What this interface does not construct

The encoding is a finite map from selected classical classes to probe labels. It is not an injective linear representation of ${{\mathcal{S}}_{r_{\ast }}}^{\mathrm{red}}$, a quantization of its symplectic structure, or an apparatus coupling to an unknown field.

A physical field-measurement bridge would additionally need:

1. a field representation, admitted states, and input class;

2. a specified field–probe coupling and localized access;

3. a complete selective-instrument comparison;

4. a controlled approximation topology and error bound.

Those data are not supplied by classical descent or by naming $X$ a matter residual.

For a finite catalogue of jet configurations, the two real coefficients of (eq:jet-observable) can similarly be encoded as separate settings. A dual-number coefficient is not inserted as a probability or a numerical quantum amplitude.