The Ballagh Unified Field Theory: Deriving the Fundamental Constants, Mass Spectrum, and Gravitational Mechanics from a Discrete 2.5D Hyperelastic Manifold

The Ballagh Unified Field Theory presents a comprehensive structural unification of General Relativity and Quantum Field Theory by abandoning the orthodox assumption of a continuous, integer-dimensional spacetime. Superseding and rigorously correcting earlier exploratory models published by the author, this finalized framework redefines the vacuum as a discrete, locally fractional 2.5D hyperelastic manifold. By applying strict continuum mechanics to this topological lattice, fundamental particles are reclassified not as abstract point-masses, but as localized acoustic standing waves and topological vortices. Concurrently, macroscopic forces emerge deterministically as the longitudinal and transverse strain responses of the structural metric pore. Operating under a strict mandate that prohibits empirical back-fitting and arbitrary scaling scalars, the theory establishes a rigid causal hierarchy between irreducible empirical boundary conditions and derived predictions. The foundational geometry of the space-frame and the universally recognized kinetic rest energy of the electron are utilized to forward-calculate the exact phenomenological mass spectrum of the universe. The derivations of the stable hadronic structures, heavy leptons, and electroweak gauge bosons are mathematically proven to be strict thermodynamic yield limits and phase-space saturation points. These derivations perfectly conserve the mass-energy of physical decay kinematics, successfully mapping the exact structural strain budgets of phenomena such as Beta decay and multi-stage cascade fractures. The theoretical architecture culminates in the Complete Non-Linear Ballagh Lagrangian Density, which permanently unifies macroscopic gravitational displacement with the internal torsional strain of the metric, bounded by an anharmonic elasticity tensor that naturally prevents mathematical infinities. The framework provides immediately falsifiable predictions, mathematically proving that prior to the macroscopic topological crossover scale, gravitational wave amplitude must attenuate at a rigid geometric rate of $1/r^{0.75}$. By translating the fundamental forces of nature into the uncompromising language of discrete lattice kinematics, this finalized manuscript replaces all prior incorrect phenomenological assumptions with a mathematically transparent, deterministic mechanical engine for the cosmos.