SpectrumFalsifier
plain-language theorem explainer
This structure packages the conditions under which the RS derivation of the primordial power spectrum from J-cost fluctuations would be falsified. Cosmologists comparing RS predictions to CMB data would cite it to list explicit failure modes for the spectral index, tensor ratio, and non-Gaussianity. The definition is a bare structure that assembles three propositions plus an embedded implication to falsehood with no further steps.
Claim. A structure with fields: a proposition that the spectral index $n_s$ has no connection to the golden ratio, a proposition that the tensor-to-scalar ratio $r$ contradicts the prediction of order $(φ^{-1})^4$, a proposition asserting large non-Gaussianity, and a proposition that the conjunction of the first two implies falsehood.
background
The module COS-009 targets derivation of the CMB power spectrum $P(k) ∝ k^{n_s-1}$ from J-cost quantum fluctuations during inflation, with the φ-ladder fixing the tilt. J-cost is the recognition cost function $J(x) = (x + x^{-1})/2 - 1$ and φ is the self-similar fixed point from the forcing chain. The module states the target as a PRL paper proposition linking the spectral index to the golden ratio, citing observed values $n_s ≈ 0.965$ and $A_s ≈ 2.1 × 10^{-9}$.
proof idea
This is a structure definition with an empty proof body. It directly encodes the three falsification conditions stated in the module documentation together with the implication to falsehood under the first two propositions.
why it matters
The definition specifies the empirical tests that would falsify the COS-009 derivation of the primordial spectrum from J-cost fluctuations. It implements the falsification criteria listed for the module's PRL target on the CMB spectral index from the golden ratio. It touches the open question of whether observations will confirm the φ-connection for $n_s$ or the $(φ^{-1})^4$ scaling for $r$.
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