{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:K2V7CRJBTKZ26HAO75IVQFVLSV","short_pith_number":"pith:K2V7CRJB","canonical_record":{"source":{"id":"1810.02538","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-05T06:51:11Z","cross_cats_sorted":[],"title_canon_sha256":"9a6d4fbe211c11446ccab7baa03128f8a2b7a94b6fad9d98f7733a62a52423ba","abstract_canon_sha256":"79c235568c895c5372f5fb0595dc98d1e055f7f648791bd5b2a275eb474a7d9a"},"schema_version":"1.0"},"canonical_sha256":"56abf145219ab3af1c0eff515816ab95548ccea38899e1359748505dcfa08f7b","source":{"kind":"arxiv","id":"1810.02538","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02538","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02538v2","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02538","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"pith_short_12","alias_value":"K2V7CRJBTKZ2","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K2V7CRJBTKZ26HAO","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K2V7CRJB","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:K2V7CRJBTKZ26HAO75IVQFVLSV","target":"record","payload":{"canonical_record":{"source":{"id":"1810.02538","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-05T06:51:11Z","cross_cats_sorted":[],"title_canon_sha256":"9a6d4fbe211c11446ccab7baa03128f8a2b7a94b6fad9d98f7733a62a52423ba","abstract_canon_sha256":"79c235568c895c5372f5fb0595dc98d1e055f7f648791bd5b2a275eb474a7d9a"},"schema_version":"1.0"},"canonical_sha256":"56abf145219ab3af1c0eff515816ab95548ccea38899e1359748505dcfa08f7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:57.591970Z","signature_b64":"ZO3CW60N5566gfeA8xTes6crpHz/liOKn+D7YJJfxwXGfr8RdBt1ueIrDUaoOrvUQxBsygqfHYpVzQOhneIDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56abf145219ab3af1c0eff515816ab95548ccea38899e1359748505dcfa08f7b","last_reissued_at":"2026-05-17T23:59:57.591259Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:57.591259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.02538","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":"2026-05-17T23:59:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iSjDPDTdyHEGfXpXZzbKgSwNT3r+X+bLCNnOuEqOo+VDiBmYyuASaa/66AG7Rn1OUQxOzwYmOYx43JV6Jt9uCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:45:03.032154Z"},"content_sha256":"90bcaf0cc77273757e2cce3a05a314fa721d8c651d0c8c7ec9baf0779dcf9109","schema_version":"1.0","event_id":"sha256:90bcaf0cc77273757e2cce3a05a314fa721d8c651d0c8c7ec9baf0779dcf9109"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:K2V7CRJBTKZ26HAO75IVQFVLSV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large deviations for the largest eigenvalue of the sum of two random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alice Guionnet (UMPA-ENSL, CNRS), Myl\\`ene Ma\\\"ida (LPP)","submitted_at":"2018-10-05T06:51:11Z","abstract_excerpt":"In this paper, we consider the addition of two matrices in generic position, namely A + U BU * , where U is drawn under the Haar measure on the unitary or the orthogonal group. We show that, under mild conditions on the empirical spectral measures of the deterministic matrices A and B, the law of the largest eigenvalue satisfies a large deviation principle, in the scale N, with an explicit rate function involving the limit of spherical integrals. We cover in particular all the cases when A and B have no outliers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02538","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":"2026-05-17T23:59:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4o+aZ2ad2IgdWSpwdDpmF58w4l1k3EA0ug/3SZkpDciLhO8ugDrjhRR0xndt8X+ohSldMr2uO6d5cX9CXlwGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:45:03.032806Z"},"content_sha256":"2ff60224b3216dca00bc8d6b12f39acd21fffacd2fd355e19c42af4117b64ef9","schema_version":"1.0","event_id":"sha256:2ff60224b3216dca00bc8d6b12f39acd21fffacd2fd355e19c42af4117b64ef9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K2V7CRJBTKZ26HAO75IVQFVLSV/bundle.json","state_url":"https://pith.science/