rs_omega_b_h2
plain-language theorem explainer
The declaration supplies the RS baryon density parameter as the numerical constant 0.022 for use in BAO sound-horizon calculations. Cosmologists working inside the Recognition Science framework cite it when comparing predicted Ω_b h² to Planck data or when establishing the baryon loading ratio R(z). The definition is introduced by direct assignment with no reduction steps or lemmas.
Claim. The Recognition Science baryon density parameter is defined by the equation $Ω_b h^2 = 0.022$.
background
The BAO module derives the sound horizon r_s ≈ 147 Mpc from RS-predicted cosmological parameters, including the baryon-to-photon ratio that enters the sound-speed formula c_s = c / √(3(1+R)). The upstream theorem from PrimitiveDistinction maps seven independent axioms to four substantive structural conditions plus three definitional facts, supplying the axiomatic grounding for all subsequent numerical constants in the framework.
proof idea
This is a direct numerical definition with no lemmas applied. The assignment 0.022 is inserted verbatim and serves as an input constant for downstream comparisons.
why it matters
The definition supplies the baryon density input to the theorem matter_exceeds_baryons, which proves rs_omega_b_h2 < rs_omega_m_h2 and thereby isolates the dark-matter contribution. It fills the RS baryon density slot required by the BAO sound-horizon integral and the baryon-loading ratio R(z) = 3ρ_b/(4ρ_γ) listed in the module documentation. The value is consistent with the framework's baryogenesis prediction and with the spectral-index result n_s ≈ 0.967 that appears in the same downstream block.
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