Gradient spikes and the SOAP preconditioner

A set of executed-notebook walkthroughs of how different optimizers respond to a sudden gradient spike, and how that exposed a TF32 precision bug in the SOAP/REKLS KL-Shampoo preconditioner. Read in order:

1. Optimizer update comparison — per-step update magnitude and spike-recovery behavior of AdamW, LaProp, Muon, SOAP, and REKLS.

2. Preconditioner eigenbasis rotation — how the SOAP/REKLS eigenbasis Q_L rotates around a spike, and how it depends on fp32_matmul_prec.

3. TF32 eigenvalue precision loss — a standalone demo of the underlying diag(Qᵀ L Q) precision failure that drives the rotation.