{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:P6YLRRWNYD5U7A3PQJJW4HQR36","short_pith_number":"pith:P6YLRRWN","canonical_record":{"source":{"id":"1703.03658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-03-10T12:42:32Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"493f15911c59d1192a8c9678e71c8001beff703416b3b10844716614157c289b","abstract_canon_sha256":"8174c3f68bd5a7ff5b4d436a096868e08c58ab2376d9a8bc7f7bab9d643dd08d"},"schema_version":"1.0"},"canonical_sha256":"7fb0b8c6cdc0fb4f836f82536e1e11dfa0cf3f07ed74282dd264c147bb1f4d23","source":{"kind":"arxiv","id":"1703.03658","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03658","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03658v1","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03658","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"P6YLRRWNYD5U","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P6YLRRWNYD5U7A3P","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P6YLRRWN","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:P6YLRRWNYD5U7A3PQJJW4HQR36","target":"record","payload":{"canonical_record":{"source":{"id":"1703.03658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-03-10T12:42:32Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"493f15911c59d1192a8c9678e71c8001beff703416b3b10844716614157c289b","abstract_canon_sha256":"8174c3f68bd5a7ff5b4d436a096868e08c58ab2376d9a8bc7f7bab9d643dd08d"},"schema_version":"1.0"},"canonical_sha256":"7fb0b8c6cdc0fb4f836f82536e1e11dfa0cf3f07ed74282dd264c147bb1f4d23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:58.418697Z","signature_b64":"uKOIKvekrJv2VoqhFgjdQ4zQa3Ib0egJ/B21azJPF1FtfqTQ9DgD84qf7HkalUyjq/Woja4AEV6QXsb8bKrqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fb0b8c6cdc0fb4f836f82536e1e11dfa0cf3f07ed74282dd264c147bb1f4d23","last_reissued_at":"2026-05-18T00:48:58.417995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:58.417995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.03658","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xLg0SvshJ3gJkmMfPQVdqDSL042ePCsX/vXZStB7qCePYvIpuaBHeNN/29NzzUTdayMjDZSh8LSdFaR9y60bDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:43:19.478134Z"},"content_sha256":"bd684bf67cc4c047845f2de4aa10820846e74cf10641f822c54a570c86e8d08d","schema_version":"1.0","event_id":"sha256:bd684bf67cc4c047845f2de4aa10820846e74cf10641f822c54a570c86e8d08d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:P6YLRRWNYD5U7A3PQJJW4HQR36","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of Non-asymptotic Confidence Sets in 2-Wasserstein Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alexandra Suvorikova, Johannes Ebert, Vladimir Spokoiny","submitted_at":"2017-03-10T12:42:32Z","abstract_excerpt":"In this paper, we consider a probabilistic setting where the probability measures are considered to be random objects. We propose a procedure of construction non-asymptotic confidence sets for empirical barycenters in 2-Wasserstein space and develop the idea further to construction of a non-parametric two-sample test that is then applied to the detection of structural breaks in data with complex geometry. Both procedures mainly rely on the idea of multiplier bootstrap (Spokoiny and Zhilova (2015), Chernozhukov et al. (2014)). The main focus lies on probability measures that have commuting cova"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03658","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QZNciNL/T1d+IGy7v5Icqh3+XrPwNVSkJVFhnbJSsNP1meXFk+nRvq+msfcd8VNKWydLEJk4KW60mDG2M1C6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:43:19.479322Z"},"content_sha256":"6b93b826f87affecdd8f5d4fd8784765ddca8a3bf6f77588363e0d6ceb001a1e","schema_version":"1.0","event_id":"sha256:6b93b826f87affecdd8f5d4fd8784765ddca8a3bf6f77588363e0d6ceb001a1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6YLRRWNYD5U7A3PQJJW4HQR36/bundle.json","state_url":"https://pith.science/pith/P6YLRRWNYD5U7A3PQJJW4HQR36/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6YLRRWNYD5U7A3PQJJW4HQR36/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":"2026-06-23T21:43:19Z","links":{"resolver":"https://pith.science/pith/P6YLRRWNYD5U7A3PQJJW4HQR36","bundle":"https://pith.science/pith/P6YLRRWNYD5U7A3PQJJW4HQR36/bundle.json","state":"https://pith.science/pith/P6YLRRWNYD5U7A3PQJJW4HQR36/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6YLRRWNYD5U7A3PQJJW4HQR36/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P6YLRRWNYD5U7A3PQJJW4HQR36","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":"8174c3f68bd5a7ff5b4d436a096868e08c58ab2376d9a8bc7f7bab9d643dd08d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-03-10T12:42:32Z","title_canon_sha256":"493f15911c59d1192a8c9678e71c8001beff703416b3b10844716614157c289b"},"schema_version":"1.0","source":{"id":"1703.03658","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03658","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03658v1","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03658","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"P6YLRRWNYD5U","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P6YLRRWNYD5U7A3P","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P6YLRRWN","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:6b93b826f87affecdd8f5d4fd8784765ddca8a3bf6f77588363e0d6ceb001a1e","target":"graph","created_at":"2026-05-18T00:48:58Z","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":"In this paper, we consider a probabilistic setting where the probability measures are considered to be random objects. We propose a procedure of construction non-asymptotic confidence sets for empirical barycenters in 2-Wasserstein space and develop the idea further to construction of a non-parametric two-sample test that is then applied to the detection of structural breaks in data with complex geometry. Both procedures mainly rely on the idea of multiplier bootstrap (Spokoiny and Zhilova (2015), Chernozhukov et al. (2014)). The main focus lies on probability measures that have commuting cova","authors_text":"Alexandra Suvorikova, Johannes Ebert, Vladimir Spokoiny","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-03-10T12:42:32Z","title":"Construction of Non-asymptotic Confidence Sets in 2-Wasserstein Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03658","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:bd684bf67cc4c047845f2de4aa10820846e74cf10641f822c54a570c86e8d08d","target":"record","created_at":"2026-05-18T00:48:58Z","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":"8174c3f68bd5a7ff5b4d436a096868e08c58ab2376d9a8bc7f7bab9d643dd08d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-03-10T12:42:32Z","title_canon_sha256":"493f15911c59d1192a8c9678e71c8001beff703416b3b10844716614157c289b"},"schema_version":"1.0","source":{"id":"1703.03658","kind":"arxiv","version":1}},"canonical_sha256":"7fb0b8c6cdc0fb4f836f82536e1e11dfa0cf3f07ed74282dd264c147bb1f4d23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fb0b8c6cdc0fb4f836f82536e1e11dfa0cf3f07ed74282dd264c147bb1f4d23","first_computed_at":"2026-05-18T00:48:58.417995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:58.417995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uKOIKvekrJv2VoqhFgjdQ4zQa3Ib0egJ/B21azJPF1FtfqTQ9DgD84qf7HkalUyjq/Woja4AEV6QXsb8bKrqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:58.418697Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.03658","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd684bf67cc4c047845f2de4aa10820846e74cf10641f822c54a570c86e8d08d","sha256:6b93b826f87affecdd8f5d4fd8784765ddca8a3bf6f77588363e0d6ceb001a1e"],"state_sha256":"9acda751d5d2103d480a6dac72c18c7cab4c0508304fb4f389c6f1228f7d62f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WXmCJWoypGDAX7dT/v/uAggw7dwncuFGbGkYKgJSb315mdxnsHFvHR/JoEMmYl5s/hWZWWan6ZaejFPB6gyVAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T21:43:19.481295Z","bundle_sha256":"a1649943b68478ac453b1c395f8d4c85efc4498f86f839f944ddaab395d60935"}}