Abstract

We develop a paired negative and constructive identifiability analysis for the superconducting-microsphere interferometer proposed by Pino and collaborators. For a shared residual force-diffusion amplitude independently restricted to an interval, proportional quadratic environmental and gravitational responses produce an exact complete-record match whenever the gravitational coefficient shift does not exceed the calibration width. This establishes family overlap, not containment of the entire alternative family. We distinguish calibration of the environmental source from calibration of total centre-of-mass heating, and derive a regularized-model near-obstruction bound with explicit domain and implementation errors.

A complementary three-separation contrast cancels a common preparation offset and quadratic environmental attenuation. For a continuous homogeneous sphere at separations $R/4,R/2,3R/4$, its unsmeared gravitational coefficient is $-5041/81920$, in units $G{M}^2/(\hslash R)$. We prove that the contrast remains strictly negative for every finite Gaussian regularization length, obtain a uniform quantitative lower bound for $0<r_{\mathrm{c}}\le R/100$, and give validated spectral quadrature and large-smearing bounds. A robust signed contrast margin survives only when setting-dependent preparation, environmental-shape, trajectory, and sensing errors are sufficiently small.

Log-visibility inference is connected to complete attempted-run records through confidence intervals; it is not treated as a bounded per-run statistic. A separate bounded-statistic route provides uniform sample certificates. The analytical results and embedded regressions do not claim reproduced apparatus performance or an experimental exclusion.