The convolution input contract

The bound $1/8$ is a source-coordinate bound, not a new physical length or time calibration. The symbol $x^1$ in (eq:gap) is a rod coordinate on the analytical completion; it is not asserted to be a global Cartesian function on the cone.

The positive charge $c_{\epsilon }$ is fixed during an orbit comparison. The variable being read is $a$. An output may depend on frozen calibration data such as $c_{\epsilon },\epsilon$, or an encoding scale while being independent of $a$. The orbit theorem forbids informativeness about $a$, not the reporting of fixed metadata.