{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UHJWFWI2HY2O4E56ZVKELS3I7Q","short_pith_number":"pith:UHJWFWI2","canonical_record":{"source":{"id":"1201.3828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-18T15:37:12Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"98df4aa38a2ed5e8539f8031b98f070e97bff3c65754a930e6e06ec4df432e20","abstract_canon_sha256":"238cd7d9a47f8588658b19cb68f371eca6f5ef6640739c9d1ff3fe392b0fa165"},"schema_version":"1.0"},"canonical_sha256":"a1d362d91a3e34ee13becd5445cb68fc008164d52bad9043d75090bf9f7d8b44","source":{"kind":"arxiv","id":"1201.3828","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3828","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3828v1","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3828","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"UHJWFWI2HY2O","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UHJWFWI2HY2O4E56","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UHJWFWI2","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UHJWFWI2HY2O4E56ZVKELS3I7Q","target":"record","payload":{"canonical_record":{"source":{"id":"1201.3828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-18T15:37:12Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"98df4aa38a2ed5e8539f8031b98f070e97bff3c65754a930e6e06ec4df432e20","abstract_canon_sha256":"238cd7d9a47f8588658b19cb68f371eca6f5ef6640739c9d1ff3fe392b0fa165"},"schema_version":"1.0"},"canonical_sha256":"a1d362d91a3e34ee13becd5445cb68fc008164d52bad9043d75090bf9f7d8b44","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:17.888801Z","signature_b64":"xLJJAe3D7esm4SVrtA5KkmZd3+p6mgMiJ4S7mgWRRiFnXQoks4/K50RQOpU2ZAW2PoeRv+P8PANrcQcP+whMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1d362d91a3e34ee13becd5445cb68fc008164d52bad9043d75090bf9f7d8b44","last_reissued_at":"2026-05-18T04:04:17.888256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:17.888256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.3828","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":"2026-05-18T04:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"St7sbCe+rn+eJGssdAJ4LVGv4wMVwmFKrtXLkfXnGNr79GZZDKjMcGe/YzGgRDf5jBXA1/Q0BW7BmAM8tC2bBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:07:36.589634Z"},"content_sha256":"e3d15832cc0d2ae51f364d201ed4e842f1a0d7b83e5ba3fe0ba7914ba56e8542","schema_version":"1.0","event_id":"sha256:e3d15832cc0d2ae51f364d201ed4e842f1a0d7b83e5ba3fe0ba7914ba56e8542"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UHJWFWI2HY2O4E56ZVKELS3I7Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalue distribution of large sample covariance matrices of linear processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Eckhard Schlemm, Oliver Pfaffel","submitted_at":"2012-01-18T15:37:12Z","abstract_excerpt":"We derive the distribution of the eigenvalues of a large sample covariance matrix when the data is dependent in time. More precisely, the dependence for each variable $i=1,...,p$ is modelled as a linear process $(X_{i,t})_{t=1,...,n}=(\\sum_{j=0}^\\infty c_j Z_{i,t-j})_{t=1,...,n}$, where $\\{Z_{i,t}\\}$ are assumed to be independent random variables with finite fourth moments. If the sample size $n$ and the number of variables $p=p_n$ both converge to infinity such that $y=\\lim_{n\\to\\infty}{n/p_n}>0$, then the empirical spectral distribution of $p^{-1}\\X\\X^T$ converges to a non\\hyp{}random distri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3828","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":"2026-05-18T04:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TvJbD9R9MckqAgSsTyniWSzCw3Vk6gL0Qlt42sGDFZDnFDAUtrKSpmG0wXqQXextu9pTbZgb3eV1RHDNTuKbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:07:36.589988Z"},"content_sha256":"57f268f5d1eb4dd6733c7973bebb586e6eddec1c261d5d6f735ef924f65d33cb","schema_version":"1.0","event_id":"sha256:57f268f5d1eb4dd6733c7973bebb586e6eddec1c261d5d6f735ef924f65d33cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UHJWFWI2HY2O4E56ZVKELS3I7Q/bundle