{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XPEGLYAQKCMFAMQAHUDOK63GUA","short_pith_number":"pith:XPEGLYAQ","canonical_record":{"source":{"id":"1703.08102","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-23T15:23:32Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"dc3ce58d9e9563fb595bcc964d7ad19d41cd660686a7d8c9796b40457ec06bb4","abstract_canon_sha256":"ca9f55f9af9b960e118cc114440a53472073e84ae23cd26be2860895091fbcc0"},"schema_version":"1.0"},"canonical_sha256":"bbc865e01050985032003d06e57b66a01f14f522b3446ca7e368093e08306457","source":{"kind":"arxiv","id":"1703.08102","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08102","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08102v2","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08102","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"pith_short_12","alias_value":"XPEGLYAQKCMF","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XPEGLYAQKCMFAMQA","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XPEGLYAQ","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XPEGLYAQKCMFAMQAHUDOK63GUA","target":"record","payload":{"canonical_record":{"source":{"id":"1703.08102","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-23T15:23:32Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"dc3ce58d9e9563fb595bcc964d7ad19d41cd660686a7d8c9796b40457ec06bb4","abstract_canon_sha256":"ca9f55f9af9b960e118cc114440a53472073e84ae23cd26be2860895091fbcc0"},"schema_version":"1.0"},"canonical_sha256":"bbc865e01050985032003d06e57b66a01f14f522b3446ca7e368093e08306457","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:30.639058Z","signature_b64":"9n8eyeV0J+9VNY92yUXPsEIK2FNogXsqdkUyhukg4ouVuhVFeMTeVYt3hsKn/d2x4jJ1RaDlxj+Vx+5nn7SKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbc865e01050985032003d06e57b66a01f14f522b3446ca7e368093e08306457","last_reissued_at":"2026-05-18T00:01:30.638553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:30.638553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.08102","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":"2026-05-18T00:01:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bcoebaYRW2ULuz8VEJAtT8yHNrYFHBp7eg2noMPx6wANfXLPnS76itXsWZql11OMhpQWr5InfTpmPpydQ+o/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:13:18.325295Z"},"content_sha256":"a9021b17acbd65deebe639aab4ac2b24005c1ba732751f9453da622d280b7126","schema_version":"1.0","event_id":"sha256:a9021b17acbd65deebe639aab4ac2b24005c1ba732751f9453da622d280b7126"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XPEGLYAQKCMFAMQAHUDOK63GUA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the outlying eigenvalues of a polynomial in large independent random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OA","authors_text":"Hari Bercovici, Mireille Capitaine (IMT), Serban Belinschi (IMT)","submitted_at":"2017-03-23T15:23:32Z","abstract_excerpt":"Given a selfadjoint polynomial $P(X,Y)$ in two noncommuting selfadjoint indeterminates, we investigate the asymptotic eigenvalue behavior of the random matrix $P(A\\_N,B\\_N)$, where $A\\_N$ and $B\\_N$ are independent Hermitian random matrices and the distribution of $B\\_N$ is invariant under conjugation by unitary operators. We assume that the empirical eigenvalue distributions of $A\\_N$ and $B\\_N$ converge almost surely to deterministic probability measures $\\mu $ and $\\nu$, respectively. In addition, the eigenvalues of $A\\_N$ and $B\\_N$ are assumed to converge uniformly almost surely to the su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08102","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":"2026-05-18T00:01:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QV1ABjZbnB22VCe7dsB6bUHkm+YPiqzfc8yqNCTXBmbP0aYT5yAqf6+lhYpXQNuGF/gh2wA/iYKYtgHCmTJ7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:13:18.326076Z"},"content_sha256":"d88ae0b38ab31f42c531d58583051c023888ed24b5d96670953a14faa76b21ce","schema_version":"1.0","event_id":"sha256:d88ae0b38ab31f42c531d58583051c023888ed24b5d96670953a14faa76b21ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XPEGLYAQKCMFAMQAHUDOK63GUA/bundle.json","state_url":"https://