The maximality conjecture for the $t=8$ circle construction

Let $R$ have only prime factors $p$ satisfying $p\equiv 1\pmod 4$, and let $\operatorname{circle}(R,8)$ be the integral point set obtained from the scaling construction by taking a maximal clique in the associated graph. $t=8$ circle-construction conjecture. The construction gives maximal integral point sets of cardinality $\tau(R)$. The statement is a more specific maximality claim for the scaled circle construction; no proof or resolution is supplied in the text.