nsRS_val
plain-language theorem explainer
Recognition Science predicts the inflationary spectral index to be exactly 1 minus 2 over 45. Cosmologists comparing RS models to Planck CMB data would cite this equality to obtain the interval (0.955, 0.957). The proof is a one-line wrapper that unfolds the spectral-index definition and the gap-45 constant then normalizes the cast.
Claim. The Recognition Science spectral index satisfies $n_s = 1 - 2/45$.
background
The module formalizes the Recognition Science prediction for the scalar spectral index in inflation. Planck 2018 observations give $n_s = 0.965 ± 0.004$. RS sets $n_s = 1 - 2/gap45$ with gap45 fixed at 45, which encodes the effective e-fold count $N_e$ arising from the phi-ladder rung structure plus corrections, yielding the RS-Starobinsky formula $n_s = 1 - 2/gap45$ in the interval (0.955, 0.957).
proof idea
The proof is a one-line wrapper. It unfolds the definitions of the spectral index and gap45, then applies norm_cast to equate the expression to the numerical value 1 - 2/45.
why it matters
This equality supplies the exact value required by the band theorem establishing membership in (0.955, 0.957) and by the near-Planck theorem showing absolute deviation less than 0.015 from the observed value. It realizes the RS-Starobinsky relation inside the formal system, linking the phi-ladder to CMB observables. The result closes the formal step between abstract Recognition constants and concrete spectral-index data.
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