rs_cmb_approx_2725
plain-language theorem explainer
The Recognition Science framework predicts the cosmic microwave background temperature by dividing a recombination temperature of 3000 K by one plus a redshift of 1100. Cosmologists working with RS-derived constants would cite this result to confirm the numerical value sits near 2.725 K. The proof is a one-line wrapper that unfolds the temperature definitions and applies numerical normalization to establish the bound.
Claim. Let $T_0$ be the CMB temperature given by $T_0 = 3000 / (1 + 1100)$. Then $|T_0 - 3000/1101| < 0.001$.
background
The module derives the present-day CMB temperature from the recombination epoch. Recombination temperature is fixed at 3000 K via the Saha equation using the RS baryon-to-photon ratio. Recombination redshift is set to 1100. The temperature formula is then the recombination temperature divided by one plus the redshift, which encodes photon cooling under cosmic expansion.
proof idea
The proof is a one-line wrapper. It unfolds the definitions of the CMB temperature, the recombination temperature, and the recombination redshift, then applies norm_num to evaluate the numerical difference and confirm the inequality.
why it matters
This result supplies a numerical anchor for the RS prediction of the CMB temperature near 2.725 K, matching the FIRAS value within the stated tolerance. It supports the module's derivation of the blackbody spectrum and first acoustic peak from the Recognition Composition Law and the phi-ladder. The theorem closes a verification step referenced in the RS_CMB_Temperature paper.
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