predictions
plain-language theorem explainer
Recognition Science supplies explicit numerical predictions for the CMB spectral index, tensor-to-scalar ratio, running, and non-Gaussianity parameter. Observational cosmologists would reference this list when testing the phi-ladder against Planck and CMB-S4 data. The definition simply enumerates four strings obtained by substituting the J-cost fluctuation spectrum into the standard slow-roll formulas.
Claim. The Recognition Science model predicts a scalar spectral index $n_s - 1 ≈ -1/(8φ^3)$, tensor-to-scalar ratio $r ≈ (φ-1)^4 ≈ 0.02$, running of $n_s ≈ 0$, and non-Gaussianity parameter $f_{NL} ≈ 0$.
background
In the Recognition Science framework, primordial fluctuations arise from J-cost quantum fluctuations during inflation, with the phi-ladder fixing the spectral tilt. The module COS-009 derives the CMB power spectrum $P(k) ∝ k^{n_s-1}$ from these principles, targeting a slightly red spectrum consistent with $n_s ≈ 0.965$. Upstream structures include the J-cost definition from PhiForcingDerived.of and the spectral emergence from SpectralEmergence.of that forces the gauge content and particle generations. The DAlembert ledger factorization calibrates J, while PrimitiveDistinction.from supplies the axiom-to-structure map. These feed the discrete phi-tiers used for nuclear densities and spectral peaks in the astrophysics and engineering modules.
proof idea
This declaration is a direct definition that lists the four predicted observables. It assembles the values by direct substitution of the phi-structure relations from the upstream PhiForcingDerived and SpectralEmergence structures into the standard expressions for $n_s$, $r$, and $f_{NL}$.
why it matters
This definition supplies the concrete observables that close the COS-009 derivation of the primordial spectrum from J-cost fluctuations. It connects the phi-forcing chain (T5 J-uniqueness through T8 D=3) to testable CMB quantities, supporting the proposed PRL paper on the spectral index from the golden ratio. No downstream uses are recorded, leaving open the question of embedding these predictions into a full likelihood comparison with Planck data.
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