Designing a Coherence-Gravity Test with Bose-Einstein Condensates

A Bose-Einstein condensate and a thermal cloud can contain the same isotope and nearly the same number of atoms while differing strongly in condensate fraction, spatial coherence, density profile, interaction energy, temperature, expansion, and preparation history. That combination makes a condensed-versus-thermal comparison scientifically attractive and causally difficult. This paper turns an earlier collaboration pitch into a quantitative experimental-design framework. The tested hypothesis is explicit: the Penrose-Onsager condensate density sources a neutral scalar through a dimension-four phenomenological operator. Inside a weak-field, linear, unscreened benchmark, that operator produces a differential acceleration proportional to the measured condensate-fraction contrast and an idealized interferometer phase proportional to the same contrast. Its conclusions are limited to the assumptions, evidence, and testing conditions stated in the manuscript. It belongs to the Super Information Theory, Super Dark Time, and QGTCD physics research program. This is a corrected preprint edition released under the Creative Commons Attribution 4.0 license.