SpectrumFalsifier
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.
claimA 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 in Recognition Science
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.
scope and limits
- Does not derive the power spectrum or its amplitude.
- Does not compute numerical values for n_s or r.
- Does not incorporate the Recognition Composition Law.
- Does not address the eight-tick octave or spatial dimensions.
formal statement (Lean)
235structure SpectrumFalsifier where
236 ns_no_phi : Prop
237 r_contradicts : Prop
238 large_nongaussianity : Prop
239 falsified : ns_no_phi ∧ r_contradicts → False
240
241end PrimordialSpectrum
242end Cosmology
243end IndisputableMonolith