{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:F575U2I52JHOHQI732P2L4U6CA","short_pith_number":"pith:F575U2I5","canonical_record":{"source":{"id":"1604.03638","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-13T02:51:31Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"89ff826245e80281f8415ffdb9e0eda44789bf75e634335fb0bd844f0e896220","abstract_canon_sha256":"6ac23d8ac981963141e7c604e8dfdeb9a626822a040cefb65deca98a8b75f9ad"},"schema_version":"1.0"},"canonical_sha256":"2f7fda691dd24ee3c11fde9fa5f29e10027de0b1dfe3129c67de25289257186c","source":{"kind":"arxiv","id":"1604.03638","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03638","created_at":"2026-05-18T00:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03638v2","created_at":"2026-05-18T00:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03638","created_at":"2026-05-18T00:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"F575U2I52JHO","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F575U2I52JHOHQI7","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F575U2I5","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:F575U2I52JHOHQI732P2L4U6CA","target":"record","payload":{"canonical_record":{"source":{"id":"1604.03638","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-13T02:51:31Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"89ff826245e80281f8415ffdb9e0eda44789bf75e634335fb0bd844f0e896220","abstract_canon_sha256":"6ac23d8ac981963141e7c604e8dfdeb9a626822a040cefb65deca98a8b75f9ad"},"schema_version":"1.0"},"canonical_sha256":"2f7fda691dd24ee3c11fde9fa5f29e10027de0b1dfe3129c67de25289257186c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:47.085253Z","signature_b64":"MsDNDEwWTYpFFMm/idrZkDjr7mqgqDlax8QKLTL5t30QYa20G/UWGagwQWVYOKjfBlk+p5IiReGUiNPzmXxmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f7fda691dd24ee3c11fde9fa5f29e10027de0b1dfe3129c67de25289257186c","last_reissued_at":"2026-05-18T00:49:47.084717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:47.084717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.03638","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":"2026-05-18T00:49:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1TwQUCICDZH6x3CYOmqp14/OoNTVcfjvO2ix6NB3c0oBmjqgbadEJdVyMebpJueByyLLVaxbm6yahORjGXkHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:09:45.429142Z"},"content_sha256":"2cca9bbb8f02cb86304e0af2d810dad25f0f5b5a5c24f53cb1a54073b3b65f1f","schema_version":"1.0","event_id":"sha256:2cca9bbb8f02cb86304e0af2d810dad25f0f5b5a5c24f53cb1a54073b3b65f1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:F575U2I52JHOHQI732P2L4U6CA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the inference about the spectral distribution of high-dimensional covariance matrix based on high-frequency noisy observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Ningning Xia, Xinghua Zheng","submitted_at":"2016-04-13T02:51:31Z","abstract_excerpt":"In practice, observations are often contaminated by noise, making the resulting sample covariance matrix a signal-plus-noise sample covariance matrix. Aiming to make inferences about the spectral distribution of the population covariance matrix under such a situation, we establish an asymptotic relationship that describes how the limiting spectral distribution of (signal) sample covariance matrices depends on that of signal-plus-noise-type sample covariance matrices. As an application, we consider inferences about the spectral distribution of integrated covolatility (ICV) matrices of high-dime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03638","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":"2026-05-18T00:49:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SjR9zqrT2jUmn+ddXfLwxl4QrEoi0uVpkuBHdGiimB7IuEVGJrFrmDErTl8CIEATgORddT1844QHDNsio1HnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:09:45.429852Z"},"content_sha256":"90c6e34550229af763b1f6604635b7f9f0a7fae38a8d9e6fb68cf113a37cbab0","schema_version":"1.0","event_id":"sha256:90c6e34550229af763b1f6604635b7f9f0a7fae38a8d9e6fb68cf113a37cbab0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F575U2I52JHOHQI732P2L4U6CA/bundle.json","state_url":"https://pith.science/pith/F575U2I52JHOHQI732P2L4U6CA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F575U2I52JHOHQI732P2L4U6CA/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":"2026-06-11T08:09:45Z","links":{"resolver":"https://pith.science/pith/F575U2I52JHOHQI732P2L4U6CA","bundle":"https://pith.science/pith/F575U2I52JHOHQI732P2L4U6CA/bundle.json","state":"https://pith.science/pith/F575U2I52JHOHQI732P2L4U6CA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F575U2I52JHOHQI732P2L4U6CA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:F575U2I52JHOHQI732P2L4U6CA","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":"6ac23d8ac981963141e7c604e8dfdeb9a626822a040cefb65deca98a8b75f9ad","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-13T02:51:31Z","title_canon_sha256":"89ff826245e80281f8415ffdb9e0eda44789bf75e634335fb0bd844f0e896220"},"schema_version":"1.0","source":{"id":"1604.03638","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03638","created_at":"2026-05-18T00:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03638v2","created_at":"2026-05-18T00:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03638","created_at":"2026-05-18T00:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"F575U2I52JHO","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F575U2I52JHOHQI7","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F575U2I5","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:90c6e34550229af763b1f6604635b7f9f0a7fae38a8d9e6fb68cf113a37cbab0","target":"graph","created_at":"2026-05-18T00:49:47Z","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 practice, observations are often contaminated by noise, making the resulting sample covariance matrix a signal-plus-noise sample covariance matrix. Aiming to make inferences about the spectral distribution of the population covariance matrix under such a situation, we establish an asymptotic relationship that describes how the limiting spectral distribution of (signal) sample covariance matrices depends on that of signal-plus-noise-type sample covariance matrices. As an application, we consider inferences about the spectral distribution of integrated covolatility (ICV) matrices of high-dime","authors_text":"Ningning Xia, Xinghua Zheng","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-13T02:51:31Z","title":"On the inference about the spectral distribution of high-dimensional covariance matrix based on high-frequency noisy observations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03638","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":"sha256:2cca9bbb8f02cb86304e0af2d810dad25f0f5b5a5c24f53cb1a54073b3b65f1f","target":"record","created_at":"2026-05-18T00:49:47Z","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":"6ac23d8ac981963141e7c604e8dfdeb9a626822a040cefb65deca98a8b75f9ad","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-13T02:51:31Z","title_canon_sha256":"89ff826245e80281f8415ffdb9e0eda44789bf75e634335fb0bd844f0e896220"},"schema_version":"1.0","source":{"id":"1604.03638","kind":"arxiv","version":2}},"canonical_sha256":"2f7fda691dd24ee3c11fde9fa5f29e10027de0b1dfe3129c67de25289257186c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f7fda691dd24ee3c11fde9fa5f29e10027de0b1dfe3129c67de25289257186c","first_computed_at":"2026-05-18T00:49:47.084717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:47.084717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MsDNDEwWTYpFFMm/idrZkDjr7mqgqDlax8QKLTL5t30QYa20G/UWGagwQWVYOKjfBlk+p5IiReGUiNPzmXxmDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:47.085253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.03638","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cca9bbb8f02cb86304e0af2d810dad25f0f5b5a5c24f53cb1a54073b3b65f1f","sha256:90c6e34550229af763b1f6604635b7f9f0a7fae38a8d9e6fb68cf113a37cbab0"],"state_sha256":"1da06156f303ccda76219830e9632fe789d8db374e006a4d0c425f0b864cadd4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4/eKrqUxmVS3bzRwxN+JYs8uFGcjrMWPEgPac4XDLgCkXRV0pXuFIk+v/7pYojGAFGAtGuqaEUFZ6XNnjeadAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:09:45.434259Z","bundle_sha256":"a4a03a0ca26a7f76947d42ebeba00ed844b31a3cad77f8f1276b7e66f0954d9a"}}