{"paper":{"title":"Schrijver Number Quasi-Tensorization and Multicolor Ramsey Bounds via Robust OR Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ijay Narang, Yukai Tang","submitted_at":"2026-07-27T19:32:34Z","abstract_excerpt":"We introduce a robust OR polynomial framework for composing positive semidefinite certificates across OR constraints. We demonstrate the power of this method in two applications.\n  The first is on acute-free families. A set $\\mathcal F=\\{(x_i^{(1)},\\ldots,x_i^{(r)})\\}_{i=1}^M \\subseteq (S^{n-1})^r$ is $r$-way acute-free if, for every $i\\neq j$, there is a coordinate $t\\in[r]$ such that $\\langle x_i^{(t)},x_j^{(t)}\\rangle\\leq 0$. We write $M_r(n)$ for the maximum size of such a set, and $M_r^{\\pm}(n)$ for the hypercube restriction. On the hypercube, $r$-way acute-free sets are independent sets "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25023","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/2607.25023/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"}