ZGeometricDynamicsIII_GeometricUnificationₒfForces

Building upon the Kaluza-Klein (1926) five-dimensional unification framework, and extending Z-Geometric Dynamics (Paper I) and its sequel (Paper II), this paper constructs an extended geometric theory that incorporates gravity, electromagnetism, weak interactions, and the strong force into a common five- and seven-dimensional parameter space. Paper II established the geometric entropy constant α=1/π (Rᵢ/lP) ², derived the inequality α≤0. 007067, excluded α=αEM, and introduced the physical picture of "spatial thickness". Starting from five-dimensional Riemannian geometry and using Kaluza-Klein reduction, we derive the Einstein-Maxwell equations, showing that electromagnetism emerges as the projection of the fifth-dimensional fiber. Introducing torsion in Riemann-Cartan geometry naturally yields an SU (2) weak gauge field, leading to the weak coupling constant g²/4π=1/32 and the weak mixing angle sin²θW=32 αEM, in excellent agreement with experiment. More importantly, from the five-dimensional topological excision model we independently derive a 1/32 correction factor and, combined with the macroscopic constraint of Paper II to fix the direction, determine αEM=32/31 α, yielding α=31/32 αEM ≈0. 007069. This value is highly consistent with the estimate independently obtained from cosmic information dynamics in Paper II, constituting a bidirectional self-consistent verification between microscopic geometry and macroscopic cosmology. Extending to seven dimensions, using the Hopf fibration S³↪S⁷→S⁴ together with a three-brane structure, we project the SU (3) gauge field from the mixed components of the seven-dimensional spin connection and obtain the strong coupling constant αₛ=32/ (9π³). Through a "three-lobe topological excision" model, we unify the electron, proton, and quarks as different configurations of excised regions, naturally yielding fractional charges and color confinement, and derive the proton-electron mass ratio mₚ/mₑ=6π⁵ from geometric topology in a heuristic manner, consistent with experiment to within 2×10⁻⁵. The framework also gives the cosmic baryon asymmetry η=9 (αEM−α) / (mₚ/mₑ) ² ≈6×10⁻¹⁰, in agreement with Planck observations. Furthermore, the geometric origin of parity violation is revealed: the electron is captured on the y=0 brane by a black hole horizon, the proton resides on the y=L brane, and the weak force originates from the torsion field connecting the two branes; this asymmetric "two-sided thickness" naturally leads to left-handed electrons participating in weak interactions while right-handed electrons remain decoupled. Finally, the paper argues from geometric stability that gravity is the spacetime background, electromagnetism is a property of stable structures, the weak force is the "force" of unstable-to-stable collapse, and the strong force is the resistance when stable structures are disrupted. All "extra dimensions" in this paper refer to a mathematical parameter space describing the internal topological structure of particles, not physical spacetime dimensions. All dimensionless ratios (such as mₚ/mₑ, αEM/α, sin²θW, αₛ, etc. ) are rigidly determined by geometry and contain no free parameters; absolute scales (such as the electron mass mₑ and the compactification radius R) currently still require experimental input as anchor points for the theoretical scale.