# Claim 3

**Result: falsified as literally registered.** The authored source
states that whenever SYM ν=2 learns the target, its NTK *cannot* be stable. A
literal `f=UᵀU` RK4 gradient-flow run has loss 20.3012 →
5.31587e-07, model drift 0.722976, and NTK
drift **0.655313**. The closed-form NTK identity agrees
with an independently formed Jacobian Gram matrix to
1.78e-15.

The counterexample targets only the static-kernel clause inserted into the
registered claim; it is consistent with the paper's actual proposition.

## Registered wording

An NTK-like regime, in which features do not evolve during training, appears only at points/edges B-C of the Pareto polygon in the asymmetric parameterization case, while Proposition 8.2 proves the NTK kernel stays static throughout training in the symmetric matrix case (nu=2), explaining the absence of an NTK limit there (Section 4, Proposition 8.2).