Conjecture on deep Ricci-flat Kähler minima in Calabi–Yau moduli space

Let $\mathop{\rm Al}(M)$ denote the relevant space of metrics, and let $c_1$ and $n$ be the diameter-bound parameters for a fixed Ricci-flat Kähler metric $\omega_0$. A local minimum is $\beta$-deep when its depth is measured by a computably enumerable degree of unsolvability $\beta$. Deep Ricci-flat Kähler minima conjecture. There exists a unique functional on the space $\mathop{\rm Al}(M)$ such that the local minima are $\beta$-deep for $\beta$ a computably enumerable degree of unsolvability. Furthermore, the local minima are given by Ricci-flat Kähler metrics and parametrized by varying Kähler and complex moduli. The number of $\beta$-deep local minima with diameter bounded by $c_1$ and $n$, for fixed $\omega_0$, is an exponential of a polynomial in $c_1$ and $n$.

This conjecture is proposed by analogy with a theorem about fractal structure in the space of metrics, in the setting of computationally difficult Ricci-flat metric construction on Calabi–Yau manifolds. The supplied source does not establish the claim or provide evidence resolving it.