IndisputableMonolith.Cosmology.DarkMatterXENONPrediction
The module predicts that dark matter mass over W boson mass equals 1/45 in RS units, together with the associated cross-section ratio for XENON detection. Cosmologists and direct-detection experimentalists would cite it when mapping the phi-ladder mass formula onto observable signals. The module assembles the claim through ratio definitions, positivity lemmas, band membership checks, and a final certification theorem.
claim$m_{DM}/m_W = 1/45$, with the corresponding cross-section ratio lying inside the XENON experimental band.
background
The module imports the fundamental RS time quantum τ₀ = 1 tick from Constants and the cost functions from the Cost module. These supply the J-cost and defect-distance machinery used to assign masses on the phi-ladder. The local theoretical setting is the cosmology domain, where the mass formula yardstick · ϕ^(rung − 8 + gap(Z)) is specialized to the dark-matter candidate, producing the stated ratio to the W boson.
proof idea
This is a definition module. It introduces dmMassRatio and dmCrossSectionRatio as the concrete numerical predictions, then proves dmCrossSection_pos and dmCrossSection_in_band before packaging the results in the DarkMatterXENONCert theorem.
why it matters in Recognition Science
The module supplies the terminal numerical prediction that realizes the phi-ladder mass assignment for dark matter and feeds it directly into XENON bounds. It closes the loop from the unified forcing chain (T5–T8) to an observable cross-section ratio, with the certification theorem serving as the interface to experimental cosmology.
scope and limits
- Does not derive the 1/45 ratio from the J-uniqueness axiom or forcing chain.
- Does not compute absolute masses or event rates.
- Does not incorporate halo velocity distributions.
- Does not address other direct-detection experiments.