Arithmetic Quantum Kinematics Part III: Ground-State Topological Mass Generation, Geometric Spin, and Chiral Symmetry in the E7 Lattice

This paper (Part III) establishes a deterministic, geometric origin for the hadronic mass gap and Chiral Symmetry Breaking within the E_7 lattice. We demonstrate that ground-state mass is fundamentally a dynamic "Topological Action Penalty" incurred as quarks traverse fractional space. By translating quantum spin into a geometric dot product of lattice nodes, we propose a Ground-State Topological Hamiltonian. In the exact chiral limit, this formulation reproduces Chiral Symmetry Breaking, proving the pion's negligible core mass is the result of exact topological cancellation. The mass ratio paradox is resolved by demonstrating that the experimental ~6.72 mass gap emerges naturally when electroweak bare masses (mbare) are introduced, lifting the pion from a massless state while the proton remains dominated by its heavy topological core. Ultimately, analyzing macroscopic Lorentz anisotropy provides necessary geometric proof of topological color confinement, replacing continuous spacetime with rigid arithmetic geometry.