{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JUW3M7L5J2B2WK7NULZAUPSGSF","short_pith_number":"pith:JUW3M7L5","canonical_record":{"source":{"id":"1306.2242","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-10T16:18:23Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"747310e4130ab73d0af188f1027f6085c200404511033974620b96a857641821","abstract_canon_sha256":"f3c070407369f7599f88f1bd7f7069b461172d74bb4c0bf28708107263ac0955"},"schema_version":"1.0"},"canonical_sha256":"4d2db67d7d4e83ab2beda2f20a3e4691685bcbebdead1bcfaa2e2a7896e56966","source":{"kind":"arxiv","id":"1306.2242","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2242","created_at":"2026-05-18T03:09:48Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2242v2","created_at":"2026-05-18T03:09:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2242","created_at":"2026-05-18T03:09:48Z"},{"alias_kind":"pith_short_12","alias_value":"JUW3M7L5J2B2","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JUW3M7L5J2B2WK7N","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JUW3M7L5","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JUW3M7L5J2B2WK7NULZAUPSGSF","target":"record","payload":{"canonical_record":{"source":{"id":"1306.2242","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-10T16:18:23Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"747310e4130ab73d0af188f1027f6085c200404511033974620b96a857641821","abstract_canon_sha256":"f3c070407369f7599f88f1bd7f7069b461172d74bb4c0bf28708107263ac0955"},"schema_version":"1.0"},"canonical_sha256":"4d2db67d7d4e83ab2beda2f20a3e4691685bcbebdead1bcfaa2e2a7896e56966","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:48.289517Z","signature_b64":"WQrKcxd1ccEiIwUQQ5b5g568MqyJRoTiE93yvxEw77C4NTFbI9OuWXP6Q1m9aq0zlXriVuR+qq7G20AM5IZwCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d2db67d7d4e83ab2beda2f20a3e4691685bcbebdead1bcfaa2e2a7896e56966","last_reissued_at":"2026-05-18T03:09:48.288604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:48.288604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.2242","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":"2026-05-18T03:09:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XsjCkNFOm8V2Q4SdirCu4iqlsSHa9In2DxRA6kOTqBgP98vaaqmpVsOoQbpvcP+X9wXzTugzMhwxSUc3khhrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:03:16.844837Z"},"content_sha256":"775bea334ce7f679b8a6c4d3e3d479680c3da3f906d0c4d9589a1faef10e5af7","schema_version":"1.0","event_id":"sha256:775bea334ce7f679b8a6c4d3e3d479680c3da3f906d0c4d9589a1faef10e5af7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JUW3M7L5J2B2WK7NULZAUPSGSF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral density of a Wishart model for nonsymmetric Correlation Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Vinayak","submitted_at":"2013-06-10T16:18:23Z","abstract_excerpt":"The Wishart model for real symmetric correlation matrices is defined as $\\mathsf{W}=\\mathsf{AA}^{t}$, where matrix $\\mathsf{A}$ is usually a rectangular Gaussian random matrix and $\\mathsf{A}^{t}$ is the transpose of $\\mathsf{A}$. Analogously, for nonsymmetric correlation matrices, a model may be defined for two statistically equivalent but different matrices $\\mathsf{A}$ and $\\mathsf{B}$ as $\\mathsf{AB}^{t}$. The corresponding Wishart model, thus, is defined as $\\mathbf{C}=\\mathsf{AB}^{t}\\mathsf{BA}^{t}$. We study the spectral density of $\\mathbf{C}$ for the case when $\\mathsf{A}$ and $\\maths"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2242","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":"2026-05-18T03:09:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w99I0d0ukUm1yXTW7KO9cbDUiatjjxZ24P0bLZB2CAwUo9IgwJ8Z8mVwCnQycZqOtfcStqMF8KcFT30RciSkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:03:16.845199Z"},"content_sha256":"0d6f0f11f26acb3c752a28c8e3bcb6b75e90f3b11a75935219bdc861d97b4a62","schema_version":"1.0","event_id":"sha256:0d6f0f11f26acb3c752a28c8e3bcb6b75e90f3b11a75935219bdc861d97b4a62"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JUW3M7L5J2B2WK7NULZAUPSGSF/bundle.json","state_url":"https://pith.science/