M21 Satured Grid Theorem : Geometry unifying dark matter and gark energy

The Saturated Grid Theorem M21 proposes a 21-dimensional geometry (3 branes × 7 dimensions) where dark matter and dark energy emerge as pure geometric effects, without hypothetical particles. This complete version presents the model's architecture, founded on an axial anisotropic metric with ξ₀ = 2.3866, and 14 quantitative validations covering the cosmological spectrum: CMB peaks, BAO, gravitational lensing, gravitational waves, BBN, neutrinos, and JWST galaxies at high redshift (typical deviations < 1 %, zero free parameters). The foundations include a dimensional partition (1/21 baryons, 5/21 apparent DM, 15/21 DE confinement) and an evolution f(z) = 1/[1 + (z/3)^2]. Three falsifiable predictions for 2026-2030 (JWST ancient UDG, g_max limit, cosmic axis) will allow to decide. With epistemological honesty, the open problems are assumed: tension with ultra-diffuse galaxies (UDG), S8, and formal derivation of the 21D action. M21 offers a geometric unification of the physics of scales, inviting interdisciplinary exploration. Keywords: anisotropic cosmology, geometric dark matter, emergent dark energy, extra dimensions, saturated grid, 21D, branes, cosmic anisotropy.