{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5K66XZ2QRZJDSVW5J25QH5YDXX","short_pith_number":"pith:5K66XZ2Q","canonical_record":{"source":{"id":"1705.01788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-05-04T10:46:23Z","cross_cats_sorted":[],"title_canon_sha256":"6d7f8371a2db74cae654ec35b03260f3c29f804f797aefb4604d6a776a5b1808","abstract_canon_sha256":"71c7c893524d0c88720416dafd0fac7360fd4178c45134de19cdd56ba9635024"},"schema_version":"1.0"},"canonical_sha256":"eabdebe7508e523956dd4ebb03f703bdce55a33b1ca09ae6706d1614c71e0615","source":{"kind":"arxiv","id":"1705.01788","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01788","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01788v1","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01788","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"pith_short_12","alias_value":"5K66XZ2QRZJD","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5K66XZ2QRZJDSVW5","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5K66XZ2Q","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5K66XZ2QRZJDSVW5J25QH5YDXX","target":"record","payload":{"canonical_record":{"source":{"id":"1705.01788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-05-04T10:46:23Z","cross_cats_sorted":[],"title_canon_sha256":"6d7f8371a2db74cae654ec35b03260f3c29f804f797aefb4604d6a776a5b1808","abstract_canon_sha256":"71c7c893524d0c88720416dafd0fac7360fd4178c45134de19cdd56ba9635024"},"schema_version":"1.0"},"canonical_sha256":"eabdebe7508e523956dd4ebb03f703bdce55a33b1ca09ae6706d1614c71e0615","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:02.308514Z","signature_b64":"FQHIcKfdXKc8v3NNcFa41bWw03HXZtRxf9HR4WbFoAcGXpAD/hfmIsWzCg2u2r6Ci5Ewkgp6N81MKiPXnw4oDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eabdebe7508e523956dd4ebb03f703bdce55a33b1ca09ae6706d1614c71e0615","last_reissued_at":"2026-05-18T00:45:02.307981Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:02.307981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.01788","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":"2026-05-18T00:45:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PrkZ2eKih/pob35h2Ysi8t5xTFz3ebf1lL5TjwufEvitNPS0zJrJuDvNJsmQ+Gb+CDoNbzeMwgGdxohjXKafBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T09:07:45.926825Z"},"content_sha256":"2e1cb71c4ac03b28f282ad0d2681d23359c8d86f06c8b4fba4637e670e901305","schema_version":"1.0","event_id":"sha256:2e1cb71c4ac03b28f282ad0d2681d23359c8d86f06c8b4fba4637e670e901305"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5K66XZ2QRZJDSVW5J25QH5YDXX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An optimal transportation approach for assessing almost stochastic order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"C. Matr\\'an, E. del Barrio, J.A. Cuesta-Albertos","submitted_at":"2017-05-04T10:46:23Z","abstract_excerpt":"When stochastic dominance $F\\leq_{st}G$ does not hold, we can improve agreement to stochastic order by suitably trimming both distributions. In this work we consider the $L_2-$Wasserstein distance, $\\mathcal W_2$, to stochastic order of these trimmed versions. Our characterization for that distance naturally leads to consider a $\\mathcal W_2$-based index of disagreement with stochastic order, $\\varepsilon_{\\mathcal W_2}(F,G)$. We provide asymptotic results allowing to test $H_0: \\varepsilon_{\\mathcal W_2}(F,G)\\geq \\varepsilon_0$ vs $H_a: \\varepsilon_{\\mathcal W_2}(F,G)<\\varepsilon_0$, that, un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01788","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":"2026-05-18T00:45:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XmtR/Q+yo7Y36eCQOk1BYYH2uJ2PK3Wr74kU9mcNu3ZnUQXepwMYxVKszaNRaS/goooTfKtjsysLtNQpwnUABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T09:07:45.927165Z"},"content_sha256":"24fd98ec76ae77ce0f30683da968d246f4281571115a3a1d9483d60cfb27f4d2","schema_version":"1.0","event_id":"sha256:24fd98ec76ae77ce0f30683da968d246f4281571115a3a1d9483d60cfb27f4d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5K66XZ2QRZJDSVW5J25QH5YDXX/bundle.json","state_url":"https://pith.science/pith