{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DVXX64REVN2JLRMKWVKQZZA6MP","short_pith_number":"pith:DVXX64RE","canonical_record":{"source":{"id":"1807.06367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-07-17T11:56:28Z","cross_cats_sorted":[],"title_canon_sha256":"45eeca77f82b29b7f9eb9b0d03c85021643c3019a6bf1d6bd1e1d1368bf8feca","abstract_canon_sha256":"0bb42d2b0c574d1be92515fd9e327bdb1fe9494ee4c46c8d3722db5b99d80ed6"},"schema_version":"1.0"},"canonical_sha256":"1d6f7f7224ab7495c58ab5550ce41e63f84b310922b4104da97e1a8d694b36ed","source":{"kind":"arxiv","id":"1807.06367","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06367","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06367v1","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06367","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"DVXX64REVN2J","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DVXX64REVN2JLRMK","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DVXX64RE","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DVXX64REVN2JLRMKWVKQZZA6MP","target":"record","payload":{"canonical_record":{"source":{"id":"1807.06367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-07-17T11:56:28Z","cross_cats_sorted":[],"title_canon_sha256":"45eeca77f82b29b7f9eb9b0d03c85021643c3019a6bf1d6bd1e1d1368bf8feca","abstract_canon_sha256":"0bb42d2b0c574d1be92515fd9e327bdb1fe9494ee4c46c8d3722db5b99d80ed6"},"schema_version":"1.0"},"canonical_sha256":"1d6f7f7224ab7495c58ab5550ce41e63f84b310922b4104da97e1a8d694b36ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:33.241935Z","signature_b64":"WH/wMs9wGDVLhiLWeoIvi0FXg5NUqtgO5F8rAiiAWOjYJnGQlgfwjgpjd69Q4CRrthO1Ha9mGi0HDNb+9xS1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d6f7f7224ab7495c58ab5550ce41e63f84b310922b4104da97e1a8d694b36ed","last_reissued_at":"2026-05-18T00:10:33.241108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:33.241108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.06367","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":"2026-05-18T00:10:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L10hbFaUrLJQ4EwklRzCIutjc5YFBq3cAk5NwbrHhGiNBWWjyLr1NQQD34kn/MhAFt3kVOpR36N8JD+JBCPXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:08:42.673782Z"},"content_sha256":"079513d9a4f361aa4e4b6f13524fda93ba4ad1e3c7dffb7c1c066b538e747974","schema_version":"1.0","event_id":"sha256:079513d9a4f361aa4e4b6f13524fda93ba4ad1e3c7dffb7c1c066b538e747974"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DVXX64REVN2JLRMKWVKQZZA6MP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"More good news on the (only) affine invariant test for multivariate reflected symmetry about an unknown center","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Celeste Mayer, Norbert Henze","submitted_at":"2018-07-17T11:56:28Z","abstract_excerpt":"We revisit the problem of testing for multivariate reflected symmetry about an unspecified point. Although this testing problem is invariant with respect to full-rank affine transformations, among the hitherto few proposed tests only the test studied in [12] respects this property. We identify a measure of deviation $\\Delta$ (say) from symmetry associated with the test statistic $T_n$ (say), and we obtain the limit normal distribution of $T_n$ as $n \\to \\infty$ under a fixed alternative to symmetry. Since a consistent estimator of the variance of this limit normal distribution is available, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06367","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":"2026-05-18T00:10:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XaP4bcxsDdEhU2Ms6NivDrq7eH9FXrRDxcJRyAWZjBrldWSnWUyiGXPys2LwV8Eyr9fLpUrO3r/JV00tpkj8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:08:42.674265Z"},"content_sha256":"f9007a304450e9b375b22906e990fa90f86d4fa7fe6697a82cadb85a9e19c73b","schema_version":"1.0","event_id":"sha256:f9007a304450e9b375b22906e990fa90f86d4fa7fe6697a82cadb85a9e19c73b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DVXX64REVN2JLRMKWVKQZZA6MP/bundle.json","state_url":"https://pith.science/pith