sigma_DM_over_sigma_nu_RS
plain-language theorem explainer
Recognition Science predicts the dark-matter to neutrino cross-section ratio equals phi minus three halves. Experimentalists comparing direct-detection limits to theory cite this value to anchor the expected band. The declaration is realized by a direct definition that evaluates the J recognition function at the golden-ratio fixed point.
Claim. The dark-matter to neutrino cross-section ratio equals $J(phi)$, where $J(x) = (x + x^{-1})/2 - 1$ and $phi$ is the golden ratio satisfying $phi = 1 + 1/phi$.
background
The module P0-A6 sets the structural band for the dark-matter cross-section ratio. The predicted ratio is the golden-section recognition quantum J(phi) = phi - 3/2. The J function is the unique solution satisfying the recognition composition law from the forcing chain T5.
proof idea
This is a direct definition. It assigns the ratio the value phi minus 3/2, which is the simplified expression for J(phi) at the self-similar fixed point.
why it matters
The definition is used in DarkMatterCrossSectionBandScoreCardCert to certify the ratio band 0.11 < ratio < 0.13 and in the absolute cross-section scorecard to scale the prediction to cm squared units. It fills the P0-A6 slot in the Recognition Science framework, linking the cross-section prediction to the J-uniqueness result T5 and the phi fixed point T6. The module flags that absolute normalization remains an empirical input.
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