Ravenel's Local Conjecture for local formal module Ext groups

Let $K/\mathbb{Q}_p$ be a finite field extension with ring of integers $A$, uniformizer $\pi$, and residue field $\mathbb{F}_q$. Ravenel's Local Conjecture.

$$\operatorname{Ext}_{(V^A,V^AT)}^{1,2n(q-1)}(V^A,V^A) \cong A/I_n,$$

where $I_n$ is the ideal of $A$ generated by all $a^n-1$ with $a\in A$ congruent to $1$ modulo $\pi$. This is the local counterpart of Ravenel's global Ext-group prediction. The source reports proofs in broad classes of extensions and proves it when $\log_p(e/(p-1))$ is not an integer, but does not establish the conjecture in full generality.