We present a falsifiable brane-world framework that addresses the S8 tensionvia Kaluza–Klein dark matter (KK-DM) in a Randall–Sundrum bulk. The modelmakes a unique prediction: an oscillatory void–galaxy correlation at r~15 h-1Mpc,testable with DESI and absent in common alternatives such as f(R), Horndeski, ormassive neutrinos. Current data allow (but do not require) the framework; upcomingsurveys will decisively test it.Mechanism. KK tower modes projected via the Shiromizu–Maeda–Sasaki (SMS)construction behave as quasi-CDM while inducing late-time growth screening (weff ˜-10-2 for z < 1), reducing S8 by .S8~0.04–0.06 and preserving cT = 1 (GW170817).A chronon (cuscuton with fixed-norm constraint) enforces a timelike foliation withoutpropagating scalar DOF. A mass-gap crossing around z~6–10 explains the early/latesign flip; a controlled early pulse can raise H0 by ~2–3kms-1 Mpc-1 while remainingCMB-safe.Falsifiability. We adopt a Bayesian kill-switch: either a consistent multi-probe latetimesuppression and the void oscillation are detected, or ßS8.0 and the frameworkcollapses to .CDM. With BAO-only, KK-DM is statistically equivalent to .CDM;discriminating power lies in RSD/WL/voids/CMB-lensing.

We construct a brane–bulk EFT targeting the S8 tension while enforcingcT=1. The observable imprint resides in (µ, ., S), anchored to SMS (App. A). Amass-gap crossing generates an early small-scale enhancement and a late largescalesuppression. The W sector explains weff <0 without a new propagatingscalar. We add a controlled early phantom-like pulse that raises H0 whileremaining CMB-safe, and a perturbative bulk anisotropy sector predicting Gpcscalesignatures.