{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:I4GHIHBIDVIROI2KJI52FYRNHE","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":"b40f03d157873f077835c2cf93dd286edf2f360f5d04d5be472857c6af56ea5d","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-18T18:59:24Z","title_canon_sha256":"1e3b4e8267d0f6ff854da1f166e7f56bf6616d72833ae7006fefec9f4e053cf8"},"schema_version":"1.0","source":{"id":"1505.04762","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04762","created_at":"2026-05-18T02:07:24Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04762v1","created_at":"2026-05-18T02:07:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04762","created_at":"2026-05-18T02:07:24Z"},{"alias_kind":"pith_short_12","alias_value":"I4GHIHBIDVIR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I4GHIHBIDVIROI2K","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I4GHIHBI","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:5c60a073f692e61ec398276948b2cbd0abef10675da6337815b463bcf8e86a41","target":"graph","created_at":"2026-05-18T02:07:24Z","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 study the expected number of real zeros for random linear combinations of orthogonal polynomials. It is well known that Kac polynomials, spanned by monomials with i.i.d. Gaussian coefficients, have only $(2/\\pi + o(1))\\log{n}$ expected real zeros in terms of the degree $n$. On the other hand, if the basis is given by orthonormal polynomials associated to a finite Borel measure with compact support on the real line, then random linear combinations have $n/\\sqrt{3} + o(n)$ expected real zeros under mild conditions. We prove that the latter asymptotic relation holds for all random orthogonal p","authors_text":"Igor E. Pritsker, Xiaoju Xie","cross_cats":["math.CA","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-18T18:59:24Z","title":"Expected number of real zeros for random Freud orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04762","kind":"arxiv","version":1},"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":"sha256:324471c9928cb59c2505d0f528be276c8d4c7226927aa6271ba853cf44718633","target":"record","created_at":"2026-05-18T02:07:24Z","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":"b40f03d157873f077835c2cf93dd286edf2f360f5d04d5be472857c6af56ea5d","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-18T18:59:24Z","title_canon_sha256":"1e3b4e8267d0f6ff854da1f166e7f56bf6616d72833ae7006fefec9f4e053cf8"},"schema_version":"1.0","source":{"id":"1505.04762","kind":"arxiv","version":1}},"canonical_sha256":"470c741c281d5117234a4a3ba2e22d391b569cad8c3bbbcaafee0cb375e4fed0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"470c741c281d5117234a4a3ba2e22d391b569cad8c3bbbcaafee0cb375e4fed0","first_computed_at":"2026-05-18T02:07:24.680397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:24.680397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fmSxD3ShyyAHyqxMsHKFJT7YW+bm3s/ISwXzgV9Pd7dcOBpW0zZbVz8ScHYjoP3lVFYHDnzbCC6r2aw0fxKyBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:24.681256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04762","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:324471c9928cb59c2505d0f528be276c8d4c7226927aa6271ba853cf44718633","sha256:5c60a073f692e61ec398276948b2cbd0abef10675da6337815b463bcf8e86a41"],"state_sha256":"ea531134153714585253c88d79e08bb73e478981e142da8dcb96bb34effbc14d"}