Phantom-divide crossing and suppressed structure growth in kinetically braided dark energy with momentum exchange

We construct a linearly stable scalar-field model that realizes both an upward crossing of the dark-energy equation of state, from $w_{\rm DE}<-1$ to $w_{\rm DE}>-1$, and weakened gravitational clustering in the cold dark matter (CDM) sector. An exponential potential breaks shift symmetry and drives the background from a stable phantom phase toward the nonphantom regime, while a pure momentum-transfer interaction increases the dynamical inertia of CDM without altering its background dilution law. We derive the background and linear perturbation equations and establish the no-ghost and Laplacian-stability conditions. For perturbations deep inside the Hubble radius, where the quasi-static approximation applies, the effective gravitational coupling for CDM can fall below Newton's constant, suppressing late-time growth and small-scale matter power, while the baryonic coupling remains enhanced by Galileon braiding. A modified CLASS calculation, including the scalar-field perturbation and the full Boltzmann hierarchies, reveals signatures of transient braiding around radiation--matter equality. For the representative stable solutions studied here, these signatures include an enhancement of matter power toward the lowest wavenumbers probed numerically and a reduction of CMB temperature power over the multipole range $2\leq\ell\leq30$. We also find small shifts in the acoustic scale and the position of the first temperature peak. These results motivate a full likelihood analysis of the model.