{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JJTU4TOKOVKLAS6D4AHXMVH4LK","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":"920258cbef08ad0d6cd102432e41372c6efc0936c642d11fa679b067d2088ee8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-28T20:02:15Z","title_canon_sha256":"e26a18989763fa30016b8e9ab61ca45e1df4f888c9b90df42c7d6e3b9da4ebb7"},"schema_version":"1.0","source":{"id":"1110.6449","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6449","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6449v2","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6449","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"JJTU4TOKOVKL","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JJTU4TOKOVKLAS6D","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JJTU4TOK","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:2b4555c6c4cb0da8b13e166b625086bf20744a1c036bfd38267c035ae0bc121f","target":"graph","created_at":"2026-05-18T03:55:12Z","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 analyse the spectrum of additive finite-rank deformations of $N \\times N$ Wigner matrices $H$. The spectrum of the deformed matrix undergoes a transition, associated with the creation or annihilation of an outlier, when an eigenvalue $d_i$ of the deformation crosses a critical value $\\pm 1$. This transition happens on the scale $|d_i| - 1 \\sim N^{-1/3}$. We allow the eigenvalues $d_i$ of the deformation to depend on $N$ under the condition $|\\abs{d_i} - 1| \\geq (\\log N)^{C \\log \\log N} N^{-1/3}$. We make no assumptions on the eigenvectors of the deformation. In the limit $N \\to \\infty$, we ","authors_text":"Antti Knowles, Jun Yin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-28T20:02:15Z","title":"The Isotropic Semicircle Law and Deformation of Wigner Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6449","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":"sha256:811c3e17fd9db925281004a79ae920a4f7c137689a068326277f207c33b67cf9","target":"record","created_at":"2026-05-18T03:55:12Z","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":"920258cbef08ad0d6cd102432e41372c6efc0936c642d11fa679b067d2088ee8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-28T20:02:15Z","title_canon_sha256":"e26a18989763fa30016b8e9ab61ca45e1df4f888c9b90df42c7d6e3b9da4ebb7"},"schema_version":"1.0","source":{"id":"1110.6449","kind":"arxiv","version":2}},"canonical_sha256":"4a674e4dca7554b04bc3e00f7654fc5ab691f5123b4ddb7a46dd61cc9583161b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a674e4dca7554b04bc3e00f7654fc5ab691f5123b4ddb7a46dd61cc9583161b","first_computed_at":"2026-05-18T03:55:12.230079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:12.230079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tg/wJwhbNXoy+pnOLneWNOEHdFFWzk0Hzv+D27yg8XJKk2RBKPaqTd7g9e32ceUZebu7p8UmSW0xcdlg9f/OBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:12.230515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6449","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:811c3e17fd9db925281004a79ae920a4f7c137689a068326277f207c33b67cf9","sha256:2b4555c6c4cb0da8b13e166b625086bf20744a1c036bfd38267c035ae0bc121f"],"state_sha256":"336eab49ec1d526bcc1993321327bf54595882dc2a0d571766587a66d978806d"}