Conclusion and submission boundary

The paired contribution is precise. A calibrated common force-noise amplitude leaves an exact quadratic family-overlap region under a declared proportionality condition. Centre-of-mass heating of matched total generators cannot identify the source. Beyond the quadratic approximation, a full-protocol near-obstruction requires operator-level and implementation error bounds.

Conversely, three proposed separations cancel a shared constant and quadratic attenuation while retaining a nonquadratic continuous-sphere response. Its coefficient is evaluated exactly. Gaussian regularization preserves its sign at every finite width, and an explicit uniform magnitude certificate is available for $0<r_{\mathrm{c}}\le R/100$. The positive conclusion survives only below the stated residual margin.

The constructive attenuation theorem is not yet a validation of the reference apparatus's three-setting operation. Actual sensitivity requires calibrated preparation laws, transfer functions, detector response, and uniform propagation errors. The paper supplies the mathematical certificates and a reproducible test artifact; it does not invent those empirical inputs.

No result is imported from characteristic-product, free-shell, retarded-graph, or field-theory admission programmes. A positive detector certificate would not resolve their separate analytic obligations. No Born-rule uniqueness result, ultraviolet completion, or experimental gravity measurement is claimed.