{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YEZ3KJF4AUTSRAZJDITNYE3DOH","short_pith_number":"pith:YEZ3KJF4","canonical_record":{"source":{"id":"1406.4184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-16T22:06:50Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"40570962b149cdf4b05e5ec79b970a4d0894e1ed1868b17149d7e76e0c728a2f","abstract_canon_sha256":"4edf2ca4cfcaff3b3fdb10652cbd2541992c2632adf5ab629b481d086500aa3b"},"schema_version":"1.0"},"canonical_sha256":"c133b524bc05272883291a26dc136371db8039046606a6eca0254242bd927258","source":{"kind":"arxiv","id":"1406.4184","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4184","created_at":"2026-05-18T02:38:43Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4184v1","created_at":"2026-05-18T02:38:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4184","created_at":"2026-05-18T02:38:43Z"},{"alias_kind":"pith_short_12","alias_value":"YEZ3KJF4AUTS","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YEZ3KJF4AUTSRAZJ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YEZ3KJF4","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YEZ3KJF4AUTSRAZJDITNYE3DOH","target":"record","payload":{"canonical_record":{"source":{"id":"1406.4184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-16T22:06:50Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"40570962b149cdf4b05e5ec79b970a4d0894e1ed1868b17149d7e76e0c728a2f","abstract_canon_sha256":"4edf2ca4cfcaff3b3fdb10652cbd2541992c2632adf5ab629b481d086500aa3b"},"schema_version":"1.0"},"canonical_sha256":"c133b524bc05272883291a26dc136371db8039046606a6eca0254242bd927258","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:43.979681Z","signature_b64":"c0wkpHTnSNb/HeJRBd3HmAanfzFkUeCDcs/fGiIm9YmaskCKRR8Omgwiai0zdxnjQVBK1S5uTb5v1e7l/9VtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c133b524bc05272883291a26dc136371db8039046606a6eca0254242bd927258","last_reissued_at":"2026-05-18T02:38:43.979280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:43.979280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.4184","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":"2026-05-18T02:38:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1SF9Kh64byZOSTWWw9YCLGgm4b1ZE/QMnKbz9IubnBADpfcgfT022rvtm4pprBW3aV4kRo7QyRflbguQawDfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T22:36:51.381840Z"},"content_sha256":"e9e207493c3074824b0f323a6781e0cb6bf6c67de6e240d44c92cb1e5d9a3a55","schema_version":"1.0","event_id":"sha256:e9e207493c3074824b0f323a6781e0cb6bf6c67de6e240d44c92cb1e5d9a3a55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YEZ3KJF4AUTSRAZJDITNYE3DOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral density of the non-central correlated Wishart ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Vinayak","submitted_at":"2014-06-16T22:06:50Z","abstract_excerpt":"Wishart ensembles of random matrix theory have been useful in modeling positive definite matrices encountered in classical and quantum chaotic systems. We consider nonzero means for the entries of the constituting matrix A which defines the correlated Wishart matrix as W = AA{\\dag}, and refer to the ensemble of such Wishart matrices as the non-central correlated Wishart ensemble (nc-CWE). We derive the Pastur self-consistent equation which describes the spectral density of nc-CWE at large matrix dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4184","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":"2026-05-18T02:38:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bIzr5poKhjh+jxOnFSMeirepCGjlzRIgw4lvlbrhW1MnGoayfwt0youwl3POPFogY2w0VYJBAN082bxkTLxpAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T22:36:51.382173Z"},"content_sha256":"51824c351cf43f2d892d3098ba1cd0bb3c1eca6c524f41971673378f3d41cde8","schema_version":"1.0","event_id":"sha256:51824c351cf43f2d892d3098ba1cd0bb3c1eca6c524f41971673378f3d41cde8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YEZ3KJF4AUTSRAZJDITNYE3DOH/bundle.json","state_url":"https://pith.science