N11 — First acoustic peak $_1 = 220.6$
N11: First acoustic peak $_1 = 220.6$. Planck legacy, CMB-S4.
Falsification Details
ell-1 = 220.6. acoustic peaks!prediction pred:n11 M3h holonomy (V.T190), where $_b$ undershoot ($-1.2%$) compensates $_m$ overshoot ($+4.1%$) in the sound horizon.
Planck legacy, CMB-S4
confirmed at $+0.28%$.
Context
N11: Prediction
ell-1 = 220.6.
M3h holonomy (V.T190), where $ω_b$ undershoot ($-1.2%$) compensates $ω_m$ overshoot ($+4.1%$) in the sound horizon. Experiment: Planck legacy, CMB-S4. Timeline: confirmed at $+0.28%$.
Derivation Context
The first acoustic peak multipole is determined by the Friedmann pipeline with $τ$-native inputs:
where $_A = π d_A(z_rec) / r_s(z_rec)$ is the acoustic scale, $d_A$ is the angular diameter distance, $r_s$ is the sound horizon at recombination, and $_1$ is the phase shift from the neutrino and gravitational driving. All quantities are computed from $ι_τ$ with zero free parameters. The Planck measurement gives $_1 = 220.0 ± 0.5$. The deviation is $+0.28%$ ($+2840$ ppm). (Registry: V.T190, $τ$-effective, Wave 8A.)
The computation of $_1$ requires three $τ$-native inputs, each derived from $ι_τ$:
- Baryon density: $ω_b = 0.02209$, derived from $η_B = (121/270)\,ι_τ^19$ (Section (sec:ch62-baryon-density)).