secondPeakRatio
plain-language theorem explainer
The second acoustic peak ratio is defined as the rational 507/220, which equals approximately 2.305 and satisfies the open interval (2.3, 2.4). Cosmologists working in the Recognition Science framework cite this constant when assembling certification structures that match predicted CMB multipoles to Planck data. The definition is a direct rational assignment chosen so that a one-line norm_num verification confirms the band constraint.
Claim. The second acoustic peak ratio is the rational number $507/220$.
background
In the Recognition Science treatment of cosmology the first CMB acoustic peak sits at multipole 220, recovered exactly as the product of baryon rung 44 and configuration dimension 5. The module therefore requires the second-to-first peak ratio to lie inside (2.3, 2.4). The present definition supplies the concrete rational 507/220 that meets this bound while remaining close to the observed value 2.305.
proof idea
The declaration is a direct definition that binds the identifier to the literal rational 507/220. The companion theorem secondPeakRatio_band unfolds the definition and applies norm_num to establish the two-sided inequality.
why it matters
This definition supplies the numerical value required by the CMBCert structure, which records that the first peak equals 220, matches the Planck value, and that the second ratio lies inside (2.3, 2.4). It thereby closes the translation from the RS-derived peak position baryonRung * configDim into an observable acoustic spectrum. The choice aligns with the eight-tick octave scaling that underlies the phi-ladder.
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