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We prove that the latter asymptotic relation holds universally for a large class of random orthogonal polynomials on the real line, and also give mo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.06376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-22T02:49:14Z","cross_cats_sorted":[],"title_canon_sha256":"01a38a66cba7d8ef1809993a637c35cf938aee7c6dae02719a8a670c64297e95","abstract_canon_sha256":"e29c9d4ed338b27410a6e4dde97ca46b56a063631162ab1bd817133b04807c22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:38.592278Z","signature_b64":"hHdoNsl6MWZX0Joyg1pyORLmfjIoR4IIbNI/D0zkXJ5FClfEscfVc9doTdXwW7aCcCp0Mmf/ms6Ys/D3PWXQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82fb3c947ef133bcb4d7ff4dcf09254b51a2c792ef567210fdfecad527c5f2ed","last_reissued_at":"2026-05-18T02:20:38.591638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:38.591638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Expected number of real zeros for random linear combinations of orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"D. 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