{"paper":{"title":"Quantum field theory over F_q","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.CO","authors_text":"Oliver Schnetz","submitted_at":"2009-09-04T14:49:01Z","abstract_excerpt":"We consider the number \\bar N(q) of points in the projective complement of graph hypersurfaces over \\F_q and show that the smallest graphs with non-polynomial \\bar N(q) have 14 edges. We give six examples which fall into two classes. One class has an exceptional prime 2 whereas in the other class \\bar N(q) depends on the number of cube roots of unity in \\F_q. At graphs with 16 edges we find examples where \\bar N(q) is given by a polynomial in q plus q^2 times the number of points in the projective complement of a singular K3 in \\P^3. In the second part of the paper we show that applying moment"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0905","kind":"arxiv","version":3},"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"}