Possible new result in random matrix theory, Looking for mistakes, references, or prior work

I’ve been working on the following problem and would appreciate any feedback.

Let (A_M) be a ((2M-1)\times M) matrix with iid standard Gaussian entries. Define

[
\omega(A_M)
\min_{S:,\mathrm{rank}(A_{S^c})<M}
\sigma_M(A_S).
]
I claim to prove that, almost surely,
[
-\frac{1}{M}\log \omega(A_M)\to \log 4,
]
equivalently,
[
\omega(A_M)=4^{-M+o(M)}.
]

The proof first reduces the problem to the minimum singular value among all (M\times M) row submatrices. The lower bound is essentially a union bound over Gaussian row-to-hyperplane distances. The upper bound uses a second-moment argument that explicitly handles dependence between overlapping submatrices via a quotient-space reduction to correlations of random spherical slabs.
What I’m looking for:
Any references proving this already (or something equivalent).
Any obvious gaps or mistakes.
Whether the result is known in frame theory / phase retrieval / random matrix theory under different terminology.

I have attached the proof and results below

Manuscript