{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:URZCXAN5KICLK4J7C3NLHC42XE","short_pith_number":"pith:URZCXAN5","canonical_record":{"source":{"id":"1502.04733","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-16T21:44:14Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"4614a225b83a88908ac5fa3d9d989c8611d4e139a6b1bb01a06c6e933eedcff2","abstract_canon_sha256":"fb1b66b3d612801a11f20ab27d46dfbbeff0efb80719f2a61206c52571b69801"},"schema_version":"1.0"},"canonical_sha256":"a4722b81bd5204b5713f16dab38b9ab917f2c387dc9ba2dba883057674fd4d53","source":{"kind":"arxiv","id":"1502.04733","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04733","created_at":"2026-05-18T01:33:16Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04733v2","created_at":"2026-05-18T01:33:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04733","created_at":"2026-05-18T01:33:16Z"},{"alias_kind":"pith_short_12","alias_value":"URZCXAN5KICL","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"URZCXAN5KICLK4J7","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"URZCXAN5","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:URZCXAN5KICLK4J7C3NLHC42XE","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04733","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-16T21:44:14Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"4614a225b83a88908ac5fa3d9d989c8611d4e139a6b1bb01a06c6e933eedcff2","abstract_canon_sha256":"fb1b66b3d612801a11f20ab27d46dfbbeff0efb80719f2a61206c52571b69801"},"schema_version":"1.0"},"canonical_sha256":"a4722b81bd5204b5713f16dab38b9ab917f2c387dc9ba2dba883057674fd4d53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:16.091072Z","signature_b64":"GK0mohWVpLsy+KktRJEXZdJmKm/Y8mJYBkKFqH23pVtMKz4AQCC7bt5P5NGYHRolwCJwUVzSi7/cRq2wUcGxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4722b81bd5204b5713f16dab38b9ab917f2c387dc9ba2dba883057674fd4d53","last_reissued_at":"2026-05-18T01:33:16.090442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:16.090442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04733","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x3DB/naEXcbwV+rbcKY7ZxkxiZBQ1fYaqzcVR1pPOtwD5g+n/l+cwgYNa3UWBLpxwjB8F1st0HbN04b7+IprBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:00:28.787247Z"},"content_sha256":"b396d1e1194e08a44c5e75dfa1e8fb31bbb64863458e90ffec97fd4e48cc369a","schema_version":"1.0","event_id":"sha256:b396d1e1194e08a44c5e75dfa1e8fb31bbb64863458e90ffec97fd4e48cc369a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:URZCXAN5KICLK4J7C3NLHC42XE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of Empirical Eigen-structure for Ultra-high Dimensional Spiked Covariance Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Jianqing Fan, Weichen Wang","submitted_at":"2015-02-16T21:44:14Z","abstract_excerpt":"We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the spike magnitude of leading eigenvalues, sample size, and dimensionality. This new regime allows high dimensionality and diverging eigenvalue spikes and provides new insights into the roles the leading eigenvalues, sample size, and dimensionality play in principal component analysis. The results are proven by a technical device, which swaps the role of rows and columns and converts the high-dimensional problems into low-dimensional one"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04733","kind":"arxiv","version":2},"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":"2026-05-18T01:33:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m1SH333XB7inFgs7y7ywHbPGxorVVjmdXsy+9aKEXlHE3uZtxCD1kV/DwVv+Ispt3ajE64FC/+EgupzFHpMFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:00:28.787609Z"},"content_sha256":"d9a88164e548e5256f58b1d0bd0cc669a03a08f604c10c9ac798d564e5a27485","schema_version":"1.0","event_id":"sha256:d9a88164e548e5256f58b1d0bd0cc669a03a08f604c10c9ac798d564e5a27485"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/URZCXAN5KICLK4J7C3NLHC42XE/bundle.json","state_url":"https://pith.science/pith/URZCXAN5KICLK4J7C3NLHC42XE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/URZCXAN5KICLK4J7C3NLHC42XE/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":"2026-05-31T03:00:28Z","links":{"resolver":"https://pith.science/pith/URZCXAN5KICLK4J7C3NLHC42XE","bundle":"https://pith.science/pith/URZCXAN5KICLK4J7C3NLHC42XE/bundle.json","state":"https://pith.science/pith/URZCXAN5KICLK4J7C3NLHC42XE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/URZCXAN5KICLK4J7C3NLHC42XE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:URZCXAN5KICLK4J7C3NLHC42XE","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":"fb1b66b3d612801a11f20ab27d46dfbbeff0efb80719f2a61206c52571b69801","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-16T21:44:14Z","title_canon_sha256":"4614a225b83a88908ac5fa3d9d989c8611d4e139a6b1bb01a06c6e933eedcff2"},"schema_version":"1.0","source":{"id":"1502.04733","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04733","created_at":"2026-05-18T01:33:16Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04733v2","created_at":"2026-05-18T01:33:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04733","created_at":"2026-05-18T01:33:16Z"},{"alias_kind":"pith_short_12","alias_value":"URZCXAN5KICL","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"URZCXAN5KICLK4J7","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"URZCXAN5","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:d9a88164e548e5256f58b1d0bd0cc669a03a08f604c10c9ac798d564e5a27485","target":"graph","created_at":"2026-05-18T01:33:16Z","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 derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the spike magnitude of leading eigenvalues, sample size, and dimensionality. This new regime allows high dimensionality and diverging eigenvalue spikes and provides new insights into the roles the leading eigenvalues, sample size, and dimensionality play in principal component analysis. The results are proven by a technical device, which swaps the role of rows and columns and converts the high-dimensional problems into low-dimensional one","authors_text":"Jianqing Fan, Weichen Wang","cross_cats":["stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-16T21:44:14Z","title":"Asymptotics of Empirical Eigen-structure for Ultra-high Dimensional Spiked Covariance Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04733","kind":"arxiv","version":2},"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:b396d1e1194e08a44c5e75dfa1e8fb31bbb64863458e90ffec97fd4e48cc369a","target":"record","created_at":"2026-05-18T01:33:16Z","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":"fb1b66b3d612801a11f20ab27d46dfbbeff0efb80719f2a61206c52571b69801","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-16T21:44:14Z","title_canon_sha256":"4614a225b83a88908ac5fa3d9d989c8611d4e139a6b1bb01a06c6e933eedcff2"},"schema_version":"1.0","source":{"id":"1502.04733","kind":"arxiv","version":2}},"canonical_sha256":"a4722b81bd5204b5713f16dab38b9ab917f2c387dc9ba2dba883057674fd4d53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4722b81bd5204b5713f16dab38b9ab917f2c387dc9ba2dba883057674fd4d53","first_computed_at":"2026-05-18T01:33:16.090442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:16.090442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GK0mohWVpLsy+KktRJEXZdJmKm/Y8mJYBkKFqH23pVtMKz4AQCC7bt5P5NGYHRolwCJwUVzSi7/cRq2wUcGxDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:16.091072Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04733","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b396d1e1194e08a44c5e75dfa1e8fb31bbb64863458e90ffec97fd4e48cc369a","sha256:d9a88164e548e5256f58b1d0bd0cc669a03a08f604c10c9ac798d564e5a27485"],"state_sha256":"dd244bb2da42806ada0b53826200b7b338d0945bce4954024e688d088307267b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fEERnpx1h0Nnny5rIrY/hIyzdyhJ9KFM/yUy82d+lLTy/WMAk69t07nasVJr+y9CBfi1U/7/NVQGrMAdgz6BBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:00:28.790337Z","bundle_sha256":"a490f2cfe73d4a0d94fb12023531d23c5da492c41254033b5d1405f2ba5396b4"}}