Monotonicity conjecture for Gaussian and inverse multiquadric RBF condition numbers

Let $\boldsymbol{x}\subset\Omega\subset\mathbb{R}^n$ be any set of distinct points, and let $\boldsymbol{A}(\boldsymbol{x},\varepsilon)$ be the RBF interpolation matrix. For $\varepsilon_1>\varepsilon_2$, set

$$A_1=\boldsymbol{A}(\boldsymbol{x},\varepsilon_1),\qquad A_2=\boldsymbol{A}(\boldsymbol{x},\varepsilon_2).$$

Condition-number monotonicity conjecture. For the Gaussian or inverse multiquadric RBF,

$$\operatorname{cond}(A_1)\leq\operatorname{cond}(A_2).$$

The claim formalizes the observed decrease of the matrix condition number as the shape parameter increases. It was proved in the source only for the case $N=2$; a proof for arbitrary sets of distinct points and dimensions remains open.