SpectrumFalsifier
plain-language theorem explainer
SpectrumFalsifier packages the three observational conditions that would refute the Recognition Science derivation of the CMB power spectrum from J-cost fluctuations. Cosmologists testing the phi-ladder prediction for the spectral index n_s would cite this structure when confronting data. It is a pure definition that simply declares three propositions and one implication with no computational steps.
Claim. A structure consisting of the propositions that the spectral index $n_s$ lacks a connection to the golden ratio, that the tensor-to-scalar ratio $r$ contradicts the prediction $r = (phi^{-1})^4$, and that large non-Gaussianity is observed, together with the implication that the conjunction of the first two propositions yields a contradiction.
background
The module derives the primordial power spectrum from J-cost quantum fluctuations during inflation, with the phi-ladder fixing the spectral tilt so that $n_s - 1$ is expected to be phi-related. The local setting is the COS-009 target of obtaining the observed nearly scale-invariant spectrum $P(k) propto k^{n_s-1}$ with $n_s approx 0.965$ directly from Recognition Science principles. No upstream lemmas are referenced; the structure stands as the explicit falsification interface for the claimed phi-connection.
proof idea
This declaration is a pure definition of a structure; it contains no proof body, tactics, or applied lemmas.
why it matters
The structure supplies the concrete falsification criteria for the COS-009 paper proposition that the CMB spectral index arises from the golden ratio via the phi-ladder. It anchors the cosmological application of the forcing chain by specifying how violations of J-uniqueness or the phi fixed point would manifest in observables. It leaves open the empirical question of whether current data satisfy the three listed conditions or instead support the derivation.
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