Z_Geometric_Dynamics_III__Geometric_Unification_of_Forces

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(R_i/l_P)^2] = 1/ln(R_p/l_P), derived the subset inequality with saturation value α_max = 1/I_obs ≈ 0.0070692, excluded α = α_EM, 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 g^2/4π = 1/32 and the weak mixing angle sin^2 θ_W = 32α_EM, in excellent agreement with experiment. More importantly, the five-dimensional topological excision model independently yields the 1/32 correction factor; combined with the direction constraint α < α_EM established in Paper II from the information saturation paradigm, this determines α_EM as the corrected value, giving α_EM = (32/31)α, i.e. α = (31/32)α_EM ≈ 0.0070693. This value agrees with the saturation value of the observational path to within a relative deviation of 1.9×10^(-5), constituting a bidirectional self-consistent verification between microscopic geometry and macroscopic cosmology. Extending to seven dimensions, using the Hopf fibration S^3 ↪ S^7 → S^4 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 α_s = 32/(9π^3). 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 m_p/m_e = 6π^5 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(α_EM - α)/(m_p/m_e)^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 m_p/m_e, α_EM/α, sin^2 θ_W, α_s, etc.) are rigidly determined by geometry and contain no free parameters; absolute scales (such as the electron mass m_e and the compactification radius R) currently still require experimental input as anchor points for the theoretical scale.