Amplitude, phase, and verdict

Using the rounded exploratory $\eta \approx 0.613132$ only as a planning estimate gives $|q|\approx 0.7830$. The estimated amplitude margin to $\sqrt{3}/2$ is about $0.0830$. The corresponding defect target is roughly $0.0063$, before any additional center/modulus allowances. These are refinement targets, not validated bounds. The reported $0.117$ defect is too wide for this purpose.

Refine according to the source of width:

1. tighten $B_0$ when pulse-normalization uncertainty dominates;

2. refine validation cells when kernel/interpolant range wrapping dominates;

3. refine solver nodes when the approximation defect dominates;

4. increase arithmetic precision only when rounding contributes materially.

Validation-cell refinement does not improve a fixed interpolant; it only tightens its enclosure.