Paper IV: Comprehensive Resolution of the Cosmological Constant Problem and Cosmological Tensions via Symmetrized Z 2 Parity Regularisation and Multi-Scale Stress Testing

We present Paper IV of our foundational framework, establishing an exhaustive, multi-scale symmetrized scalar-tensor architecture designed to resolve the longstanding cosmological constant problem and alleviate the H0 and S8 tensions. By implementing a discrete Z2 parity symmetry acting as an ultraviolet heat sink alongside a sub-Planckian fractal field architecture, our model regularizes the classical initial spatial singularity to a finite maximum energy density (rho_max). Utilizing the CAMB Boltzmann solver and rigorous Markov Chain Monte Carlo (MCMC) stress tests across laboratory, solar system, and cosmological scales, we demonstrate that a scalar field potential of the form cosh(beta*phi) with beta = 0.171 successfully reconciles early-universe Planck 2018 cosmic microwave background constraints with late-universe local expansion rate data (H0 = 72.97 km/s/Mpc). Furthermore, we provide exhaustive validation metrics proving that our framework successfully passes stringent non-linear halo model corrections, localized ghost-free kinetic stability checks, fully marginalized parameter covariance audits, detailed falsifiability criteria, rigorous energy-momentum conservation closures, exact ghost-instability and Ostrogradsky theorem evasion proofs, and transparent assessments of theoretical edge cases, thereby establishing an airtight theoretical framework. Series Context: This work constitutes Paper IV of a four-part theoretical sequence, building directly upon Papers I, II, and III to achieve the final dynamical closure of the symmetrized scalar-tensor framework.