Twenty-one-ball total-clearance existence conjecture in snooker

Let $\Omega$ be the shot-parameter space, let $c_0^{\varepsilon}$ denote the initial cue-ball configuration with ball radius or clearance parameter $\varepsilon$, and let $N(c_0^{\varepsilon},x)$ be the number of balls pocketed from initial state $c_0^{\varepsilon}$ under shot parameters $x$. Twenty-one-ball total-clearance conjecture. The set

$$\{\,x\in\Omega:N(c_0^{\varepsilon},x)=21\,\}$$

is nonempty, and, by continuity at a regular witness, has positive measure for $\varepsilon=0.5$ mm. The claim concerns the existence and rarity of a single-stroke snooker clearance of all twenty-one balls; the supplied text reports a numerically verified witness and describes the result as computer-assisted, but gives no rigorous interval-arithmetic certificate in the quoted statement.