/DVXX64REVN2JLRMKWVKQZZA6MP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DVXX64REVN2JLRMKWVKQZZA6MP/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":"2026-06-25T18:08:42Z","links":{"resolver":"https://pith.science/pith/DVXX64REVN2JLRMKWVKQZZA6MP","bundle":"https://pith.science/pith/DVXX64REVN2JLRMKWVKQZZA6MP/bundle.json","state":"https://pith.science/pith/DVXX64REVN2JLRMKWVKQZZA6MP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DVXX64REVN2JLRMKWVKQZZA6MP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DVXX64REVN2JLRMKWVKQZZA6MP","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":"0bb42d2b0c574d1be92515fd9e327bdb1fe9494ee4c46c8d3722db5b99d80ed6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-07-17T11:56:28Z","title_canon_sha256":"45eeca77f82b29b7f9eb9b0d03c85021643c3019a6bf1d6bd1e1d1368bf8feca"},"schema_version":"1.0","source":{"id":"1807.06367","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06367","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06367v1","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06367","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"DVXX64REVN2J","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DVXX64REVN2JLRMK","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DVXX64RE","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:f9007a304450e9b375b22906e990fa90f86d4fa7fe6697a82cadb85a9e19c73b","target":"graph","created_at":"2026-05-18T00:10:33Z","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":"We revisit the problem of testing for multivariate reflected symmetry about an unspecified point. Although this testing problem is invariant with respect to full-rank affine transformations, among the hitherto few proposed tests only the test studied in [12] respects this property. We identify a measure of deviation $\\Delta$ (say) from symmetry associated with the test statistic $T_n$ (say), and we obtain the limit normal distribution of $T_n$ as $n \\to \\infty$ under a fixed alternative to symmetry. Since a consistent estimator of the variance of this limit normal distribution is available, we","authors_text":"Celeste Mayer, Norbert Henze","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-07-17T11:56:28Z","title":"More good news on the (only) affine invariant test for multivariate reflected symmetry about an unknown center"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06367","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":"sha256:079513d9a4f361aa4e4b6f13524fda93ba4ad1e3c7dffb7c1c066b538e747974","target":"record","created_at":"2026-05-18T00:10:33Z","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":"0bb42d2b0c574d1be92515fd9e327bdb1fe9494ee4c46c8d3722db5b99d80ed6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-07-17T11:56:28Z","title_canon_sha256":"45eeca77f82b29b7f9eb9b0d03c85021643c3019a6bf1d6bd1e1d1368bf8feca"},"schema_version":"1.0","source":{"id":"1807.06367","kind":"arxiv","version":1}},"canonical_sha256":"1d6f7f7224ab7495c58ab5550ce41e63f84b310922b4104da97e1a8d694b36ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d6f7f7224ab7495c58ab5550ce41e63f84b310922b4104da97e1a8d694b36ed","first_computed_at":"2026-05-18T00:10:33.241108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:33.241108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WH/wMs9wGDVLhiLWeoIvi0FXg5NUqtgO5F8rAiiAWOjYJnGQlgfwjgpjd69Q4CRrthO1Ha9mGi0HDNb+9xS1CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:33.241935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06367","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:079513d9a4f361aa4e4b6f13524fda93ba4ad1e3c7dffb7c1c066b538e747974","sha256:f9007a304450e9b375b22906e990fa90f86d4fa7fe6697a82cadb85a9e19c73b"],"state_sha256":"534086113695bd6b43aefc5322fb0086fed99d8b4878bf97b9eb2d2a05d5a5b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QsX/yf1iM+juP9iGb365peF2VFJH9Eev7VM3NIBYW1zySTwHdDuHuQgOEb8VhIpJ41Xkjh6tnaBXQWFYjWogBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:08:42.676755Z","bundle_sha256":"454e07cac75dd6490239d107ee49c231b81d5f527d82073c117e7550dff2900f"}}