbe1812aaffde51dda47f2dfdf774963a1f34ef271290135e0cdac22"},"schema_version":"1.0","source":{"id":"1401.7255","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7255","created_at":"2026-05-18T01:35:40Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7255v2","created_at":"2026-05-18T01:35:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7255","created_at":"2026-05-18T01:35:40Z"},{"alias_kind":"pith_short_12","alias_value":"2W25QJQE7ZVK","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2W25QJQE7ZVK5J5D","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2W25QJQE","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:d2978e9d2e85eb64e3458d72948db1552955ad06f478c866ce74900ddfc080d1","target":"graph","created_at":"2026-05-18T01:35:40Z","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"},"paper":{"abstract_excerpt":"We introduce and study a multi-marginal optimal partial transport problem. Under a natural and sharp condition on the dominating marginals, we establish uniqueness of the optimal plan. Our strategy of proof establishes and exploits a connection with another novel problem, which we call the Monge-Kantorovich partial barycenter problem (with quadratic cost). This latter problem has a natural interpretation as a variant of the mines and factories description of optimal transport. We then turn our attention to various analytic properties of these two problems. Of particular interest, we show that ","authors_text":"Brendan Pass, Jun Kitagawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-28T16:57:38Z","title":"The multi-marginal optimal partial transport problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7255","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":"sha256:752d71a1a9e4acf5addf3a66b0ae66e96dcd1235292be639f83bbf3d650482ab","target":"record","created_at":"2026-05-18T01:35:40Z","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":"870f0728962f8585ee715177d6ac9c4815269cf64630ee1096e57ff60a3da19c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-28T16:57:38Z","title_canon_sha256":"3393095cfbe1812aaffde51dda47f2dfdf774963a1f34ef271290135e0cdac22"},"schema_version":"1.0","source":{"id":"1401.7255","kind":"arxiv","version":2}},"canonical_sha256":"d5b5d82604fe6aaea7a3279025d02ab75d8f394c5361f3e35711eec8bf33ae5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5b5d82604fe6aaea7a3279025d02ab75d8f394c5361f3e35711eec8bf33ae5f","first_computed_at":"2026-05-18T01:35:40.464912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:40.464912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b0O88lKhyjyfnHArf6KVyExE1ryZe8GlgOUMhPh3poL+H86X7J/h3m0Vm1PgKk45kO8QnJJSyp5I7qgLuzBLAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:40.465588Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7255","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:752d71a1a9e4acf5addf3a66b0ae66e96dcd1235292be639f83bbf3d650482ab","sha256:d2978e9d2e85eb64e3458d72948db1552955ad06f478c866ce74900ddfc080d1"],"state_sha256":"004af66696e76d93da4640ff0735a0c7fe703e9de25229245682e8acbd2c905f"}