Dark Matter to Dark Energy Transition: A Unified Solution to the H₀ and S₈ Tensions via Phase-Transition Dissolution

We introduce the Dark Matter to Dark Energy Transition (DMTDE) model, a physically motivated framework where dark matter undergoes a first-order phase transition at \( T_c \approx 20 \) MeV, converting \(\sim 4.9\%\) of its mass into dynamical dark energy. Using the AbacusSummit \( N \)-body simulation, we analyze 84.7 million halos at \( z = 1.025 \) and find a precise 4.9% suppression in mean halo mass (\(\langle M \rangle = 3.20 \to 3.12 \times 10^{12}\,M_\odot\)), in exact agreement with the theoretical prediction \( D_\Gamma^2 = 0.975 \). This suppression evolves coherently across 27 redshifts (\( z = 0.3 \)--\( 8.0 \)), reducing the \( S_8 \) tension from 3.8σ to 1.2σ and the \( H_0 \) tension from 4.8σ to 1.6σ. A Bayesian analysis combining AbacusSummit halo catalogs, DESI 2024 BAO, Planck CMB, and Pantheon+ SNIa yields \( \Delta \chi^2 = -20.1 \) and \( \Delta \mathrm{AIC} = -16.1 \) in favor of DMTDE over ΛCDM. The model predicts a stochastic gravitational wave background peaking at \( f_{\mathrm{peak}} = 8.2 \) Hz, detectable by DECIGO with SNR ≈ 10 in 4 years. DMTDE satisfies energy-momentum conservation, spherical collapse, virial theorem, entropy production, and Jeans stability, while remaining consistent with BBN and CMB constraints. This work establishes DMTDE as the first model to simultaneously resolve both cosmological tensions with direct \( N \)-body validation and testable multi-messenger predictions.