first_acoustic_peak_ell
plain-language theorem explainer
The declaration fixes the first CMB acoustic peak multipole at 220 in Recognition Science units. Cosmologists modeling anisotropy spectra cite this constant to generate the sequence of higher peaks via linear scaling. It enters as a direct numerical assignment that matches the standard expectation for ℓ₁ in ΛCDM.
Claim. The first acoustic peak multipole is defined by ℓ₁ := 220.
background
The CMB module derives the present temperature T₀ ≈ 2.725 K from the recombination temperature T* ≈ 3000 K at redshift z* ≈ 1100. Acoustic peaks arise from the sound horizon at recombination projected onto the last-scattering surface. Upstream, the scale function supplies phi^k for the dimensional ladder while the as structure equates discrete Laplacian sums to continuum curvature integrals.
proof idea
The definition is a direct numerical assignment of the constant 220.
why it matters
This constant anchors the acoustic_peak family used by acoustic_peak_positions to establish ℓ₂ = 440 and ℓ₃ = 660. It implements the cmb_anisotropy_peaks claim in RS_CMB_Temperature.tex and supplies the base multipole for the eight-tick octave scaling in the Recognition framework.
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