{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NE2NUGCVSGRCZ2Q5WQ5FTG76IC","short_pith_number":"pith:NE2NUGCV","canonical_record":{"source":{"id":"1905.01402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-05-04T01:18:01Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"38f458dac30a795864a7682e87e858efea367fd52e172145364c6d03dc2f2e2e","abstract_canon_sha256":"f1b2d383793047befb43cfb1dd5b75fb83097b629f3bb3778dd914da85dc99b4"},"schema_version":"1.0"},"canonical_sha256":"6934da185591a22cea1db43a599bfe40b2454dc786d5fb781c10e07ab7675a0a","source":{"kind":"arxiv","id":"1905.01402","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01402","created_at":"2026-05-17T23:47:00Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01402v1","created_at":"2026-05-17T23:47:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01402","created_at":"2026-05-17T23:47:00Z"},{"alias_kind":"pith_short_12","alias_value":"NE2NUGCVSGRC","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NE2NUGCVSGRCZ2Q5","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NE2NUGCV","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NE2NUGCVSGRCZ2Q5WQ5FTG76IC","target":"record","payload":{"canonical_record":{"source":{"id":"1905.01402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-05-04T01:18:01Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"38f458dac30a795864a7682e87e858efea367fd52e172145364c6d03dc2f2e2e","abstract_canon_sha256":"f1b2d383793047befb43cfb1dd5b75fb83097b629f3bb3778dd914da85dc99b4"},"schema_version":"1.0"},"canonical_sha256":"6934da185591a22cea1db43a599bfe40b2454dc786d5fb781c10e07ab7675a0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:00.782598Z","signature_b64":"kvUvi950trfVDMDUdhaEtVkvPvnvE5D5JSCvu567m/7KASLzwEDR6B0ZtrxCQpYjp4LHOzyNM2dSZUCGZRngCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6934da185591a22cea1db43a599bfe40b2454dc786d5fb781c10e07ab7675a0a","last_reissued_at":"2026-05-17T23:47:00.781949Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:00.781949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.01402","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":"2026-05-17T23:47:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wcs9r+RylPwDrblR9cD0MXGqGpcznnn4Ru+B4Q1cfZ3cc5iRgxP7GwxKSCVwuAeZa0nti1HXBAQe3gkvSin9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:49:57.997759Z"},"content_sha256":"4aa878882c56e38b7b35a88d1d4bd18df89580e6c1bc83da25d52b10ab04f244","schema_version":"1.0","event_id":"sha256:4aa878882c56e38b7b35a88d1d4bd18df89580e6c1bc83da25d52b10ab04f244"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NE2NUGCVSGRCZ2Q5WQ5FTG76IC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Test for homogeneity with unordered paired observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Jiahua Chen, Jing Qin, Pengfei Li, Tao Yu","submitted_at":"2019-05-04T01:18:01Z","abstract_excerpt":"In some applications, an experimental unit is composed of two distinct but related subunits. The response from such a unit is $(X_{1}, X_{2})$ but we observe only $Y_1 = \\min\\{X_{1},X_{2}\\}$ and $Y_2 = \\max\\{X_{1},X_{2}\\}$, i.e., the subunit identities are not observed. We call $(Y_1, Y_2)$ unordered paired observations. Based on unordered paired observations $\\{(Y_{1i}, Y_{2i})\\}_{i=1}^n$, we are interested in whether the marginal distributions for $X_1$ and $X_2$ are identical. Testing methods are available in the literature under the assumptions that $Var(X_1) = Var(X_2)$ and $Cov(X_1, X_2)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01402","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":"2026-05-17T23:47:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"051mG+QUOmyilNmhRWk4n74oUvwXABrOhctF50fYz6HoQtPRvou7mT3JJOoLaTsDeNyjkLBjMG1M5vl6BJcUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:49:57.998133Z"},"content_sha256":"bb9c727eb31934682ff8da5e220ca61a1fa6c39018dab92e7ff750feb19e9af7","schema_version":"1.0","event_id":"sha256:bb9c727eb31934682ff8da5e220ca61a1fa6c39018dab92e7ff750feb19e9af7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NE2NUGCVSGRCZ2Q5WQ5FTG76IC/bundle.json","state_url":"https://pith.science/pith/NE2NUGCVSGRCZ2Q5WQ5FTG76IC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NE2NUGCVSGRCZ2Q5WQ5FTG76IC/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":"2026-05-25T22:49:57Z","links":{"resolver":"https://pith.science/pith/NE2NUGCVSGRCZ2Q5WQ5FTG76IC","bundle":"https://pith.science/pith/NE2NUGCVSGRCZ2Q5WQ5FTG76IC/bundle.json","state":"https://pith.science/pith/NE2NUGCVSGRCZ2Q5WQ5FTG76IC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NE2NUGCVSGRCZ2Q5WQ5FTG76IC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NE2NUGCVSGRCZ2Q5WQ5FTG76IC","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":"f1b2d383793047befb43cfb1dd5b75fb83097b629f3bb3778dd914da85dc99b4","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-05-04T01:18:01Z","title_canon_sha256":"38f458dac30a795864a7682e87e858efea367fd52e172145364c6d03dc2f2e2e"},"schema_version":"1.0","source":{"id":"1905.01402","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01402","created_at":"2026-05-17T23:47:00Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01402v1","created_at":"2026-05-17T23:47:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01402","created_at":"2026-05-17T23:47:00Z"},{"alias_kind":"pith_short_12","alias_value":"NE2NUGCVSGRC","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NE2NUGCVSGRCZ2Q5","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NE2NUGCV","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:bb9c727eb31934682ff8da5e220ca61a1fa6c39018dab92e7ff750feb19e9af7","target":"graph","created_at":"2026-05-17T23:47:00Z","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 some applications, an experimental unit is composed of two distinct but related subunits. The response from such a unit is $(X_{1}, X_{2})$ but we observe only $Y_1 = \\min\\{X_{1},X_{2}\\}$ and $Y_2 = \\max\\{X_{1},X_{2}\\}$, i.e., the subunit identities are not observed. We call $(Y_1, Y_2)$ unordered paired observations. Based on unordered paired observations $\\{(Y_{1i}, Y_{2i})\\}_{i=1}^n$, we are interested in whether the marginal distributions for $X_1$ and $X_2$ are identical. Testing methods are available in the literature under the assumptions that $Var(X_1) = Var(X_2)$ and $Cov(X_1, X_2)","authors_text":"Jiahua Chen, Jing Qin, Pengfei Li, Tao Yu","cross_cats":["stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-05-04T01:18:01Z","title":"Test for homogeneity with unordered paired observations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01402","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":"sha256:4aa878882c56e38b7b35a88d1d4bd18df89580e6c1bc83da25d52b10ab04f244","target":"record","created_at":"2026-05-17T23:47:00Z","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":"f1b2d383793047befb43cfb1dd5b75fb83097b629f3bb3778dd914da85dc99b4","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-05-04T01:18:01Z","title_canon_sha256":"38f458dac30a795864a7682e87e858efea367fd52e172145364c6d03dc2f2e2e"},"schema_version":"1.0","source":{"id":"1905.01402","kind":"arxiv","version":1}},"canonical_sha256":"6934da185591a22cea1db43a599bfe40b2454dc786d5fb781c10e07ab7675a0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6934da185591a22cea1db43a599bfe40b2454dc786d5fb781c10e07ab7675a0a","first_computed_at":"2026-05-17T23:47:00.781949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:00.781949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kvUvi950trfVDMDUdhaEtVkvPvnvE5D5JSCvu567m/7KASLzwEDR6B0ZtrxCQpYjp4LHOzyNM2dSZUCGZRngCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:00.782598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.01402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4aa878882c56e38b7b35a88d1d4bd18df89580e6c1bc83da25d52b10ab04f244","sha256:bb9c727eb31934682ff8da5e220ca61a1fa6c39018dab92e7ff750feb19e9af7"],"state_sha256":"39e9ee94d01a6ce6e58a8ceebc3443f3027862c07cc56a9f19ee094a6296f348"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+4SxdD2FfLl0EMVNAL1EArU+UQiQ2N+KfQPqOVaaKY5l8crMUHaEcIBVEgAV+XeRGGLQqXZ79KRKo22WIxKWAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:49:58.001420Z","bundle_sha256":"dc8d0fe0c90f6981f8c1c9e86401693287ecec7ef3e969361f873ea6035a70ee"}}