{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:PHIR5XV2VRP5QBKOABVFZSDXSH","short_pith_number":"pith:PHIR5XV2","schema_version":"1.0","canonical_sha256":"79d11edebaac5fd8054e006a5cc87791ca90be0231d38f69688beea47cd0efa8","source":{"kind":"arxiv","id":"2207.08683","version":2},"attestation_state":"computed","paper":{"title":"Limit Theorems for Entropic Optimal Transport Maps and the Sinkhorn Divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Gabriel Rioux, Kengo Kato, Ritwik Sadhu, Ziv Goldfeld","submitted_at":"2022-07-18T15:29:26Z","abstract_excerpt":"We study limit theorems for entropic optimal transport (EOT) maps, dual potentials, and the Sinkhorn divergence. The key technical tool we use is a first and second-order Hadamard differentiability analysis of EOT potentials with respect to the marginal distributions, which may be of independent interest. Given the differentiability results, the functional delta method is used to obtain central limit theorems for empirical EOT potentials and maps. The second-order functional delta method is leveraged to establish the limit distribution of the empirical Sinkhorn divergence under the null. Build"},"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":"2207.08683","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-07-18T15:29:26Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"31614d63b5a8ccc87eb9e1464f96d5213ebfe8c9d3659430ea4e5d31ec063eb0","abstract_canon_sha256":"0d14589f0e21126d077942b608be10e81600777941e32763f42e4de8417af304"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:20:35.978604Z","signature_b64":"aEJxegNCCIaIZACet5oiDNwkEmOCg2vl2RlVy22lQ2WuVM9mNFupmmIvyMV0hV6E5D62W21RFsvAHKfAxyNBAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79d11edebaac5fd8054e006a5cc87791ca90be0231d38f69688beea47cd0efa8","last_reissued_at":"2026-07-05T06:20:35.978111Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:20:35.978111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit Theorems for Entropic Optimal Transport Maps and the Sinkhorn Divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Gabriel Rioux, Kengo Kato, Ritwik Sadhu, Ziv Goldfeld","submitted_at":"2022-07-18T15:29:26Z","abstract_excerpt":"We study limit theorems for entropic optimal transport (EOT) maps, dual potentials, and the Sinkhorn divergence. The key technical tool we use is a first and second-order Hadamard differentiability analysis of EOT potentials with respect to the marginal distributions, which may be of independent interest. Given the differentiability results, the functional delta method is used to obtain central limit theorems for empirical EOT potentials and maps. The second-order functional delta method is leveraged to establish the limit distribution of the empirical Sinkhorn divergence under the null. Build"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.08683","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/2207.08683/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":"2207.08683","created_at":"2026-07-05T06:20:35.978169+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.08683v2","created_at":"2026-07-05T06:20:35.978169+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.08683","created_at":"2026-07-05T06:20:35.978169+00:00"},{"alias_kind":"pith_short_12","alias_value":"PHIR5XV2VRP5","created_at":"2026-07-05T06:20:35.978169+00:00"},{"alias_kind":"pith_short_16","alias_value":"PHIR5XV2VRP5QBKO","created_at":"2026-07-05T06:20:35.978169+00:00"},{"alias_kind":"pith_short_8","alias_value":"PHIR5XV2","created_at":"2026-07-05T06:20:35.978169+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2412.12007","citing_title":"The entropic optimal (self-)transport problem: Limit distributions for decreasing regularization with application to score function estimation","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PHIR5XV2VRP5QBKOABVFZSDXSH","json":"https://pith.science/pith/PHIR5XV2VRP5QBKOABVFZSDXSH.json","graph_json":"https://pith.science/api/pith-number/PHIR5XV2VRP5QBKOABVFZSDXSH/graph.json","events_json":"https://pith.science/api/pith-number/PHIR5XV2VRP5QBKOABVFZSDXSH/events.json","paper":"https://pith.science/paper/PHIR5XV2"},"agent_actions":{"view_html":"https://pith.science/pith/PHIR5XV2VRP5QBKOABVFZSDXSH","download_json":"https://pith.science/pith/PHIR5XV2VRP5QBKOABVFZSDXSH.json","view_paper":"https://pith.science/paper/PHIR5XV2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.08683&json=true","fetch_graph":"https://pith.science/api/pith-number/PHIR5XV2VRP5QBKOABVFZSDXSH/graph.json","fetch_events":"https://pith.science/api/pith-number/PHIR5XV2VRP5QBKOABVFZSDXSH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PHIR5XV2VRP5QBKOABVFZSDXSH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PHIR5XV2VRP5QBKOABVFZSDXSH/action/storage_attestation","attest_author":"https://pith.science/pith/PHIR5XV2VRP5QBKOABVFZSDXSH/action/author_attestation","sign_citation":"https://pith.science/pith/PHIR5XV2VRP5QBKOABVFZSDXSH/action/citation_signature","submit_replication":"https://pith.science/pith/PHIR5XV2VRP5QBKOABVFZSDXSH/action/replication_record"}},"created_at":"2026-07-05T06:20:35.978169+00:00","updated_at":"2026-07-05T06:20:35.978169+00:00"}