Option C: bounded-segment tolerance and visibility

Declare a new restriction

This is not the original convolution gauge algebra. Plateau support alone cannot supply such a bound: multiplying a supported gauge vector by any real number preserves its support. The ramp algebra likewise supplies no $\Lambda$, since every real multiple of a vector supported in its $U$ remains supported there. This observation does not introduce a convolution defect into the already invariant ramp observable.

For the direct convolution amplitude trial,

This is approximate closure, not invariance.

To make the trade-off precise, prescribe a tolerance $0<\delta <1/2$ and a desired visibility $0<v<1/2$ for a nonzero benchmark signal of magnitude $A>0$. Its flat-baseline visibility is

Both requirements hold exactly when

Indeed, monotonicity of $\tanh$ makes the tolerance condition equivalent to the lower bound and the visibility condition equivalent to the upper bound. Thus a suitable scale exists if and only if

There is no unconditional statement that the signal must dominate the defect: the required ratio depends on the visibility target relative to the tolerated variation. At $\delta =0$, no finite scale gives exact closure for $d>0$.

Calling $A$ a physical signal requires independent provenance or a justified choice of representatives. A scalar input alone does not distinguish a physical displacement from a gauge displacement.