Conjecture on outlier traps under $\Lambda$-poisedness

Let $\mathcal{Y}$ be the set of experimental points, and let $y^1,y^2,y^3\in\mathcal{Y}$. A point is called bad under $\Lambda$-poisedness when it satisfies the paper's bad-point criterion for $\Lambda$-poisedness. Outlier-trap conjecture. For every $y^4\in\mathcal{Y}\backslash\{y^1,y^2,y^3\}$, if

$$\lVert y^i-y^4\rVert>2\quad\text{for every }i\in\{1,2,3\},$$

then there is at least one $y^5\in\{y\in\mathcal{Y}\mid\lVert y-y^4\rVert\leq2\}$ that is bad under $\Lambda$-poisedness. The conjecture formalizes the experimentally observed association between distant outliers and nearby bad points under $\Lambda$-poisedness; the paper reports that more than $99\%$ of the relevant experimental points were outlier traps, but does not establish the assertion theoretically.