Geometric Origin of the CMB Peaks in a 4-Simplex 3.998D Fractional Manifold Reality

We extend the 3.998D unified geometric framework into the domain of the Cosmic Microwave Background (CMB) radiation, providing a parameter-free derivation of the acoustic peak spectrum that bypasses the necessity for ΛCDM’s Dark Matter, Dark Energy, and Inflationary priors. Building upon the framework’s success in resolving galactic rotation anomalies and particle mass hierarchies, we demonstrate that the CMB power spectrum emerges as a topological resolution of a 4-simplex unit cell within a 3.998D manifold. Using a unified Metric Resolution Protocol, we derive both the positions (l) and power amplitudes (Dl) for the first 16 acoustic peaks. The fundamental peak is determined at l1 ≈ 221.48 with a theoretical amplitude of ≈ 5914.4 μK2, aligning with Planck 2018 observations. Subsequent amplitudes for l2 ≈ 543.2, l3 ≈ 808.7, and the volumetric cell resonance at l4 ≈ 1109.1 are calculated as ≈ 1972.4 μK2, ≈ 2365.7 μK2, and ≈ 1081.7 μK2 respectively. A critical extension of this work is the resolution of the high-l damping tail. By identifying a geometric correction (1 − C ≈ 0.866), we show that the observed suppression of higher-order harmonics is a consequence of successive resolution depth within the manifold bulk rather than thermal diffusion (Silk damping). The model further predicts a geometric resolution floor, preventing premature decline of power in the extreme multipole range. A closer look at the framework reveals that the theoretical results are statistically indistinguishable from measured data, and suggests that the CMB may be a manifestation of the vacuum’s geometric architecture.