{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:UKP3LOQTWXDTPLAUPHBEBETOX6","short_pith_number":"pith:UKP3LOQT","schema_version":"1.0","canonical_sha256":"a29fb5ba13b5c737ac1479c240926ebf86de5f29a96c9aed2c6ff43fb8975880","source":{"kind":"arxiv","id":"1412.7108","version":4},"attestation_state":"computed","paper":{"title":"The eigenvectors of Gaussian matrices with an external source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"math.PR","authors_text":"Jean-Philippe Bouchaud, Jo\\\"el Bun, Romain Allez","submitted_at":"2014-12-22T19:33:48Z","abstract_excerpt":"We consider a diffusive matrix process $(X_t)_{t\\ge 0}$ defined as $X_t:=A+H_t$ where $A$ is a given deterministic Hermitian matrix and $(H_t)_{t\\ge 0}$ is a Hermitian Brownian motion. The matrix $A$ is the \"external source\" that one would like to estimate from the noisy observation $X_t$ at some time $t>0$. We investigate the relationship between the non-perturbed eigenvectors of the matrix $A$ and the perturbed eigenstates at some time $t$ for the three relevant scaling relations between the time $t$ and the dimension $N$ of the matrix $X_t$. We determine the asymptotic (mean-squared) projec"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1412.7108","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-22T19:33:48Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"6cdd3c91149edb268b9cce67c38cc369b9c1742f1d00ffc377621dc491edaf6d","abstract_canon_sha256":"00bedb1a2a3763e9b54d8c6b06c5e3eda6805e196908cd4dbf335e7c36bda7e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:02.308433Z","signature_b64":"9XMUtyxZwyWnUklmop0O7EC+bpwoFzoovuOJVc5JZar3r4uEFSVOHhyDNHwQQjjp1hTp2WYwUdcTYwZ35+KpCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a29fb5ba13b5c737ac1479c240926ebf86de5f29a96c9aed2c6ff43fb8975880","last_reissued_at":"2026-05-18T02:29:02.307963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:02.307963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The eigenvectors of Gaussian matrices with an external source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"math.PR","authors_text":"Jean-Philippe Bouchaud, Jo\\\"el Bun, Romain Allez","submitted_at":"2014-12-22T19:33:48Z","abstract_excerpt":"We consider a diffusive matrix process $(X_t)_{t\\ge 0}$ defined as $X_t:=A+H_t$ where $A$ is a given deterministic Hermitian matrix and $(H_t)_{t\\ge 0}$ is a Hermitian Brownian motion. The matrix $A$ is the \"external source\" that one would like to estimate from the noisy observation $X_t$ at some time $t>0$. We investigate the relationship between the non-perturbed eigenvectors of the matrix $A$ and the perturbed eigenstates at some time $t$ for the three relevant scaling relations between the time $t$ and the dimension $N$ of the matrix $X_t$. We determine the asymptotic (mean-squared) projec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7108","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1412.7108","created_at":"2026-05-18T02:29:02.308041+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.7108v4","created_at":"2026-05-18T02:29:02.308041+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7108","created_at":"2026-05-18T02:29:02.308041+00:00"},{"alias_kind":"pith_short_12","alias_value":"UKP3LOQTWXDT","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UKP3LOQTWXDTPLAU","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UKP3LOQT","created_at":"2026-05-18T12:28:52.271510+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2111.08031","citing_title":"Circular Rosenzweig-Porter random matrix ensemble","ref_index":61,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UKP3LOQTWXDTPLAUPHBEBETOX6","json":"https://pith.science/pith/UKP3LOQTWXDTPLAUPHBEBETOX6.json","graph_json":"https://pith.science/api/pith-number/UKP3LOQTWXDTPLAUPHBEBETOX6/graph.json","events_json":"https://pith.science/api/pith-number/UKP3LOQTWXDTPLAUPHBEBETOX6/events.json","paper":"https://pith.science/paper/UKP3LOQT"},"agent_actions":{"view_html":"https://pith.science/pith/UKP3LOQTWXDTPLAUPHBEBETOX6","download_json":"https://pith.science/pith/UKP3LOQTWXDTPLAUPHBEBETOX6.json","view_paper":"https://pith.science/paper/UKP3LOQT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.7108&json=true","fetch_graph":"https://pith.science/api/pith-number/UKP3LOQTWXDTPLAUPHBEBETOX6/graph.json","fetch_events":"https://pith.science/api/pith-number/UKP3LOQTWXDTPLAUPHBEBETOX6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UKP3LOQTWXDTPLAUPHBEBETOX6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UKP3LOQTWXDTPLAUPHBEBETOX6/action/storage_attestation","attest_author":"https://pith.science/pith/UKP3LOQTWXDTPLAUPHBEBETOX6/action/author_attestation","sign_citation":"https://pith.science/pith/UKP3LOQTWXDTPLAUPHBEBETOX6/action/citation_signature","submit_replication":"https://pith.science/pith/UKP3LOQTWXDTPLAUPHBEBETOX6/action/replication_record"}},"created_at":"2026-05-18T02:29:02.308041+00:00","updated_at":"2026-05-18T02:29:02.308041+00:00"}