darkMatterCrossSectionCert
plain-language theorem explainer
The dark-matter cross-section bound certificate assembles a record that the ratio of dark-matter to neutrino cross sections equals the J-cost of phi and lies inside the open interval (0.11, 0.13). Cosmologists testing the Recognition Science dark-matter candidate against direct-detection limits would cite the certificate when confirming consistency with the predicted band. It is assembled by a direct packaging of three component theorems into the certificate structure.
Claim. Let $r = σ_{DM}/σ_ν$. The certificate asserts $0 < r$, $0.11 < r < 0.13$, and that no real numbers $σ, σ_ν$ can satisfy both membership in the predicted band and falsification of the prediction simultaneously.
background
The module records the structural bound implied by the Recognition Science dark-matter prediction, which identifies the candidate as the consciousness-sector boundary of the Higgs vacuum. The cross-section ratio is defined to equal the J-cost quantum $J(φ)$, where $J$ is the cost function satisfying the Recognition Composition Law. The local setting requires the ratio to be strictly positive and confined to the band (0.11, 0.13), with the band and any falsifying measurement declared mutually exclusive.
proof idea
One-line wrapper that packages the positivity theorem, the band theorem, and the mutual-exclusion theorem into the three fields of the certificate structure.
why it matters
The certificate supplies the concrete bound required by the dark-matter identification in the Cosmology module. It rests on the J-cost lying inside the stated interval, consistent with the phi fixed-point and eight-tick octave structure of the forcing chain. No downstream theorems are recorded, so the declaration closes the local structural claim without further propagation.
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