crossSectionRatio
plain-language theorem explainer
Recognition Science defines the dark-matter cross-section ratio as J(φ). Cosmologists testing direct-detection experiments cite this quantity when checking the interval (0.11, 0.13) against observed limits. The declaration is a direct abbreviation that evaluates the J-cost function at the golden ratio.
Claim. Let $r$ be the dark-matter to neutrino cross-section ratio. Then $r = J(φ)$, where $J(x) = (x + x^{-1})/2 - 1$.
background
The module records the RS dark-matter prediction that identifies the candidate at mass $m_{DM} = m_W / 45$ with cross-section ratio $r = σ_{DM}/σ_ν$ equal to the J-cost of φ. The J-cost satisfies the Recognition Composition Law and supplies the canonical cost measure in RS-native units. Phi is the self-similar fixed point forced by the unified forcing chain (T5–T6).
proof idea
The declaration is a one-line definition that evaluates the J-cost at phi. No lemmas or reductions are invoked inside the definition itself.
why it matters
This definition supplies the central quantity required by the structure DarkMatterCrossSectionCert and the theorems crossSectionRatio_band and crossSectionRatio_pos. It realizes the module-level claim that the ratio equals J(φ) and lies in (0.11, 0.13), with any lower exclusion falsifying the identification. The construction draws on J-uniqueness from the forcing chain (T5).
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