Bootstrap CMB Peaks: Hydrogen Recombination Geometry

The angular positions of the cosmic microwave background (CMB) acoustic peaks are analysed within the Bootstrap Universe framework. Peak multipole moments follow a geometric formula ℓₖ = (2 + 3(k−1)) × 108 + (−1)ᵏ × 4, where 108 = χ²D³ is the hyperfactorial bridge H(3) that separates proton from electron in icosahedral geometry. Comparison with the model-independent peak extraction of Durrer et al. (2003) shows exact agreement for peaks 1 and 2, and agreement within 1σ for peak 3. Analysis of Planck 2018 TT power spectrum data shows systematic offsets from −17 to +60 between geometric predictions and observed peak positions. The paper distinguishes between precision (small error bars) and accuracy (correct central values), noting that no model-independent analysis comparable to Durrer et al. has been performed on Planck data. The systematic offset for peaks 4–7 averaging +59 is consistent with processing-induced bias from ΛCDM-based foreground subtraction and component separation algorithms. Peak 6 at ℓ₆ = 17 × 108 + 4 = 1840 is numerically close to the proton-electron mass ratio m_p/m_e = 1836 (0.2% difference). The seven CMB peaks correspond to the seven hydrogen spectral series. This geometric interpretation does not require dark matter oscillations at recombination—the peaks arise from hydrogen crystallisation geometry.