{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HXKZJLLCENAVOIYVLNJRKBSI7Q","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":"d63db5997595be03d57ef0d6a0661747a26ccfc24f11ede3327cb33ae727512b","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-13T08:18:09Z","title_canon_sha256":"838e89604cbc76dd94cb8b676155d1765fcb30817c72e7edf5f96caf2feb4d36"},"schema_version":"1.0","source":{"id":"1808.04098","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04098","created_at":"2026-05-18T00:08:18Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04098v1","created_at":"2026-05-18T00:08:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04098","created_at":"2026-05-18T00:08:18Z"},{"alias_kind":"pith_short_12","alias_value":"HXKZJLLCENAV","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HXKZJLLCENAVOIYV","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HXKZJLLC","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:85ada21a345ded534e7d4830c3601b9c012a973dd27a1c6153e1ba75c854652f","target":"graph","created_at":"2026-05-18T00:08:18Z","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 investigate eigenvectors of rank-one deformations of random matrices $\\boldsymbol B = \\boldsymbol A + \\theta \\boldsymbol {uu}^*$ in which $\\boldsymbol A \\in \\mathbb R^{N \\times N}$ is a Wigner real symmetric random matrix, $\\theta \\in \\mathbb R^+$, and $\\boldsymbol u$ is uniformly distributed on the unit sphere. It is well known that for $\\theta > 1$ the eigenvector associated with the largest eigenvalue of $\\boldsymbol B$ closely estimates $\\boldsymbol u$ asymptotically, while for $\\theta < 1$ the eigenvectors of $\\boldsymbol B$ are uninformative about $\\boldsymbol u$. We examine $\\mathcal","authors_text":"Arash Amini, Farzan Haddadi","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-13T08:18:09Z","title":"Eigenvectors of Deformed Wigner Random Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04098","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":"sha256:5c6326145bbe8aaaf53108202facdb26d3c294fe6323ff7baf0ad4b9ae08b9c2","target":"record","created_at":"2026-05-18T00:08:18Z","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":"d63db5997595be03d57ef0d6a0661747a26ccfc24f11ede3327cb33ae727512b","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-13T08:18:09Z","title_canon_sha256":"838e89604cbc76dd94cb8b676155d1765fcb30817c72e7edf5f96caf2feb4d36"},"schema_version":"1.0","source":{"id":"1808.04098","kind":"arxiv","version":1}},"canonical_sha256":"3dd594ad6223415723155b53150648fc017fe462d58815e65d1b3ee189225772","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dd594ad6223415723155b53150648fc017fe462d58815e65d1b3ee189225772","first_computed_at":"2026-05-18T00:08:18.885466Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:18.885466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MTtDtzMniXh5wSFzsE0UCzEgFxzRaZuvs64K476Op1zHCQpV4r8nGNWmkliZQ6HOWVBbucVdSLon/psWgQeAAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:18.885929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.04098","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c6326145bbe8aaaf53108202facdb26d3c294fe6323ff7baf0ad4b9ae08b9c2","sha256:85ada21a345ded534e7d4830c3601b9c012a973dd27a1c6153e1ba75c854652f"],"state_sha256":"46a4802b8522985c765ad72ceeda59f288cddb711541ac0b3d09c29cd3cd2518"}