pith/JUW3M7L5J2B2WK7NULZAUPSGSF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JUW3M7L5J2B2WK7NULZAUPSGSF/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":"2026-06-26T23:03:16Z","links":{"resolver":"https://pith.science/pith/JUW3M7L5J2B2WK7NULZAUPSGSF","bundle":"https://pith.science/pith/JUW3M7L5J2B2WK7NULZAUPSGSF/bundle.json","state":"https://pith.science/pith/JUW3M7L5J2B2WK7NULZAUPSGSF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JUW3M7L5J2B2WK7NULZAUPSGSF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JUW3M7L5J2B2WK7NULZAUPSGSF","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":"f3c070407369f7599f88f1bd7f7069b461172d74bb4c0bf28708107263ac0955","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-10T16:18:23Z","title_canon_sha256":"747310e4130ab73d0af188f1027f6085c200404511033974620b96a857641821"},"schema_version":"1.0","source":{"id":"1306.2242","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2242","created_at":"2026-05-18T03:09:48Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2242v2","created_at":"2026-05-18T03:09:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2242","created_at":"2026-05-18T03:09:48Z"},{"alias_kind":"pith_short_12","alias_value":"JUW3M7L5J2B2","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JUW3M7L5J2B2WK7N","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JUW3M7L5","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:0d6f0f11f26acb3c752a28c8e3bcb6b75e90f3b11a75935219bdc861d97b4a62","target":"graph","created_at":"2026-05-18T03:09:48Z","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":"The Wishart model for real symmetric correlation matrices is defined as $\\mathsf{W}=\\mathsf{AA}^{t}$, where matrix $\\mathsf{A}$ is usually a rectangular Gaussian random matrix and $\\mathsf{A}^{t}$ is the transpose of $\\mathsf{A}$. Analogously, for nonsymmetric correlation matrices, a model may be defined for two statistically equivalent but different matrices $\\mathsf{A}$ and $\\mathsf{B}$ as $\\mathsf{AB}^{t}$. The corresponding Wishart model, thus, is defined as $\\mathbf{C}=\\mathsf{AB}^{t}\\mathsf{BA}^{t}$. We study the spectral density of $\\mathbf{C}$ for the case when $\\mathsf{A}$ and $\\maths","authors_text":"Vinayak","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-10T16:18:23Z","title":"Spectral density of a Wishart model for nonsymmetric Correlation Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2242","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":"sha256:775bea334ce7f679b8a6c4d3e3d479680c3da3f906d0c4d9589a1faef10e5af7","target":"record","created_at":"2026-05-18T03:09:48Z","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":"f3c070407369f7599f88f1bd7f7069b461172d74bb4c0bf28708107263ac0955","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-10T16:18:23Z","title_canon_sha256":"747310e4130ab73d0af188f1027f6085c200404511033974620b96a857641821"},"schema_version":"1.0","source":{"id":"1306.2242","kind":"arxiv","version":2}},"canonical_sha256":"4d2db67d7d4e83ab2beda2f20a3e4691685bcbebdead1bcfaa2e2a7896e56966","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d2db67d7d4e83ab2beda2f20a3e4691685bcbebdead1bcfaa2e2a7896e56966","first_computed_at":"2026-05-18T03:09:48.288604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:48.288604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WQrKcxd1ccEiIwUQQ5b5g568MqyJRoTiE93yvxEw77C4NTFbI9OuWXP6Q1m9aq0zlXriVuR+qq7G20AM5IZwCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:48.289517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2242","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:775bea334ce7f679b8a6c4d3e3d479680c3da3f906d0c4d9589a1faef10e5af7","sha256:0d6f0f11f26acb3c752a28c8e3bcb6b75e90f3b11a75935219bdc861d97b4a62"],"state_sha256":"149a4fa9cf0d343970bad21edba7fca0a3cc645f50d13d5b6d540210234ebbcc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gt72Th2ZCR695iI/ZkOCcU3BAplvLVL5DIa6mMCglZjWq4mqF/9L9LdjlFAWL2AqiBpr7zWZR0v9Pc6u0M+JAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:03:16.847909Z","bundle_sha256":"13d94e6b613228d58de0d620e796643d4a7350a682817003e8c5fe14cf47d730"}}