{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SSHO3GASBNA6VTJNCEWKIGI2BJ","short_pith_number":"pith:SSHO3GAS","schema_version":"1.0","canonical_sha256":"948eed98120b41eacd2d112ca4191a0a62add2775dc16ac726fee8a0e6a2ce93","source":{"kind":"arxiv","id":"1402.5457","version":1},"attestation_state":"computed","paper":{"title":"Some Notes on Flat Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.SP"],"primary_cat":"math.CV","authors_text":"E. H. El Abdalaoui, M. G. Nadkarni","submitted_at":"2014-02-22T01:03:05Z","abstract_excerpt":"Connection of flat polynomials with some spectral questions in ergodic theory is discussed. A necessary condition for a sequence of polynomials of the type $\\frac{1}{\\sqrt{N}} \\big(1 +\\sum_{j=1}^{N-1} z^{n_j}\\big)$ to be flat in almost everywhere sense is given, which contrasts with a similar necessary condition for a sequence of polynomials to be ultraflat."},"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":"1402.5457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-02-22T01:03:05Z","cross_cats_sorted":["math.DS","math.SP"],"title_canon_sha256":"166286e20c702aff4c7f516b6f552e9e0bfc2f914ce3520440fdfe2506fbd875","abstract_canon_sha256":"2263f631c4f69e5291ab0d286c4e68724985f127bd77682f029b318ca5201641"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:21.083388Z","signature_b64":"xoea8yeEPu7b+I1/j+frOuRU8HenpWOi1rgXIhsIgBs/qPB76mZLgFGVsWDaruip2POSVFWH8gAqsZifrLejDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"948eed98120b41eacd2d112ca4191a0a62add2775dc16ac726fee8a0e6a2ce93","last_reissued_at":"2026-05-18T02:58:21.082856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:21.082856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Notes on Flat Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.SP"],"primary_cat":"math.CV","authors_text":"E. H. El Abdalaoui, M. G. Nadkarni","submitted_at":"2014-02-22T01:03:05Z","abstract_excerpt":"Connection of flat polynomials with some spectral questions in ergodic theory is discussed. A necessary condition for a sequence of polynomials of the type $\\frac{1}{\\sqrt{N}} \\big(1 +\\sum_{j=1}^{N-1} z^{n_j}\\big)$ to be flat in almost everywhere sense is given, which contrasts with a similar necessary condition for a sequence of polynomials to be ultraflat."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5457","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":"1402.5457","created_at":"2026-05-18T02:58:21.082933+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.5457v1","created_at":"2026-05-18T02:58:21.082933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5457","created_at":"2026-05-18T02:58:21.082933+00:00"},{"alias_kind":"pith_short_12","alias_value":"SSHO3GASBNA6","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SSHO3GASBNA6VTJN","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SSHO3GAS","created_at":"2026-05-18T12:28:49.207871+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/SSHO3GASBNA6VTJNCEWKIGI2BJ","json":"https://pith.science/pith/SSHO3GASBNA6VTJNCEWKIGI2BJ.json","graph_json":"https://pith.science/api/pith-number/SSHO3GASBNA6VTJNCEWKIGI2BJ/graph.json","events_json":"https://pith.science/api/pith-number/SSHO3GASBNA6VTJNCEWKIGI2BJ/events.json","paper":"https://pith.science/paper/SSHO3GAS"},"agent_actions":{"view_html":"https://pith.science/pith/SSHO3GASBNA6VTJNCEWKIGI2BJ","download_json":"https://pith.science/pith/SSHO3GASBNA6VTJNCEWKIGI2BJ.json","view_paper":"https://pith.science/paper/SSHO3GAS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.5457&json=true","fetch_graph":"https://pith.science/api/pith-number/SSHO3GASBNA6VTJNCEWKIGI2BJ/graph.json","fetch_events":"https://pith.science/api/pith-number/SSHO3GASBNA6VTJNCEWKIGI2BJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SSHO3GASBNA6VTJNCEWKIGI2BJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SSHO3GASBNA6VTJNCEWKIGI2BJ/action/storage_attestation","attest_author":"https://pith.science/pith/SSHO3GASBNA6VTJNCEWKIGI2BJ/action/author_attestation","sign_citation":"https://pith.science/pith/SSHO3GASBNA6VTJNCEWKIGI2BJ/action/citation_signature","submit_replication":"https://pith.science/pith/SSHO3GASBNA6VTJNCEWKIGI2BJ/action/replication_record"}},"created_at":"2026-05-18T02:58:21.082933+00:00","updated_at":"2026-05-18T02:58:21.082933+00:00"}