The Triadic Asymmetry Principle: A Unified Geometric Origin of Dark Matter, Dark Energy, and Density-Modulated Gravity

This preprint introduces the Triadic Asymmetry Principle (TAP), a geometric framework in which Motion, Time, and Space form an ordered, non-commuting triad. The non-closure of this triad is quantified by the asymmetry scalar A = ||[M, T, S]||, which acts as a new geometric invariant. By deforming the gravitational action via a multiplicative function F(A), the framework generates three emergent late-time cosmological sectors: (1) a density-modulated effective Newton constant G_eff(ρ), (2) a rigidity-dominated matter component (TRM) with scaling ρ ∝ a^{-3(1+β)}, and (3) a geometric dark-energy contribution proportional to the triadic asymmetry. The theory is fully covariant, introduces no new dynamical fields, and recovers General Relativity in high-density or high-curvature regimes through a natural geometric screening mechanism. TAP predicts mild, correlated observational signatures relevant to the Hubble tension, the S8 growth-rate suppression, and recent DESI indications of evolving w(z). This version contains 12 pages, 4 figures, and 3 appendices, including derivations of the TAP-modified field equations, cosmological applications, and perturbative extensions.