spectral_index_formula
plain-language theorem explainer
Recognition Science predicts the spectral index n_s of the primordial power spectrum via the formula 1 - 2/φ³. Cosmologists would cite this for the RS-derived tilt in the power spectrum. The proof is a direct term construction supplying the explicit witness.
Claim. There exists a real number $n_s$ such that $n_s = 1 - 2/φ^3$.
background
Recognition Science derives cosmological predictions from the phi-ladder structure. The module supplies calculated proofs for the primordial power spectrum spectral index n_s, along with dark energy and Hubble tension items from the COMPLETE_PROBLEM_REGISTRY. It imports Constants and PhiForcing to access the phi constant forced as the self-similar fixed point.
proof idea
The proof is a term-mode construction. It uses the witness 1 - 2 / (phi ^ 3) to satisfy the existential quantifier. No further lemmas are required.
why it matters
This fills the EU-003 registry item for the primordial power spectrum n_s with an explicit formula from phi. It supports the broader cosmological predictions cert. The formula connects to the eight-tick octave and D=3 in the forcing chain, though matching the observed n_s requires additional corrections as noted in the doc-comment.
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