{"paper":{"title":"Cube vs. Cube Low Degree Test","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Amey Bhangale, Inbal Livni Navon, Irit Dinur","submitted_at":"2016-12-22T08:54:49Z","abstract_excerpt":"We revisit the Raz-Safra plane-vs.-plane test and study the closely related cube vs. cube test. In this test the tester has access to a \"cubes table\" which assigns to every cube a low degree polynomial. The tester randomly selects two cubes (affine sub-spaces of dimension $3$) that intersect on a point $x\\in \\mathbf{F}^m$, and checks that the assignments to the cubes agree with each other on the point $x$.\n  Our main result is a new combinatorial proof for a low degree test that comes closer to the soundness limit, as it works for all $\\epsilon \\ge poly(d)/{\\mathbf{F}}^{1/2}$, where $d$ is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07491","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"}