/5K66XZ2QRZJDSVW5J25QH5YDXX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5K66XZ2QRZJDSVW5J25QH5YDXX/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":"2026-07-02T09:07:45Z","links":{"resolver":"https://pith.science/pith/5K66XZ2QRZJDSVW5J25QH5YDXX","bundle":"https://pith.science/pith/5K66XZ2QRZJDSVW5J25QH5YDXX/bundle.json","state":"https://pith.science/pith/5K66XZ2QRZJDSVW5J25QH5YDXX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5K66XZ2QRZJDSVW5J25QH5YDXX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5K66XZ2QRZJDSVW5J25QH5YDXX","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":"71c7c893524d0c88720416dafd0fac7360fd4178c45134de19cdd56ba9635024","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-05-04T10:46:23Z","title_canon_sha256":"6d7f8371a2db74cae654ec35b03260f3c29f804f797aefb4604d6a776a5b1808"},"schema_version":"1.0","source":{"id":"1705.01788","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01788","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01788v1","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01788","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"pith_short_12","alias_value":"5K66XZ2QRZJD","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5K66XZ2QRZJDSVW5","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5K66XZ2Q","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:24fd98ec76ae77ce0f30683da968d246f4281571115a3a1d9483d60cfb27f4d2","target":"graph","created_at":"2026-05-18T00:45:02Z","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":"When stochastic dominance $F\\leq_{st}G$ does not hold, we can improve agreement to stochastic order by suitably trimming both distributions. In this work we consider the $L_2-$Wasserstein distance, $\\mathcal W_2$, to stochastic order of these trimmed versions. Our characterization for that distance naturally leads to consider a $\\mathcal W_2$-based index of disagreement with stochastic order, $\\varepsilon_{\\mathcal W_2}(F,G)$. We provide asymptotic results allowing to test $H_0: \\varepsilon_{\\mathcal W_2}(F,G)\\geq \\varepsilon_0$ vs $H_a: \\varepsilon_{\\mathcal W_2}(F,G)<\\varepsilon_0$, that, un","authors_text":"C. Matr\\'an, E. del Barrio, J.A. Cuesta-Albertos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-05-04T10:46:23Z","title":"An optimal transportation approach for assessing almost stochastic order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01788","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":"sha256:2e1cb71c4ac03b28f282ad0d2681d23359c8d86f06c8b4fba4637e670e901305","target":"record","created_at":"2026-05-18T00:45:02Z","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":"71c7c893524d0c88720416dafd0fac7360fd4178c45134de19cdd56ba9635024","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-05-04T10:46:23Z","title_canon_sha256":"6d7f8371a2db74cae654ec35b03260f3c29f804f797aefb4604d6a776a5b1808"},"schema_version":"1.0","source":{"id":"1705.01788","kind":"arxiv","version":1}},"canonical_sha256":"eabdebe7508e523956dd4ebb03f703bdce55a33b1ca09ae6706d1614c71e0615","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eabdebe7508e523956dd4ebb03f703bdce55a33b1ca09ae6706d1614c71e0615","first_computed_at":"2026-05-18T00:45:02.307981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:02.307981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FQHIcKfdXKc8v3NNcFa41bWw03HXZtRxf9HR4WbFoAcGXpAD/hfmIsWzCg2u2r6Ci5Ewkgp6N81MKiPXnw4oDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:02.308514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01788","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e1cb71c4ac03b28f282ad0d2681d23359c8d86f06c8b4fba4637e670e901305","sha256:24fd98ec76ae77ce0f30683da968d246f4281571115a3a1d9483d60cfb27f4d2"],"state_sha256":"8d1f8982524b9019c0718476e48ac7770b8fe1e19711000ef0d7713575c2395b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CuxEH2RI2FWSZweiEn8w5TTXPUIJFDx7VhHygxcQn5PqDiVy84ynmGX/9meDQKN7MTFm5PdpcY1X1erHhwgIAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T09:07:45.929099Z","bundle_sha256":"cd89e446e03f90edeab623ba5c2e24b242f071a7ee9c71b3bfbfe4807676aa07"}}