The proposed functional form for collinearity as a function of correlation and dimension

Let $c$ denote the collinearity parameter, $\Delta$ the correlation parameter, and $p$ the number of variables in the latent linear-regression framework described above. Proposed functional-form conjecture. Based on empirical observations, $c$ takes the form

$$c(\Delta, p) = \frac{2\Delta + (p-2)\Delta^2}{1-4\Delta + 2p\Delta + p^2\Delta^2 -3p\Delta^2 + 3\Delta^2}.$$

This postulate is intended to specify the theoretically expected dependence of the collinearity parameter on $\Delta$ and $p$, following the derived closed-form expression for LOCO importance. The supplied text gives empirical motivation but does not state a proof or resolution.