Emergent Modified Growth from KK Dark Matter: Chronon-Regulated Foliation, S8-Targeted Phenomenology, and Multi-Probe Falsifiability

We present a falsifiable brane-world framework that addresses the S8 tension via Kaluza–Klein dark matter (KK-DM)
in a Randall–Sundrum bulk. The model predicts an oscillatory void–galaxy correlation at r ∼ 15 h−1Mpc, testable with DESI and absent in f (R), Horndeski, or massive-neutrino alternatives. Current DESI DR1 full-shape constraints show no clear S8 suppression (central value slightly above Planck), placing pressure on the scenario; upcoming scale-dependent growth and void analyses will be decisive.
Gap closures integrated. (i) Microscopic RS derivation with ηλ= 0.01, ηψ =0.005 (App. F′′′); (ii) Non-linear EFT extension μ → μ + ηT k/(k + kd) + ηS Φ/Ψ (§IV); (iii) Bulk anisotropy with εaniso=5 × 10−5, zcoh=1.5 (App. J); (iv) Void selection VIDE with Rvoid ∈ [10, 20] h−1Mpc, αvoid ≈ 2.5(μ − 1) (§VI); (v) Early pulse stability with σa= 0.3 and R |1 + w| dN < 0.1 (App. I).
These improve kc precision (±0.01 h Mpc¹) and stabilize DR3 phenomenology (RSD/WL/voids).