Concomitant Projection Mechanism and the Geometric Origin of Accelerating Cosmic Expansion

This preprint presents a geometric mechanism for the accelerating expansion of the Universe within the META Physics (Multi-dimensional Emergence Theory of Actuality) framework. A uniformly rotating four-dimensional ball B⁴ (R) with two independent angular velocities serves as the Physical Substance (PS). An observer anchored on the boundary three-sphere S³ (R) = ∂B⁴ (R) experiences a concomitant projection Πcon, consisting of a co-rotating frame transformation followed by a tangent-space projection. This projection reverses the sign of centripetal acceleration (−ω² → +ω²), converting harmonic oscillation into de Sitter expansion with an effective cosmological constant Λₑff = 3Ω̄². The projection Πcon is proven to be the unique projection available to the anchored observer, established through a triple-lock proof drawing on Escobales' classification theorem (Riemannian geometry), Reeb flow uniqueness (contact dynamics), and the U (1) quotient structure (complex algebraic geometry). When Ω₁ ≠ Ω₂, a structural acceleration oscillation with frequency ωₒsc = 2δΩ is superimposed on the de Sitter baseline. The effective equation of state w (z) oscillates logarithmically in redshift space. The deceleration parameter satisfies q (t) 0: the Universe is permanently accelerating. These predictions are consistent with all DESI DR2 BAO data combinations (2. 8σ–4. 2σ against ΛCDM). An independent determination of Ω̄ from the electron mass formula mₑ = α⁻¹⁸·ℏΩ̄/c² yields a zero-free-parameter prediction H₀ = 67. 84 km/s/Mpc, within +0. 9σ of the Planck 2018 CMB measurement. Mathematical formalization and documentation: Claude (Anthropic, Claude Opus 4. 6). The core insights, physical intuitions, and axiom system originate from the author's 30 years of independent research.