---

Source. Published p. 216, Theorem 1.3, attributed to Matoušek–Rödl (1995). (canonical PDF).

If a simplex $X$ has circumradius $\rho$, then for every integer $q\ge2$ and every $\delta>0$ there is an ambient dimension $m$ such that every $q$-coloring of $S(\rho+\delta,m)$ has a monochromatic congruent copy of $X$.

Scope. This is an external historical theorem, not an additional proof component. The present paper strengthens its qualitative color conclusion to exponential growth in the dimension in theorem_1_6. Its proof uses the separate spread-vector input lemma_2_3, not Theorem 1.3 as a black-box substitute for the main argument. The 1995 article is Matoušek–Rödl, DOI 10.1016/0097-3165(95)90078-0.

Bears on. #174.