Five dependences kept separate

1. Nonlocal response. The threshold and discontinuity (eq:absorptive) are fixed by the printed insertion, mass, and vacuum. Permitted local contacts cannot change them.

2. Local calibration. The three real coefficients $\alpha ,\beta ,\gamma$ are the entire freedom in Definition def:contacts. Condition (eq:zeronorm) fixes them uniquely. It is a calibration choice, not a theorem that every physical application must choose zero local coefficients.

3. Preparation. The map $h\mapsto {\sigma }_{\epsilon }h$, its width, and its ramp shape are part of the external source experiment. Varying $\epsilon$ or the physical preparation changes the source, not the finite renormalization prescription. The residual (eq:residual) keeps that distinction visible.

4. Subtraction prescription. For a fixed $\mu >0$, replacing $1/u$ in (eq:subtracted) by $1/(u+{\mu }^2)$ gives

   $$F_{i,\mu }(z)=F_i(z)+c_i(\mu ),c_i(\mu )={{\int }_a}^{\infty }{r}_i(u)\left(\frac{1}{u}-\frac{1}{u+{\mu }^2}\right)\mathrm{d}u.$$

   The difference is finite and independent of $z$. It changes only the quartic contact coefficients. Transporting the local calibration recovers the same normalized response. This subtraction-point comparison is not, by itself, a physical beta function.

5. State. The Minkowski vacuum is explicitly fixed. A different state generally changes the stress two-point function and destroys this particular Lorentz-invariant spectral description. No state change is absorbed into the three vacuum contact constants.

These distinctions do not introduce a ultraviolet cutoff, a gravitational RG flow, or a continuum-matching theorem. A convergent subtracted dispersion integral is not a proof of ultraviolet completeness.