{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BEDSEQM3F3KD2Q23LFL6UFNGF4","short_pith_number":"pith:BEDSEQM3","schema_version":"1.0","canonical_sha256":"090722419b2ed43d435b5957ea15a62f0c47d6de301c43087d73a05d6fdc1188","source":{"kind":"arxiv","id":"1610.05360","version":1},"attestation_state":"computed","paper":{"title":"Universality of the nodal length of bivariate random trigonometric polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guillaume Poly, Hung Pham Viet, J\\\"urgen Angst","submitted_at":"2016-10-17T21:12:04Z","abstract_excerpt":"We consider random trigonometric polynomials of the form \\[ f_n(x,y)=\\sum_{1\\le k,l \\le n} a_{k,l} \\cos(kx) \\cos(ly), \\] where the entries $(a_{k,l})_{k,l\\ge 1}$ are i.i.d. random variables that are centered with unit variance. We investigate the length $\\ell_K(f_n)$ of the nodal set $Z_K(f_n)$ of the zeros of $f_n$ that belong to a compact set $K \\subset \\mathbb R^2$. We first establish a local universality result, namely we prove that, as $n$ goes to infinity, the sequence of random variables $n\\, \\ell_{K/n}(f_n)$ converges in distribution to a universal limit which does not depend on the pa"},"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":"1610.05360","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-17T21:12:04Z","cross_cats_sorted":[],"title_canon_sha256":"14c00c7ea1d135503faca4e9db2a8f3fdfbfe9f718916bbcb10443d594a98fdb","abstract_canon_sha256":"08c0cc5496295523e8cc5f8ff213964492060328b404d52e823df5169678463f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:59.532125Z","signature_b64":"t88wjT3c9HgTUr4Aiugd3SUl/b/rXoY9UztXiD8mYm44xp0WFcx38x9i4SJME6LDimImDEQU+t+HmEx9s683CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"090722419b2ed43d435b5957ea15a62f0c47d6de301c43087d73a05d6fdc1188","last_reissued_at":"2026-05-18T01:01:59.531642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:59.531642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universality of the nodal length of bivariate random trigonometric polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guillaume Poly, Hung Pham Viet, J\\\"urgen Angst","submitted_at":"2016-10-17T21:12:04Z","abstract_excerpt":"We consider random trigonometric polynomials of the form \\[ f_n(x,y)=\\sum_{1\\le k,l \\le n} a_{k,l} \\cos(kx) \\cos(ly), \\] where the entries $(a_{k,l})_{k,l\\ge 1}$ are i.i.d. random variables that are centered with unit variance. We investigate the length $\\ell_K(f_n)$ of the nodal set $Z_K(f_n)$ of the zeros of $f_n$ that belong to a compact set $K \\subset \\mathbb R^2$. We first establish a local universality result, namely we prove that, as $n$ goes to infinity, the sequence of random variables $n\\, \\ell_{K/n}(f_n)$ converges in distribution to a universal limit which does not depend on the pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05360","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":"1610.05360","created_at":"2026-05-18T01:01:59.531712+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.05360v1","created_at":"2026-05-18T01:01:59.531712+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05360","created_at":"2026-05-18T01:01:59.531712+00:00"},{"alias_kind":"pith_short_12","alias_value":"BEDSEQM3F3KD","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"BEDSEQM3F3KD2Q23","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"BEDSEQM3","created_at":"2026-05-18T12:30:07.202191+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/BEDSEQM3F3KD2Q23LFL6UFNGF4","json":"https://pith.science/pith/BEDSEQM3F3KD2Q23LFL6UFNGF4.json","graph_json":"https://pith.science/api/pith-number/BEDSEQM3F3KD2Q23LFL6UFNGF4/graph.json","events_json":"https://pith.science/api/pith-number/BEDSEQM3F3KD2Q23LFL6UFNGF4/events.json","paper":"https://pith.science/paper/BEDSEQM3"},"agent_actions":{"view_html":"https://pith.science/pith/BEDSEQM3F3KD2Q23LFL6UFNGF4","download_json":"https://pith.science/pith/BEDSEQM3F3KD2Q23LFL6UFNGF4.json","view_paper":"https://pith.science/paper/BEDSEQM3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.05360&json=true","fetch_graph":"https://pith.science/api/pith-number/BEDSEQM3F3KD2Q23LFL6UFNGF4/graph.json","fetch_events":"https://pith.science/api/pith-number/BEDSEQM3F3KD2Q23LFL6UFNGF4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BEDSEQM3F3KD2Q23LFL6UFNGF4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BEDSEQM3F3KD2Q23LFL6UFNGF4/action/storage_attestation","attest_author":"https://pith.science/pith/BEDSEQM3F3KD2Q23LFL6UFNGF4/action/author_attestation","sign_citation":"https://pith.science/pith/BEDSEQM3F3KD2Q23LFL6UFNGF4/action/citation_signature","submit_replication":"https://pith.science/pith/BEDSEQM3F3KD2Q23LFL6UFNGF4/action/replication_record"}},"created_at":"2026-05-18T01:01:59.531712+00:00","updated_at":"2026-05-18T01:01:59.531712+00:00"}