muonspectral

the question

What are the full fixed-point dynamics of Muon's Newton-Schulz iteration, and does it actually orthogonalize the momentum matrix?

what came out

Newton-Schulz has three repelling positive fixed points and no stable one, so it never converges to orthogonal. Below 1.2637 singular values fall onto a period-4 attractor band [0.68, 1.13], a 1.66x anisotropic rescaling (bf16 equals fp32); above it they diverge, held off by a rank-1-tight 26.4% Frobenius margin.

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