{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2VO6KH3TN6JL5ZMZP565V53C4J","short_pith_number":"pith:2VO6KH3T","canonical_record":{"source":{"id":"1011.2288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2010-11-10T08:02:49Z","cross_cats_sorted":[],"title_canon_sha256":"a31ceb2777a539c0d8d8123b76c3d45ebce71166ede4a7a36910b74df228b001","abstract_canon_sha256":"5f68b003d680d5331e18d90d3da07fe4371b478db0c37352b6df422cd14243e4"},"schema_version":"1.0"},"canonical_sha256":"d55de51f736f92bee5997f7ddaf762e25d10f917e5cbb32cd6c2a3a6c4385268","source":{"kind":"arxiv","id":"1011.2288","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2288","created_at":"2026-05-18T04:36:30Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2288v1","created_at":"2026-05-18T04:36:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2288","created_at":"2026-05-18T04:36:30Z"},{"alias_kind":"pith_short_12","alias_value":"2VO6KH3TN6JL","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2VO6KH3TN6JL5ZMZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2VO6KH3T","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2VO6KH3TN6JL5ZMZP565V53C4J","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2010-11-10T08:02:49Z","cross_cats_sorted":[],"title_canon_sha256":"a31ceb2777a539c0d8d8123b76c3d45ebce71166ede4a7a36910b74df228b001","abstract_canon_sha256":"5f68b003d680d5331e18d90d3da07fe4371b478db0c37352b6df422cd14243e4"},"schema_version":"1.0"},"canonical_sha256":"d55de51f736f92bee5997f7ddaf762e25d10f917e5cbb32cd6c2a3a6c4385268","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:30.675750Z","signature_b64":"5PLgJPMKQJqYvbg4+YwWAm5XUnNoaJ6bfYse8rMzgHdyarYMBV/Oo16LlTDvL8dxEJgemXImGEpq/+AlmeFOCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d55de51f736f92bee5997f7ddaf762e25d10f917e5cbb32cd6c2a3a6c4385268","last_reissued_at":"2026-05-18T04:36:30.675329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:30.675329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2288","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":"2026-05-18T04:36:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WxrfX8BMuzGADfRt/izerUBLijLsW0AcoCxUA7oTSEPrj6Gvxj9HRW3kmsvge5uQ6CskCQi6raMlXTO0y3KGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:10:21.416681Z"},"content_sha256":"f1db27e49cb156636fe24d22264b35d3b77ac12b8977f30c4ff498f3d63061cf","schema_version":"1.0","event_id":"sha256:f1db27e49cb156636fe24d22264b35d3b77ac12b8977f30c4ff498f3d63061cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2VO6KH3TN6JL5ZMZP565V53C4J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"DISCO analysis: A nonparametric extension of analysis of variance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.AP","authors_text":"G\\'abor J. Sz\\'ekely, Maria L. Rizzo","submitted_at":"2010-11-10T08:02:49Z","abstract_excerpt":"In classical analysis of variance, dispersion is measured by considering squared distances of sample elements from the sample mean. We consider a measure of dispersion for univariate or multivariate response based on all pairwise distances between-sample elements, and derive an analogous distance components (DISCO) decomposition for powers of distance in $(0,2]$. The ANOVA F statistic is obtained when the index (exponent) is 2. For each index in $(0,2)$, this decomposition determines a nonparametric test for the multi-sample hypothesis of equal distributions that is statistically consistent ag"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2288","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":"2026-05-18T04:36:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZOGNjpXDMSx8UVUlm1C4AEpIQpWmHrxrLfy04sf+5zWab8Ra4OfFv55Gr6IRYF6B5UBYFdDQBKdSX1ysfiyHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:10:21.417246Z"},"content_sha256":"bfc62d0e7df3a1506c170b34bfa3e42dd157b54ab8c1a23189024d3cbe80dd65","schema_version":"1.0","event_id":"sha256:bfc62d0e7df3a1506c170b34bfa3e42dd157b54ab8c1a23189024d3cbe80dd65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2VO6KH3TN6JL5ZMZP565V53C4J/bundle.json","state_url":"https://pith.