A Unified Kaluza-Klein Framework for Processing-Driven Dark Sector Dynamics and Gauge Coupling Evolution (MetaTime v35.6)

We present MetaTime v35.6, a covariant Einstein-frame effective field theory (EFT) in whichlate-time dark-sector exchange is generated by a processing-driven deformation of a Kaluza–Klein(KK) radion potential, while gauge-coupling evolution arises from a sequestered Standard Model(SM) photon and a strongly coupled KK dark gauge sector U(1)D. Relative to prior work, weimplement three shielding upgrades that address naturalness and fifth-force constraints: (i) TrackB sequestering with controlled kinetic mixing—the SM photon is brane-localized while the radioncontrols the KK U(1)D kinetic function; a technically natural portal ζ ∼ 10−6induces a smallbut potentially detectable visible drift ∆α/α ∼ 10−7at z ≃ 1.5 without destabilizing the darkdynamics; (ii) Damour–Polyakov least-coupling evolution—the radion dynamically relaxes toward aminimum of the visible-sector coupling as a → 1, suppressing equivalence-principle violations todaywhile maintaining an active dark exchange Q; (iii) geometric diagnostics from varying constants—the ratio Rµα ≡ ∆µ/∆α is promoted to a topology-sensitive discriminator: Rµα ∼ O(1) suggestsKK-simple internal spaces (e.g. toroidal compactifications), whereas Rµα ≫ 1 points to QCDamplifying threshold structure typical of Calabi–Yau-like geometries. A benchmark window centeredat β1 ≃ 0.052 yields a representative late-time distance–growth deformation consistent with H0 ≃72.8 km s−1 Mpc−1and a clustering reduction ∆S8/S8 ≃ −3.8%, while remaining compatible withperturbative stability under a parameterized post-Friedmann (PPF) closure. We conclude withfalsifiable “double-key” tests combining distance/growth cross-correlations and redshift-dependentdrift templates in fundamental constants.