{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:I4GHIHBIDVIROI2KJI52FYRNHE","short_pith_number":"pith:I4GHIHBI","schema_version":"1.0","canonical_sha256":"470c741c281d5117234a4a3ba2e22d391b569cad8c3bbbcaafee0cb375e4fed0","source":{"kind":"arxiv","id":"1505.04762","version":1},"attestation_state":"computed","paper":{"title":"Expected number of real zeros for random Freud orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV"],"primary_cat":"math.PR","authors_text":"Igor E. Pritsker, Xiaoju Xie","submitted_at":"2015-05-18T18:59:24Z","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"},"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":"1505.04762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-18T18:59:24Z","cross_cats_sorted":["math.CA","math.CV"],"title_canon_sha256":"1e3b4e8267d0f6ff854da1f166e7f56bf6616d72833ae7006fefec9f4e053cf8","abstract_canon_sha256":"b40f03d157873f077835c2cf93dd286edf2f360f5d04d5be472857c6af56ea5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:24.681256Z","signature_b64":"fmSxD3ShyyAHyqxMsHKFJT7YW+bm3s/ISwXzgV9Pd7dcOBpW0zZbVz8ScHYjoP3lVFYHDnzbCC6r2aw0fxKyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"470c741c281d5117234a4a3ba2e22d391b569cad8c3bbbcaafee0cb375e4fed0","last_reissued_at":"2026-05-18T02:07:24.680397Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:24.680397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Expected number of real zeros for random Freud orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV"],"primary_cat":"math.PR","authors_text":"Igor E. Pritsker, Xiaoju Xie","submitted_at":"2015-05-18T18:59:24Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04762","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.04762","created_at":"2026-05-18T02:07:24.680523+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.04762v1","created_at":"2026-05-18T02:07:24.680523+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04762","created_at":"2026-05-18T02:07:24.680523+00:00"},{"alias_kind":"pith_short_12","alias_value":"I4GHIHBIDVIR","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"I4GHIHBIDVIROI2K","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"I4GHIHBI","created_at":"2026-05-18T12:29:25.134429+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I4GHIHBIDVIROI2KJI52FYRNHE","json":"https://pith.science/pith/I4GHIHBIDVIROI2KJI52FYRNHE.json","graph_json":"https://pith.science/api/pith-number/I4GHIHBIDVIROI2KJI52FYRNHE/graph.json","events_json":"https://pith.science/api/pith-number/I4GHIHBIDVIROI2KJI52FYRNHE/events.json","paper":"https://pith.science/paper/I4GHIHBI"},"agent_actions":{"view_html":"https://pith.science/pith/I4GHIHBIDVIROI2KJI52FYRNHE","download_json":"https://pith.science/pith/I4GHIHBIDVIROI2KJI52FYRNHE.json","view_paper":"https://pith.science/paper/I4GHIHBI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.04762&json=true","fetch_graph":"https://pith.science/api/pith-number/I4GHIHBIDVIROI2KJI52FYRNHE/graph.json","fetch_events":"https://pith.science/api/pith-number/I4GHIHBIDVIROI2KJI52FYRNHE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I4GHIHBIDVIROI2KJI52FYRNHE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I4GHIHBIDVIROI2KJI52FYRNHE/action/storage_attestation","attest_author":"https://pith.science/pith/I4GHIHBIDVIROI2KJI52FYRNHE/action/author_attestation","sign_citation":"https://pith.science/pith/I4GHIHBIDVIROI2KJI52FYRNHE/action/citation_signature","submit_replication":"https://pith.science/pith/I4GHIHBIDVIROI2KJI52FYRNHE/action/replication_record"}},"created_at":"2026-05-18T02:07:24.680523+00:00","updated_at":"2026-05-18T02:07:24.680523+00:00"}