pith.science/pith/XPEGLYAQKCMFAMQAHUDOK63GUA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XPEGLYAQKCMFAMQAHUDOK63GUA/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":"2026-06-06T14:13:18Z","links":{"resolver":"https://pith.science/pith/XPEGLYAQKCMFAMQAHUDOK63GUA","bundle":"https://pith.science/pith/XPEGLYAQKCMFAMQAHUDOK63GUA/bundle.json","state":"https://pith.science/pith/XPEGLYAQKCMFAMQAHUDOK63GUA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XPEGLYAQKCMFAMQAHUDOK63GUA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XPEGLYAQKCMFAMQAHUDOK63GUA","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":"ca9f55f9af9b960e118cc114440a53472073e84ae23cd26be2860895091fbcc0","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-23T15:23:32Z","title_canon_sha256":"dc3ce58d9e9563fb595bcc964d7ad19d41cd660686a7d8c9796b40457ec06bb4"},"schema_version":"1.0","source":{"id":"1703.08102","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08102","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08102v2","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08102","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"pith_short_12","alias_value":"XPEGLYAQKCMF","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XPEGLYAQKCMFAMQA","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XPEGLYAQ","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:d88ae0b38ab31f42c531d58583051c023888ed24b5d96670953a14faa76b21ce","target":"graph","created_at":"2026-05-18T00:01:30Z","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":"Given a selfadjoint polynomial $P(X,Y)$ in two noncommuting selfadjoint indeterminates, we investigate the asymptotic eigenvalue behavior of the random matrix $P(A\\_N,B\\_N)$, where $A\\_N$ and $B\\_N$ are independent Hermitian random matrices and the distribution of $B\\_N$ is invariant under conjugation by unitary operators. We assume that the empirical eigenvalue distributions of $A\\_N$ and $B\\_N$ converge almost surely to deterministic probability measures $\\mu $ and $\\nu$, respectively. In addition, the eigenvalues of $A\\_N$ and $B\\_N$ are assumed to converge uniformly almost surely to the su","authors_text":"Hari Bercovici, Mireille Capitaine (IMT), Serban Belinschi (IMT)","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-23T15:23:32Z","title":"On the outlying eigenvalues of a polynomial in large independent random matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08102","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:a9021b17acbd65deebe639aab4ac2b24005c1ba732751f9453da622d280b7126","target":"record","created_at":"2026-05-18T00:01:30Z","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":"ca9f55f9af9b960e118cc114440a53472073e84ae23cd26be2860895091fbcc0","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-23T15:23:32Z","title_canon_sha256":"dc3ce58d9e9563fb595bcc964d7ad19d41cd660686a7d8c9796b40457ec06bb4"},"schema_version":"1.0","source":{"id":"1703.08102","kind":"arxiv","version":2}},"canonical_sha256":"bbc865e01050985032003d06e57b66a01f14f522b3446ca7e368093e08306457","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbc865e01050985032003d06e57b66a01f14f522b3446ca7e368093e08306457","first_computed_at":"2026-05-18T00:01:30.638553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:30.638553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9n8eyeV0J+9VNY92yUXPsEIK2FNogXsqdkUyhukg4ouVuhVFeMTeVYt3hsKn/d2x4jJ1RaDlxj+Vx+5nn7SKAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:30.639058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.08102","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9021b17acbd65deebe639aab4ac2b24005c1ba732751f9453da622d280b7126","sha256:d88ae0b38ab31f42c531d58583051c023888ed24b5d96670953a14faa76b21ce"],"state_sha256":"c7e5d44905a2195815a7f96577b27f3b8a6cee82428f810bb16270874e8e4fc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1w/v9GCqZ+FzRRPugKpx0HFra5pO9mcW1/SdPdUpnO40BHK7xn0MRRiaG94Z7v56gOgfWvConLBgYY/vgB00Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:13:18.330644Z","bundle_sha256":"c0270a8ba41ba9dcb8f306aafe1f94be48ab6e94ce86944a371f6ada41bac3b7"}}