Abstract

We examine whether an analytical nuisance-cancelling signature remains useful after Gaussian preparation, outcome-dependent splitting, and finite squared-position sensing in a superconducting-microsphere interferometer. The first result is a limitation: a three-separation contrast that cancels quadratic attenuation also cancels every pre-split hypothesis difference encoded solely in the normalized point-pair coherence of a centred Gaussian state. A common diagonal filter preserves that diagnostic, but finite packet projections and unrecorded outcome averaging require additional amplitude and phase bounds.

We derive the stage transfer of one physical nuisance, displacement of the support of a quadratic potential. Its white-noise localization coefficient is proportional to curvature squared and vanishes in an exactly flat stage. Consequently, this nuisance cannot absorb a persistent gravitational localization contribution at the generator level across a protocol containing a nonzero flat interval. This alone does not prove detector identifiability.

A constructive complete-record result uses four free-expansion times, the same preparation before those intervals, and the same finite squared-position sensor afterwards. An exact third finite difference of the mean split record removes all shared pre-expansion second moments, including preparation changes caused by gravity, and retains the cubic contribution from diffusion during the flat interval. The identity holds for the full regularized kick model at the level of second moments, without assuming Gaussianity. Clipping the recorded outcome produces a bounded statistic with an explicit uniform gap, calibration-width condition, and attempted-run sample certificate. The resulting experiment measures total flat-stage momentum diffusion; source identification requires independent bounds on other sources.

The paper proves these results within declared dynamical and instrument models. An embedded regression artifact evaluates selected reference preparation formulas and finite-sensor identities. No executed apparatus reproduction, validated full-protocol forecast, or experimental exclusion is asserted.