/pith/YEZ3KJF4AUTSRAZJDITNYE3DOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YEZ3KJF4AUTSRAZJDITNYE3DOH/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":"2026-06-26T22:36:51Z","links":{"resolver":"https://pith.science/pith/YEZ3KJF4AUTSRAZJDITNYE3DOH","bundle":"https://pith.science/pith/YEZ3KJF4AUTSRAZJDITNYE3DOH/bundle.json","state":"https://pith.science/pith/YEZ3KJF4AUTSRAZJDITNYE3DOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YEZ3KJF4AUTSRAZJDITNYE3DOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YEZ3KJF4AUTSRAZJDITNYE3DOH","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":"4edf2ca4cfcaff3b3fdb10652cbd2541992c2632adf5ab629b481d086500aa3b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-16T22:06:50Z","title_canon_sha256":"40570962b149cdf4b05e5ec79b970a4d0894e1ed1868b17149d7e76e0c728a2f"},"schema_version":"1.0","source":{"id":"1406.4184","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4184","created_at":"2026-05-18T02:38:43Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4184v1","created_at":"2026-05-18T02:38:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4184","created_at":"2026-05-18T02:38:43Z"},{"alias_kind":"pith_short_12","alias_value":"YEZ3KJF4AUTS","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YEZ3KJF4AUTSRAZJ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YEZ3KJF4","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:51824c351cf43f2d892d3098ba1cd0bb3c1eca6c524f41971673378f3d41cde8","target":"graph","created_at":"2026-05-18T02:38:43Z","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":"Wishart ensembles of random matrix theory have been useful in modeling positive definite matrices encountered in classical and quantum chaotic systems. We consider nonzero means for the entries of the constituting matrix A which defines the correlated Wishart matrix as W = AA{\\dag}, and refer to the ensemble of such Wishart matrices as the non-central correlated Wishart ensemble (nc-CWE). We derive the Pastur self-consistent equation which describes the spectral density of nc-CWE at large matrix dimension.","authors_text":"Vinayak","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-16T22:06:50Z","title":"Spectral density of the non-central correlated Wishart ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4184","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:e9e207493c3074824b0f323a6781e0cb6bf6c67de6e240d44c92cb1e5d9a3a55","target":"record","created_at":"2026-05-18T02:38:43Z","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":"4edf2ca4cfcaff3b3fdb10652cbd2541992c2632adf5ab629b481d086500aa3b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-16T22:06:50Z","title_canon_sha256":"40570962b149cdf4b05e5ec79b970a4d0894e1ed1868b17149d7e76e0c728a2f"},"schema_version":"1.0","source":{"id":"1406.4184","kind":"arxiv","version":1}},"canonical_sha256":"c133b524bc05272883291a26dc136371db8039046606a6eca0254242bd927258","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c133b524bc05272883291a26dc136371db8039046606a6eca0254242bd927258","first_computed_at":"2026-05-18T02:38:43.979280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:43.979280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c0wkpHTnSNb/HeJRBd3HmAanfzFkUeCDcs/fGiIm9YmaskCKRR8Omgwiai0zdxnjQVBK1S5uTb5v1e7l/9VtAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:43.979681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4184","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9e207493c3074824b0f323a6781e0cb6bf6c67de6e240d44c92cb1e5d9a3a55","sha256:51824c351cf43f2d892d3098ba1cd0bb3c1eca6c524f41971673378f3d41cde8"],"state_sha256":"c55a1552907beb06051e7cd6fd11e5aa041aa43bcf0c1249f0540746535853d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ctWAqFwdaew2tOs0+Fdnk/lluC5ihjs87Y5HFp8pPd3rj1zppsaLLn7G/vFSfm63lPZD2q7whPeK22veCHKjDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T22:36:51.384113Z","bundle_sha256":"3637c5a85f59fa89ecd53e508ad90fa4e1298c6411160515da4ef2876075e726"}}