{"paper":{"title":"A Structural Condition on Point Sets with Few Distinct Dot Products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Anshula Gandhi","submitted_at":"2025-10-16T11:43:13Z","abstract_excerpt":"The distinct dot products problem, a variant of the Erd\\H{o}s distinct distances problem, asks \"Given a set $P_n$ of $n$ points in $\\mathbb{R}^2$, what is the minimum number $|D(P_n)|$ of distinct dot products they determine?\" The best proven lower bound is $|D(P_n)| = \\Omega(n^{2/3+7/1425})$, due to work by Hanson$\\unicode{x2013}$Roche-Newton$\\unicode{x2013}$Senger, and a recent improvement by Kokkinos. However, the best known construction determines $\\Theta(n)$ dot products. We provide a structural condition that a point configuration $P_n$ would have to satisfy in order to have 'few' dot pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.14585","kind":"arxiv","version":2},"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/2510.14585/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"}