{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:FFDVR5IZDSCNYV74QCTK4W3EW3","short_pith_number":"pith:FFDVR5IZ","canonical_record":{"source":{"id":"0802.0082","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-02-01T09:09:55Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"fcdbde7c91c5a15df5d71349a87f276804c84ceda3232990eba32695194e9045","abstract_canon_sha256":"c20ff7e42d5e38ae793da3f5538c2a75675405f5491d7b4d38bb471912b2515b"},"schema_version":"1.0"},"canonical_sha256":"294758f5191c84dc57fc80a6ae5b64b6f79cb5f9dfc7bc186d8ec25b8e509332","source":{"kind":"arxiv","id":"0802.0082","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.0082","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"0802.0082v3","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.0082","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"FFDVR5IZDSCN","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"FFDVR5IZDSCNYV74","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"FFDVR5IZ","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:FFDVR5IZDSCNYV74QCTK4W3EW3","target":"record","payload":{"canonical_record":{"source":{"id":"0802.0082","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-02-01T09:09:55Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"fcdbde7c91c5a15df5d71349a87f276804c84ceda3232990eba32695194e9045","abstract_canon_sha256":"c20ff7e42d5e38ae793da3f5538c2a75675405f5491d7b4d38bb471912b2515b"},"schema_version":"1.0"},"canonical_sha256":"294758f5191c84dc57fc80a6ae5b64b6f79cb5f9dfc7bc186d8ec25b8e509332","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:04.467151Z","signature_b64":"woKyOLMGzL+xQ4HZmsnN9YBVRimMKLRKrL8ygWNva9+z306R9WYUdQVx5Z4TWsHDcmlz3BWe/4fokFmJCBuZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"294758f5191c84dc57fc80a6ae5b64b6f79cb5f9dfc7bc186d8ec25b8e509332","last_reissued_at":"2026-05-18T04:05:04.466408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:04.466408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0802.0082","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LBevU4WI4xj3buLFMPpfzYt4Ot12mcbV3F8++2gLsGLG2L4cSgAiXlErGAXtcopHeD+TnoUHts0KZpDJUxQuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:57:58.090012Z"},"content_sha256":"015c8043255d7e650b30f75686525027af12fc79af85db8f1dd8241e1b4d4771","schema_version":"1.0","event_id":"sha256:015c8043255d7e650b30f75686525027af12fc79af85db8f1dd8241e1b4d4771"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:FFDVR5IZDSCNYV74QCTK4W3EW3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central limit theorem for Hotelling's $T^2$ statistic under large dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"G. M. Pan, W. Zhou","submitted_at":"2008-02-01T09:09:55Z","abstract_excerpt":"In this paper we prove the central limit theorem for Hotelling's $T^2$ statistic when the dimension of the random vectors is proportional to the sample size."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.0082","kind":"arxiv","version":3},"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":"2026-05-18T04:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+eFmb2cX0UI25ih1u36XC89MGWeJMm2pGY5JqbSOB+dMubYJxXaId2XstUzrDqMsw1v2nJlfiNXeg9G2QPAhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:57:58.090375Z"},"content_sha256":"1d2564f174e666a120850a99f7544139dfc2d420afed1f9dfae478f690e0e37c","schema_version":"1.0","event_id":"sha256:1d2564f174e666a120850a99f7544139dfc2d420afed1f9dfae478f690e0e37c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFDVR5IZDSCNYV74QCTK4W3EW3/bundle.json","state_url":"https://pith.science/pith/FFDVR5IZDSCNYV74QCTK4W3EW3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFDVR5IZDSCNYV74QCTK4W3EW3/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":"2026-06-02T14:57:58Z","links":{"resolver":"https://pith.science/pith/FFDVR5IZDSCNYV74QCTK4W3EW3","bundle":"https://pith.science/pith/FFDVR5IZDSCNYV74QCTK4W3EW3/bundle.json","state":"https://pith.science/pith/FFDVR5IZDSCNYV74QCTK4W3EW3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFDVR5IZDSCNYV74QCTK4W3EW3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:FFDVR5IZDSCNYV74QCTK4W3EW3","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":"c20ff7e42d5e38ae793da3f5538c2a75675405f5491d7b4d38bb471912b2515b","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-02-01T09:09:55Z","title_canon_sha256":"fcdbde7c91c5a15df5d71349a87f276804c84ceda3232990eba32695194e9045"},"schema_version":"1.0","source":{"id":"0802.0082","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.0082","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"0802.0082v3","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.0082","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"FFDVR5IZDSCN","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"FFDVR5IZDSCNYV74","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"FFDVR5IZ","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:1d2564f174e666a120850a99f7544139dfc2d420afed1f9dfae478f690e0e37c","target":"graph","created_at":"2026-05-18T04:05:04Z","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 prove the central limit theorem for Hotelling's $T^2$ statistic when the dimension of the random vectors is proportional to the sample size.","authors_text":"G. M. Pan, W. Zhou","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-02-01T09:09:55Z","title":"Central limit theorem for Hotelling's $T^2$ statistic under large dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.0082","kind":"arxiv","version":3},"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":"sha256:015c8043255d7e650b30f75686525027af12fc79af85db8f1dd8241e1b4d4771","target":"record","created_at":"2026-05-18T04:05:04Z","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":"c20ff7e42d5e38ae793da3f5538c2a75675405f5491d7b4d38bb471912b2515b","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-02-01T09:09:55Z","title_canon_sha256":"fcdbde7c91c5a15df5d71349a87f276804c84ceda3232990eba32695194e9045"},"schema_version":"1.0","source":{"id":"0802.0082","kind":"arxiv","version":3}},"canonical_sha256":"294758f5191c84dc57fc80a6ae5b64b6f79cb5f9dfc7bc186d8ec25b8e509332","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"294758f5191c84dc57fc80a6ae5b64b6f79cb5f9dfc7bc186d8ec25b8e509332","first_computed_at":"2026-05-18T04:05:04.466408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:04.466408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"woKyOLMGzL+xQ4HZmsnN9YBVRimMKLRKrL8ygWNva9+z306R9WYUdQVx5Z4TWsHDcmlz3BWe/4fokFmJCBuZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:04.467151Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.0082","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:015c8043255d7e650b30f75686525027af12fc79af85db8f1dd8241e1b4d4771","sha256:1d2564f174e666a120850a99f7544139dfc2d420afed1f9dfae478f690e0e37c"],"state_sha256":"b1cdd1e4f666228fe67e508048a83772f26dce070efbf22ee6fd860e8225f7ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FcYkTNqjwOScqBWeu4GBdYZHpkRcXoztFV6LHwZ7ZRuBsoV6PvnKlrW6odPUi5uq+GZAdhUxUFURFG3hnKEdDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:57:58.092420Z","bundle_sha256":"4aea09054198831f2281bea0cc880e82fd897d00904f8ed80d77d932daf0cd96"}}