{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RW2NI6GCGPD5MAQJTI6LCTXLBW","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":"b56fdd19a94cd1b6098d86a531bf4a8454b3087e56743cc2b3e555b367dd09dc","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-03T16:01:16Z","title_canon_sha256":"a5d0225c3a21a53b3f665921fab20100a671fba2c6a4c2b35a1fd28cfc64bd43"},"schema_version":"1.0","source":{"id":"1907.02006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02006","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02006v1","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02006","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"pith_short_12","alias_value":"RW2NI6GCGPD5","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RW2NI6GCGPD5MAQJ","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RW2NI6GC","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:c8cf644b0151b4ca7f6ed024a7bb6c2441b2f0ae2659993446a28ff32ac05e82","target":"graph","created_at":"2026-05-17T23:41:34Z","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":"Consider the empirical measure, $\\hat{\\mathbb{P}}_N$, associated to $N$ i.i.d. samples of a given probability distribution $\\mathbb{P}$ on the unit interval. For fixed $\\mathbb{P}$ the Wasserstein distance between $\\hat{\\mathbb{P}}_N$ and $\\mathbb{P}$ is a random variable on the sample space $[0,1]^N$. Our main result is that its normalised quantiles are asymptotically maximised when $\\mathbb{P}$ is a convex combination between the uniform distribution supported on the two points $\\{0,1\\}$ and the uniform distribution on the unit interval $[0,1]$. This allows us to obtain explicit asymptotic c","authors_text":"Johannes Wiesel, Martin N. A. Tegn\\'er, Samuel N. Cohen","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-03T16:01:16Z","title":"Bounding quantiles of Wasserstein distance between true and empirical measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02006","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":"sha256:2a8497cd3a1ae8c0bf333f36b5436cc27717ea7d59a26b90d80254ebba459fe6","target":"record","created_at":"2026-05-17T23:41:34Z","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":"b56fdd19a94cd1b6098d86a531bf4a8454b3087e56743cc2b3e555b367dd09dc","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-03T16:01:16Z","title_canon_sha256":"a5d0225c3a21a53b3f665921fab20100a671fba2c6a4c2b35a1fd28cfc64bd43"},"schema_version":"1.0","source":{"id":"1907.02006","kind":"arxiv","version":1}},"canonical_sha256":"8db4d478c233c7d602099a3cb14eeb0d9bd1549f3edfe61fe822fb74d4227236","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8db4d478c233c7d602099a3cb14eeb0d9bd1549f3edfe61fe822fb74d4227236","first_computed_at":"2026-05-17T23:41:34.256168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:34.256168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lB8O/8uVb0CplYefkp+vJi6EqUEmAb7QkWDDKgirTUW+Er6pyodV6Ads8+0Gd6lM4yCaDBANm6lvSskWcoBqDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:34.256809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.02006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a8497cd3a1ae8c0bf333f36b5436cc27717ea7d59a26b90d80254ebba459fe6","sha256:c8cf644b0151b4ca7f6ed024a7bb6c2441b2f0ae2659993446a28ff32ac05e82"],"state_sha256":"61f294fea51ee32a19aaae27453b59e195a272029c441dcc464defaec07c7ce4"}