Parameter control does not follow from action counting

If an exact construction depends only on a parameter in a specified finite-dimensional manifold, and its observable, state, and dynamics are all determined by that same parameter, the limit introduces no new independent parameters. This is conditional dependence, not existence of such a construction.

Relational insertion normalizations must be fixed by calibration or controlled within the same exact critical family. Counting bulk couplings alone is insufficient. Conversely, the infinitely many possible measurement test functions are not automatically independent couplings of the theory.

None of the supplied Cheung records or catalogue comparisons used here proves a asymptotic-safety fixed point for this prepared Einstein–scalar target. No exhaustive assertion about every manuscript in either corpus is made. Family 282 is not the missing fixed-point theorem.