A fixed-interface evaluation channel

If a table value is the normalized real part of a supplied finite-part pairing, choose $M_{ki}>0$ and set

For approximants ${\hat{z}}_{ki}$ with $|z_{ki}-{\hat{z}}_{ki}|\le E_{ki}$, clipping is one-Lipschitz. Therefore

One may use (eq:certificateerror) for $E_{ki}$, adding any supplied finite rounding allowance.

This is a complete-channel comparison for a fixed installed interface. It does not measure $z_{ki}$, approximate an unknown field, or turn the scalar estimate into a norm estimate for a quantum field product. Changing a report to a different orthogonal label is not, merely because its interpreted number is close, a small diamond-norm change. Standard channel norms and their reference extensions are treated in Watrous.