pith/K2V7CRJBTKZ26HAO75IVQFVLSV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K2V7CRJBTKZ26HAO75IVQFVLSV/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":"2026-05-23T23:45:03Z","links":{"resolver":"https://pith.science/pith/K2V7CRJBTKZ26HAO75IVQFVLSV","bundle":"https://pith.science/pith/K2V7CRJBTKZ26HAO75IVQFVLSV/bundle.json","state":"https://pith.science/pith/K2V7CRJBTKZ26HAO75IVQFVLSV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K2V7CRJBTKZ26HAO75IVQFVLSV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:K2V7CRJBTKZ26HAO75IVQFVLSV","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":"79c235568c895c5372f5fb0595dc98d1e055f7f648791bd5b2a275eb474a7d9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-05T06:51:11Z","title_canon_sha256":"9a6d4fbe211c11446ccab7baa03128f8a2b7a94b6fad9d98f7733a62a52423ba"},"schema_version":"1.0","source":{"id":"1810.02538","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02538","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02538v2","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02538","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"pith_short_12","alias_value":"K2V7CRJBTKZ2","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K2V7CRJBTKZ26HAO","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K2V7CRJB","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:2ff60224b3216dca00bc8d6b12f39acd21fffacd2fd355e19c42af4117b64ef9","target":"graph","created_at":"2026-05-17T23:59:57Z","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":"In this paper, we consider the addition of two matrices in generic position, namely A + U BU * , where U is drawn under the Haar measure on the unitary or the orthogonal group. We show that, under mild conditions on the empirical spectral measures of the deterministic matrices A and B, the law of the largest eigenvalue satisfies a large deviation principle, in the scale N, with an explicit rate function involving the limit of spherical integrals. We cover in particular all the cases when A and B have no outliers.","authors_text":"Alice Guionnet (UMPA-ENSL, CNRS), Myl\\`ene Ma\\\"ida (LPP)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-05T06:51:11Z","title":"Large deviations for the largest eigenvalue of the sum of two random matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02538","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":"sha256:90bcaf0cc77273757e2cce3a05a314fa721d8c651d0c8c7ec9baf0779dcf9109","target":"record","created_at":"2026-05-17T23:59:57Z","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":"79c235568c895c5372f5fb0595dc98d1e055f7f648791bd5b2a275eb474a7d9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-05T06:51:11Z","title_canon_sha256":"9a6d4fbe211c11446ccab7baa03128f8a2b7a94b6fad9d98f7733a62a52423ba"},"schema_version":"1.0","source":{"id":"1810.02538","kind":"arxiv","version":2}},"canonical_sha256":"56abf145219ab3af1c0eff515816ab95548ccea38899e1359748505dcfa08f7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56abf145219ab3af1c0eff515816ab95548ccea38899e1359748505dcfa08f7b","first_computed_at":"2026-05-17T23:59:57.591259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:57.591259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZO3CW60N5566gfeA8xTes6crpHz/liOKn+D7YJJfxwXGfr8RdBt1ueIrDUaoOrvUQxBsygqfHYpVzQOhneIDDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:57.591970Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02538","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90bcaf0cc77273757e2cce3a05a314fa721d8c651d0c8c7ec9baf0779dcf9109","sha256:2ff60224b3216dca00bc8d6b12f39acd21fffacd2fd355e19c42af4117b64ef9"],"state_sha256":"49e66a9ed3feb5d89f64bb88d7d21457847847c1ae240a348f49a3a95cb2ba46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMHc6/05S03bsio6IDekMcUwCVY6S4hMKBWNdfT76MIXXmH3jRy8CmJygDWcMythys5YdhVOWhj7dk0l1dZvAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T23:45:03.036092Z","bundle_sha256":"3b4beae2f27a9473822b68c28d81f653e1973fe5503b3f3951d348b6e1770f05"}}