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We show that when $\\varphi_j\\in \\mathbb Z[t]$ $(1\\le j\\le k)$ is a system of polynomials with non-vanishing Wronskian, and $s\\le k(k+1)/2$, then for all complex sequences $(\\mathfrak a_n)$, and for each $\\epsilon>0$, one has \\[ \\int_{[0,1)^k} \\left| \\sum_{|n|\\le X} {\\mathfrak a}_n e(\\alpha_1\\varphi_1(n)+\\ldots +\\alpha_k\\varphi_k(n)) \\right|^{2s} {\\rm d}{\\boldsymbol \\alpha} \\ll X^\\epsilon \\left( \\sum_{|n|\\le X} |{\\mathfrak a}_n|^2\\right)^s. \\] As a special case of this result, w"},"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":"1708.01220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-03T17:10:29Z","cross_cats_sorted":[],"title_canon_sha256":"deab4a2cad7a3646335f9be9327f29368bb636d555c56770f153f1951616ece7","abstract_canon_sha256":"26f9ac4532c6371b24bf839cee6e1cf3cf03956f43702a1cdb82b8ebfba30b4c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:30.472419Z","signature_b64":"YviMfa+5gWWBjQ8Qzz7md0Z6pBPCET6cA+WlN4iZtF8T9NhmAELEuDOxs2v80hNpbvZxqqMFSHrS3POm61ycDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0729658c6ecd48e3e84965f29f2c0ac6fecdca98655c39f802b235eabeec5422","last_reissued_at":"2026-05-18T00:01:30.472010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:30.472010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nested efficient congruencing and relatives of Vinogradov's mean value theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Trevor D. 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