IndisputableMonolith.Cosmology.InflationSpectralIndexFromJCost
This module derives the RS inflationary spectral index nsRS from the J-cost function with gap-45 fixed as the body-plan ceiling. Cosmologists working in Recognition Science cite it to obtain n_s values consistent with Planck data. The module consists of definitions for gap45 and nsRS together with bounding lemmas and a certification theorem.
claim$gap_{45} = 45$, $n_s^{RS}$ satisfying $0 < n_s^{RS} < 1$ and lying near the Planck measurement.
background
The module sits in the cosmology domain of Recognition Science and imports the fundamental time quantum τ₀ = 1 tick from Constants. It introduces gap45 as the body-plan ceiling equal to 45 and defines nsRS as the spectral index obtained from the J-cost function in the inflationary setting. Related declarations establish the band containing nsRS and its proximity to the observed Planck value.
proof idea
The module is definition- and lemma-driven. It first fixes gap45 = 45, then defines nsRS and proves the inequalities nsRS_lt_one, nsRS_gt_zero together with the band and near-Planck statements; SpectralIndexCert packages the certified result.
why it matters in Recognition Science
The module supplies the spectral index computation required by Recognition Science cosmology. It realizes the implications of the T5 J-uniqueness and T7 eight-tick octave for inflationary observables and connects to the phi-ladder used in mass formulas. No downstream uses are currently listed, yet the results support the overall forcing chain from T0 to T8.
scope and limits
- Does not derive the tensor-to-scalar ratio.
- Does not compute higher-order slow-roll corrections.
- Does not address reheating dynamics.
- Does not compare against non-RS inflationary potentials.