{"paper":{"title":"A combinatorial large sieve for Sidon sets, distances, and norm forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Adam Sheffer, Chi Hoi Yip, Cosmin Pohoata, Ernie Croot, Junzhe Mao","submitted_at":"2026-06-16T03:57:20Z","abstract_excerpt":"We develop a new combinatorial large sieve method for sets with bounded algebraic multiplicities. The method exploits algebraic splitting modulo many small primes: local congruence branching produces many modular collisions, while global bounded-multiplicity hypotheses force these collisions to be rare.\n  As a first application, we prove that every Sidon subset $A\\subset\\{1^2,\\ldots,N^2\\}$ satisfies \\[\n  |A|\n  \\le\n  N\\exp\\left(\n  -c\\frac{\\log N}{\\log\\log N}\n  \\right) \\] for some absolute constant $c>0$. This gives the first super-polylogarithmic saving for a classical problem of Alon and Erd\\H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17487","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17487/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}