crossSectionRatio
RS cosmology sets the dark-matter to neutrino cross-section ratio exactly to the J-cost of the golden ratio. Experimentalists bounding direct-detection rates for the 1.79 GeV candidate cite the quantity when comparing against neutrino backgrounds. The definition is a direct abbreviation that evaluates Cost.Jcost at phi.
claimThe dark-matter to neutrino cross-section ratio equals $J(φ)$, where $J(x) = (x + x^{-1})/2 - 1$.
background
The module records the structural bound on the RS dark-matter prediction, which identifies the candidate at the consciousness-sector boundary of the Higgs vacuum with mass $m_{DM} = m_W/45$. The cross-section ratio $r = σ_{DM}/σ_ν$ is required to equal the canonical golden-section J-cost quantum and to lie in the interval (0.11, 0.13). J-cost is the recognition-cost function drawn from the Cost abbreviation in RSNative.Core; it satisfies the Recognition Composition Law and is evaluated at the self-similar fixed point φ forced by the unified forcing chain.
proof idea
One-line definition that applies Cost.Jcost to phi.
why it matters in Recognition Science
The definition supplies the central quantity used by crossSectionRatio_pos and crossSectionRatio_band to build the DarkMatterCrossSectionCert structure. It realizes T5 J-uniqueness by fixing the observable ratio at the golden-section value, linking the eight-tick octave to cosmology. The module documentation states that exclusion below the band would falsify the identification.
scope and limits
- Does not derive the absolute cross-section value from the mass formula.
- Does not specify detector technology or exposure time.
- Does not address the consciousness-sector boundary derivation.
- Does not include loop corrections or higher-order effects.
formal statement (Lean)
31def crossSectionRatio : ℝ := Cost.Jcost phi
proof body
Definition body.
32
33/-- The cross-section ratio is strictly positive. -/