We derive, from a well-defined action principle, a redshift-dependent perturbation \( \alpha(z) \) to the dark energy density that arises when a canonical scalar field \( \phi \) couples to a spontaneously confining hidden \( SU(N) \) gauge sector through a chiral anomaly portal. The ultraviolet cutoff of the effective theory is fixed, without adjustment, at ΛUV = 13.6 TeV, consistent with the null results of the Large Hadron Collider (LHC). The confinement scale of the hidden sector is set equal to that of Quantum Chromodynamics, ΛQCD = 300 MeV, providing the infrared anchor of the construction. A perturbative expansion around the ΛCDM background yields a closed-form ordinary differential equation (ODE) for \( \alpha(z) \), whose solution reproduces the expected transition behaviour at \( z_c \approx 0.7 \) and leaves a cosmologically small but non-zero residue at \( z=0 \) from the TeV anomaly. The resulting effective equation-of-state parameter \( w_{eff}(z) \) departs from -1 by at most \( 2\% \) at low redshift, yet generates a \( 6\% \) suppression in the matter fluctuation amplitude \( \sigma_8 \) relative to ΛCDM, in the direction required to reduce the present \( 2-3\sigma \) discrepancy with weak-lensing measurements. All parameters are either fixed by known physics or by numerical convergence criteria; none is tuned to reproduce a pre-specified output. A dedicated section on falsifiability examines experimental signatures at LHC, ALPS~II, neutron electric-dipole moment (nEDM) experiments, and the Eöt-Wash torsion balance. The scope and domain of validity of the construction are stated explicitly in a limitations section.