science/pith/2VO6KH3TN6JL5ZMZP565V53C4J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2VO6KH3TN6JL5ZMZP565V53C4J/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":"2026-05-28T20:10:21Z","links":{"resolver":"https://pith.science/pith/2VO6KH3TN6JL5ZMZP565V53C4J","bundle":"https://pith.science/pith/2VO6KH3TN6JL5ZMZP565V53C4J/bundle.json","state":"https://pith.science/pith/2VO6KH3TN6JL5ZMZP565V53C4J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2VO6KH3TN6JL5ZMZP565V53C4J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2VO6KH3TN6JL5ZMZP565V53C4J","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":"5f68b003d680d5331e18d90d3da07fe4371b478db0c37352b6df422cd14243e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2010-11-10T08:02:49Z","title_canon_sha256":"a31ceb2777a539c0d8d8123b76c3d45ebce71166ede4a7a36910b74df228b001"},"schema_version":"1.0","source":{"id":"1011.2288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2288","created_at":"2026-05-18T04:36:30Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2288v1","created_at":"2026-05-18T04:36:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2288","created_at":"2026-05-18T04:36:30Z"},{"alias_kind":"pith_short_12","alias_value":"2VO6KH3TN6JL","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2VO6KH3TN6JL5ZMZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2VO6KH3T","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:bfc62d0e7df3a1506c170b34bfa3e42dd157b54ab8c1a23189024d3cbe80dd65","target":"graph","created_at":"2026-05-18T04:36:30Z","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 classical analysis of variance, dispersion is measured by considering squared distances of sample elements from the sample mean. We consider a measure of dispersion for univariate or multivariate response based on all pairwise distances between-sample elements, and derive an analogous distance components (DISCO) decomposition for powers of distance in $(0,2]$. The ANOVA F statistic is obtained when the index (exponent) is 2. For each index in $(0,2)$, this decomposition determines a nonparametric test for the multi-sample hypothesis of equal distributions that is statistically consistent ag","authors_text":"G\\'abor J. Sz\\'ekely, Maria L. Rizzo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2010-11-10T08:02:49Z","title":"DISCO analysis: A nonparametric extension of analysis of variance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2288","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:f1db27e49cb156636fe24d22264b35d3b77ac12b8977f30c4ff498f3d63061cf","target":"record","created_at":"2026-05-18T04:36:30Z","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":"5f68b003d680d5331e18d90d3da07fe4371b478db0c37352b6df422cd14243e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2010-11-10T08:02:49Z","title_canon_sha256":"a31ceb2777a539c0d8d8123b76c3d45ebce71166ede4a7a36910b74df228b001"},"schema_version":"1.0","source":{"id":"1011.2288","kind":"arxiv","version":1}},"canonical_sha256":"d55de51f736f92bee5997f7ddaf762e25d10f917e5cbb32cd6c2a3a6c4385268","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d55de51f736f92bee5997f7ddaf762e25d10f917e5cbb32cd6c2a3a6c4385268","first_computed_at":"2026-05-18T04:36:30.675329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:30.675329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5PLgJPMKQJqYvbg4+YwWAm5XUnNoaJ6bfYse8rMzgHdyarYMBV/Oo16LlTDvL8dxEJgemXImGEpq/+AlmeFOCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:30.675750Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1db27e49cb156636fe24d22264b35d3b77ac12b8977f30c4ff498f3d63061cf","sha256:bfc62d0e7df3a1506c170b34bfa3e42dd157b54ab8c1a23189024d3cbe80dd65"],"state_sha256":"7816158977072ca01aa441755b8d8e2de1a5ed06a912cb69eefe5756ef42cd38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sJRvANd0zfmOAn7p5ZbBDJDteVTmjIYPndxUqfQsQIudQ6UPhCGBr7rYprffY7cqldyIrFZO3kxlR8143aVODg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:10:21.419651Z","bundle_sha256":"dda5fc4d2a7d0b0f9b457b77b2633ba1868d04127f879c3d515b0b8ff495699b"}}