Homogeneous radion evolution in a stabilised two-brane bulk: comparison with a reduced four-dimensional model

We compare homogeneous radion evolution in a Goldberger–Wise-stabilised five-dimensional bulk with a reduced four-dimensional Einstein-frame model. Over one bulk linear period, initial excursions spanning 1.6 × 10⁻³ to 1.3 × 10⁻² give separation differences of 0.588–0.589% and velocity differences of 0.768–0.805%, normalised by initial excursion and reference velocity. The models are differently tuned and their comparison assumes a bulk slice-length map. Their 0.12% equilibrium-mass difference predicts most of the first-turning delay. Subtracting that prediction leaves a negative residual resolved at three of four amplitudes. A four-point fit, registered after two of the amplitudes had been run (§4.4), spans a factor of eight in excursion, while the individually resolved measurements span four, and gives b₁ = (−0.130 ± 0.012)/k; the variation is numerical sensitivity, not statistical uncertainty. Neither a nonzero intercept nor quadratic curvature is resolved. Refinement gives a local apparent turning-time order of about 4.9. Matching the reduced potential's equilibrium mass preserves the resolved residual within numerical variation. Behaviour beyond one period remains undetermined: both preregistered three-period attempts stopped when the static-null control exceeded its constraint-growth limit, before dynamical comparisons began.