IndisputableMonolith.Cosmology.InflationSpectralIndexFromJCost
The module defines the gap-45 body-plan ceiling and derives the RS spectral index nsRS for inflation models from the J-cost function, together with its bounds and Planck proximity certification. Cosmologists using Recognition Science frameworks cite these constants when matching the phi-ladder to CMB observables. The module consists entirely of definitions and elementary inequalities with no tactic proofs.
claimDefine the body-plan ceiling $G_{45}=45$. Let $n_s^{RS}$ be the spectral index obtained from the J-cost on the phi-ladder at rung offset $G_{45}$. Then $0<n_s^{RS}<1$ and $n_s^{RS}$ lies inside the Planck band.
background
The module belongs to the cosmology section of Recognition Science and imports the fundamental time quantum $\tau_0=1$ tick from the Constants module. Recognition Science obtains all constants from the J-cost functional equation $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$ whose fixed point forces $\phi$. The module introduces the gap-45 ceiling as the body-plan upper limit and assembles the RS-native spectral index together with its elementary bounds and certification near the observed Planck value.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the spectral index certification that feeds larger Recognition Science cosmology constructions linking the J-cost to inflation observables. It closes the gap-45 definition required by the body-plan structure and places the RS spectral index inside the Planck band, consistent with the eight-tick octave and D=3 spatial dimensions of the forcing chain.
scope and limits
- Does not derive the full slow-roll dynamics of inflation.
- Does not compute the tensor-to-scalar ratio.
- Does not address non-Gaussianity or higher-order spectral running.
- Does not connect the index to specific reheating scenarios.