CMB Peak Positions from Matrix Theory: A Zero-Parameter Prediction with Falsification Criteria

We derive a prediction for the acoustic peak positions of the cosmic microwave background (CMB) temperature power spectrum from Matrix Theory (MT) — a discrete framework based on a three-dimensional cubic lattice. The prediction has zero free parameters, and its form is ℓ_k = 36 · (8k − 1 + ε(k)), where 36 = Qn · FV encodes the lattice resolution (Qn = 3, FV = 12), the factor 8k − 1 counts the active positions in the k-th Qn layer, and ε(k) = (3/4)k − 7/3 + (3/13)(−1)^k is a structural correction whose coefficients are fixed by the invariant relations f = Qn²/FV = 3/4, λ = 2Qn/B13 = 6/13, and a boundary condition at k = Qn. The formula is valid for k ≥ 4, where ε(k) > 0. Comparison with Planck 2018 TT peak positions k = 4, 5, 6, 7 yields a root-mean-square deviation of 0.05% (χ² ≈ 0.15 over four data points) with zero fitted parameters. Predictions for k = 8, 9, 10 are ℓ₈ = 2408, ℓ₉ = 2707, ℓ₁₀ = 3038, testable with CMB-S4. We also predict an odd/even peak amplitude ratio of 2.11 (observed 2.13 ± 0.08) and an E-mode polarization shift of Δℓ = 144 (observed 141.1 ± 7.9). We discuss the relationship to ΛCDM, the current status of the ε(k) derivation, and pre-registered falsification criteria.