{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:G7XLTEBZRYWZQDZWHBJULC5Z4L","short_pith_number":"pith:G7XLTEBZ","schema_version":"1.0","canonical_sha256":"37eeb990398e2d980f363853458bb9e2cd134029377b6e7f3d8c81ca29d74f8c","source":{"kind":"arxiv","id":"1411.3602","version":1},"attestation_state":"computed","paper":{"title":"Numerical methods for matching for teams and Wasserstein barycenters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Adam Oberman, Edouard Oudet, Guillaume Carlier","submitted_at":"2014-11-13T16:22:51Z","abstract_excerpt":"Equilibrium multi-population matching (matching for teams) is a problem from mathematical economics which is related to multi-marginal optimal transport. A special but important case is the Wasserstein barycenter problem, which has applications in image processing and statistics. Two algorithms are presented: a linear programming algorithm and an efficient nonsmooth optimization algorithm, which applies in the case of the Wasserstein barycenters. The measures are approximated by discrete measures: convergence of the approximation is proved. Numerical results are presented which illustrate the "},"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":"1411.3602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-13T16:22:51Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"88d74c2ede083f4ed7080164994ce09c3300dd6f55ee6a9837f4674dcab1246c","abstract_canon_sha256":"8441fe42c53bf88335a24b9de54163c72c1db6741d5fd5bf1b54efd6a4a8051c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:43.364010Z","signature_b64":"jOnhstulPKqklae21nrQDW1N9UN57zr1EOLp0bqqRNj6yyxXyGLM6Zj2qIlQeoJJxLADeGCQ7htZFcN45wn5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37eeb990398e2d980f363853458bb9e2cd134029377b6e7f3d8c81ca29d74f8c","last_reissued_at":"2026-05-18T02:37:43.363614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:43.363614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical methods for matching for teams and Wasserstein barycenters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Adam Oberman, Edouard Oudet, Guillaume Carlier","submitted_at":"2014-11-13T16:22:51Z","abstract_excerpt":"Equilibrium multi-population matching (matching for teams) is a problem from mathematical economics which is related to multi-marginal optimal transport. A special but important case is the Wasserstein barycenter problem, which has applications in image processing and statistics. Two algorithms are presented: a linear programming algorithm and an efficient nonsmooth optimization algorithm, which applies in the case of the Wasserstein barycenters. The measures are approximated by discrete measures: convergence of the approximation is proved. Numerical results are presented which illustrate the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3602","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":""},"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":"1411.3602","created_at":"2026-05-18T02:37:43.363672+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.3602v1","created_at":"2026-05-18T02:37:43.363672+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3602","created_at":"2026-05-18T02:37:43.363672+00:00"},{"alias_kind":"pith_short_12","alias_value":"G7XLTEBZRYWZ","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"G7XLTEBZRYWZQDZW","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"G7XLTEBZ","created_at":"2026-05-18T12:28:28.263976+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/G7XLTEBZRYWZQDZWHBJULC5Z4L","json":"https://pith.science/pith/G7XLTEBZRYWZQDZWHBJULC5Z4L.json","graph_json":"https://pith.science/api/pith-number/G7XLTEBZRYWZQDZWHBJULC5Z4L/graph.json","events_json":"https://pith.science/api/pith-number/G7XLTEBZRYWZQDZWHBJULC5Z4L/events.json","paper":"https://pith.science/paper/G7XLTEBZ"},"agent_actions":{"view_html":"https://pith.science/pith/G7XLTEBZRYWZQDZWHBJULC5Z4L","download_json":"https://pith.science/pith/G7XLTEBZRYWZQDZWHBJULC5Z4L.json","view_paper":"https://pith.science/paper/G7XLTEBZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.3602&json=true","fetch_graph":"https://pith.science/api/pith-number/G7XLTEBZRYWZQDZWHBJULC5Z4L/graph.json","fetch_events":"https://pith.science/api/pith-number/G7XLTEBZRYWZQDZWHBJULC5Z4L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G7XLTEBZRYWZQDZWHBJULC5Z4L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G7XLTEBZRYWZQDZWHBJULC5Z4L/action/storage_attestation","attest_author":"https://pith.science/pith/G7XLTEBZRYWZQDZWHBJULC5Z4L/action/author_attestation","sign_citation":"https://pith.science/pith/G7XLTEBZRYWZQDZWHBJULC5Z4L/action/citation_signature","submit_replication":"https://pith.science/pith/G7XLTEBZRYWZQDZWHBJULC5Z4L/action/replication_record"}},"created_at":"2026-05-18T02:37:43.363672+00:00","updated_at":"2026-05-18T02:37:43.363672+00:00"}