{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HYM3A5JWKYPBAMHZHJHYZ3TSLS","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":"80dbb547c9614d453cb58b4318baab116679f3958c17a5473f2f0517465bb2bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-18T12:52:21Z","title_canon_sha256":"51dc96bbdeb87cc37f1b1a8159a0555fd8353765203401868bafaa8e7c866be9"},"schema_version":"1.0","source":{"id":"1006.3684","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3684","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3684v3","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3684","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"HYM3A5JWKYPB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HYM3A5JWKYPBAMHZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HYM3A5JW","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:7495751498fcc8b306651fba69025ad3fb5e5ba20ef6e47396e61521af369e8d","target":"graph","created_at":"2026-05-18T04:12:56Z","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 the asymptotic behavior of the eigenvalues of spiked perturbations of Wigner matrices when the dimension goes to infinity. The entries of the Hermitian Wigner matrix have a distribution which is symmetric and satisfies a Poincar\\'e inequality. The perturbation matrix is a deterministic Hermitian matrix whose spectral measure converges to some probability measure with compact support. We assume that this perturbation matrix has a fixed number of fixed eigenvalues (spikes) outside the support of its limiting spectral measure whereas the distance between the other eigenvalues and t","authors_text":"Catherine Donati-Martin, Delphine F\\'eral, Maxime F\\'evrier, Mireille Capitaine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-18T12:52:21Z","title":"Free convolution with a semi-circular distribution and eigenvalues of spiked deformations of Wigner matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3684","kind":"arxiv","version":3},"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":"sha256:6cc8ad534e000e95c7e6bc107a66deb13f522d154ae6c145686f6640ea90bb21","target":"record","created_at":"2026-05-18T04:12:56Z","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":"80dbb547c9614d453cb58b4318baab116679f3958c17a5473f2f0517465bb2bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-18T12:52:21Z","title_canon_sha256":"51dc96bbdeb87cc37f1b1a8159a0555fd8353765203401868bafaa8e7c866be9"},"schema_version":"1.0","source":{"id":"1006.3684","kind":"arxiv","version":3}},"canonical_sha256":"3e19b07536561e1030f93a4f8cee725ca443af1747178354a0997bbb5500e45c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e19b07536561e1030f93a4f8cee725ca443af1747178354a0997bbb5500e45c","first_computed_at":"2026-05-18T04:12:56.495308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:56.495308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0DVuICnrRBwb6G5gb4f73V6OrARHJ6/N4yX9etBFPchIU6gg5wJulHRANP12WA2yuarx6hZ+4t4zQzMxCPH2Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:56.496161Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.3684","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cc8ad534e000e95c7e6bc107a66deb13f522d154ae6c145686f6640ea90bb21","sha256:7495751498fcc8b306651fba69025ad3fb5e5ba20ef6e47396e61521af369e8d"],"state_sha256":"534b75b88aa3b8be1a6942568bd9c422017cb38065a850f6989d1906b8dc73c3"}