A Priori Deduction of the CMB Acoustic Spectrum, BAO Sound Horizon and Cosmic Energy Budget from the Five-Axiom Framework of Array Cosmology in Array Cosmology

Abstract

Array Cosmology (AC) derives the complete CMB acoustic spectrum from the five axioms {12, π, γ1, ln 2, φ} with zero free structural parameters.

We prove that the information-thermodynamic budget of the 12-axis rendering engine is L = ⌈12γ1 + 16π⌉ = 220, identical to the observed CMB first acoustic peak.

The complete peak position formula, where lA = 2 × 122 + L Znoise = 309.59 and all parameters are axiom-derived, achieves RMS 0.58% across seven observed peaks with zero free parameters. The amplitude model, where Graw = (144 − α^−1)/γ1 (verified to 0.08%) and the recycling exponent p = 24(π − 3) = δPMNS CP , achieves RMS 4.6% with D0 as the sole free parameter.

We further derive the primordial spectral index ns = 1−(π−3)/4 = 0.9646 (Planck 2018: 0.9649, error 0.03%). Seven key identities
are established, connecting the CMB to the Standard Model, neutrino sector, and Riemann zeta function within a single axiom framework. Five falsifiable predictions are presented for CMB-S4 and Simons Observatory.