.json","state_url":"https://pith.science/pith/UHJWFWI2HY2O4E56ZVKELS3I7Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UHJWFWI2HY2O4E56ZVKELS3I7Q/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":"2026-06-23T20:07:36Z","links":{"resolver":"https://pith.science/pith/UHJWFWI2HY2O4E56ZVKELS3I7Q","bundle":"https://pith.science/pith/UHJWFWI2HY2O4E56ZVKELS3I7Q/bundle.json","state":"https://pith.science/pith/UHJWFWI2HY2O4E56ZVKELS3I7Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UHJWFWI2HY2O4E56ZVKELS3I7Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UHJWFWI2HY2O4E56ZVKELS3I7Q","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":"238cd7d9a47f8588658b19cb68f371eca6f5ef6640739c9d1ff3fe392b0fa165","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-18T15:37:12Z","title_canon_sha256":"98df4aa38a2ed5e8539f8031b98f070e97bff3c65754a930e6e06ec4df432e20"},"schema_version":"1.0","source":{"id":"1201.3828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3828","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3828v1","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3828","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"UHJWFWI2HY2O","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UHJWFWI2HY2O4E56","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UHJWFWI2","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:57f268f5d1eb4dd6733c7973bebb586e6eddec1c261d5d6f735ef924f65d33cb","target":"graph","created_at":"2026-05-18T04:04:17Z","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 distribution of the eigenvalues of a large sample covariance matrix when the data is dependent in time. More precisely, the dependence for each variable $i=1,...,p$ is modelled as a linear process $(X_{i,t})_{t=1,...,n}=(\\sum_{j=0}^\\infty c_j Z_{i,t-j})_{t=1,...,n}$, where $\\{Z_{i,t}\\}$ are assumed to be independent random variables with finite fourth moments. If the sample size $n$ and the number of variables $p=p_n$ both converge to infinity such that $y=\\lim_{n\\to\\infty}{n/p_n}>0$, then the empirical spectral distribution of $p^{-1}\\X\\X^T$ converges to a non\\hyp{}random distri","authors_text":"Eckhard Schlemm, Oliver Pfaffel","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-18T15:37:12Z","title":"Eigenvalue distribution of large sample covariance matrices of linear processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3828","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:e3d15832cc0d2ae51f364d201ed4e842f1a0d7b83e5ba3fe0ba7914ba56e8542","target":"record","created_at":"2026-05-18T04:04:17Z","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":"238cd7d9a47f8588658b19cb68f371eca6f5ef6640739c9d1ff3fe392b0fa165","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-18T15:37:12Z","title_canon_sha256":"98df4aa38a2ed5e8539f8031b98f070e97bff3c65754a930e6e06ec4df432e20"},"schema_version":"1.0","source":{"id":"1201.3828","kind":"arxiv","version":1}},"canonical_sha256":"a1d362d91a3e34ee13becd5445cb68fc008164d52bad9043d75090bf9f7d8b44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1d362d91a3e34ee13becd5445cb68fc008164d52bad9043d75090bf9f7d8b44","first_computed_at":"2026-05-18T04:04:17.888256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:17.888256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xLJJAe3D7esm4SVrtA5KkmZd3+p6mgMiJ4S7mgWRRiFnXQoks4/K50RQOpU2ZAW2PoeRv+P8PANrcQcP+whMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:17.888801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3d15832cc0d2ae51f364d201ed4e842f1a0d7b83e5ba3fe0ba7914ba56e8542","sha256:57f268f5d1eb4dd6733c7973bebb586e6eddec1c261d5d6f735ef924f65d33cb"],"state_sha256":"85b10c8fec3d178a3d7f6ad29e076c178e58dc655266968472586ff35712a62c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Lj88Pr9MwJsgEdJWo053+VHy96jgoiALbCcPgYI4DjSG3+/31Y6jtbHQU5dSqxJuVKrZowZU4T/Rn7L0riqCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T20:07:36.591978Z","bundle_sha256":"517f874fc8ce6f4f98321804ce6303095dc7cd8fda398070084eb87808252fb2"}}