Phononic Screening in the Fluid Time Condensate and the Resolution of the Cassini Constraint

All modified-gravity frameworks that reproduce the low-acceleration galactic regime with a universal scale a0 ∼ 10−10 m s−2 face a severe Solar System constraint: the Cassini spacecraft measurements at Saturn’s orbit exclude anomalous constant accelerations above ∼ 3 × 10−13 m s−2. A naive MOND-like interpolation overshoots this bound by a factor ∼ 180. In this companion note to the parameter-free BTFR derivation of the Fluid Time Theory (TTF), we show that a screening mechanism, intrinsic to the Bogoliubov dispersion of the condensate, suppresses the cosmological contribution inside gravitationally bound systems. The resulting screened Radial Acceleration Relation reduces the Newtonian-regime offset from a0/2 (constant) to a02/(2gbar), which decays as 1/gbar. At Saturn’s orbit, the predicted offset is 9.0 × 10−17 m s−2, i.e. ∼ 3300 times below the Cassini bound. The deep galactic regime, and the BTFR prediction vf4 = GMbarcH0/(2π), are unchanged. The screening is a consequence of the same Gross–Pitaevskii equation that governs the rest of the theory: no new parameters, no additional postulates. The Cassini bound, previously the principal existential risk of the framework, becomes a quantitative confirmation test. A scan of the residual anomaly throughout the Solar System shows that the predicted signal grows as r2 and reaches ∼ 3 × 10−13 m s−2 at ∼ 550 AU, i.e. at the current Cassini-level sensitivity — placing a direct falsification test within the reach of future deep-space missions of the FOCAL class.