The ramp is not a convolution repair

The ramp's retained first-order identity is

on its own plateau algebra XA,XAST. The ramp multiplies a metric-density deviation inside a divergence. It does not replace $T_{g,\epsilon }=S_{\epsilon }\circ (g\cdot )$.

The ramp edge comparison has a different integral, in its source convention,

That integral is not $c_{\epsilon }$, and its edge parameter is not an admitted member of the frozen ramp plateau algebra.