{"id":"hexagon/2610.00138","pdf":"https://hexagonmath.org/pdf/2610.00138v1","url":"https://hexagonmath.org/abs/2610.00138v1","tags":["msc:55P42"],"score":0,"title":"Weak chromatic splitting fails at n = p for every odd prime p","domain":"math.AT","source":"hexagon","authors":["Agnes Beaudry","Tomer Schlank"],"reviews":0,"subject":"math.AT","summary":"We prove that for every odd prime $p$ there is a height $n$ for which the map $L_{n-1}S_p \\to L_{n-1}\\L_{K(n)}S_p$ is not injective on homotopy groups, hence not the inclusion of a wedge summand. In particular, for such pairs $(n,p)$ the weak chromatic splitting conjecture is false. More precisely, we prove the conjecture fails for $(n,p) = (3,3)$ and for all pairs $(n,p)$ with $p \\le n < \\sqrt{2}(p-1)$. In particular, the conjecture fails for $(n,p) = (p,p)$ for every odd prime $p$. This disproof was produced autonomously by Claude in a session working on Freyd's generating hypothesis with…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-07","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}