The 6D Action Principle for the (3+3) Spacetime Framework: Lagrangian Foundations, Geometric Closures Across Particle Physics, Cosmology, Gravity, and Quantum Foundations from a Discrete S² with 2¹⁵² Cells

We present a Lagrangian-level treatment of the (3+3) spacetime framework — a six-dimensional theory with three spatial and three temporal dimensions, the third time dimension compactified as a discrete two-sphere S² of radius R₃ = πℏ/(m_e c) with N_cells = 2¹⁵² Planck-area cells — building on the geometric derivations developed in the book From One Sphere to All of Physics and applied to specific phenomena in four companion preprints. The framework derives approximately fifty zero-parameter closures across particle physics, cosmology, gravity, quantum foundations, famous unsolved problems, and laboratory predictions, using only one dimensionful scale (the Planck scale, M_P = √(ℏc/G_N), equivalently L_P, G_N,…