domainCost
plain-language theorem explainer
Domain cost assigns to a mass m and energy scale e the recognition cost of their ratio m/e. Standard-Model structural arguments cite it when comparing particle masses to a reference energy under the RS cost functional. The declaration is a one-line definition wrapping J-cost.
Claim. For real numbers $m$ and $e$, the domain cost is $J(m/e)$, where $J(x)=\frac{x+x^{-1}}{2}-1$ is the recognition cost of a positive ratio.
background
Recognition Science measures mismatch of positive ratios by the J-cost $J(x)=\frac{1}{2}(x+x^{-1})-1$. Upstream docs state this is the unique cost forced by the Recognition Composition Law, and that a genuine distinction (ratio not one) has strictly positive cost. The same functional appears across Cost, Cosmology, Gravity, and Spiral modules.
This file is StandardModel structural module 9. The module doc places it on the forcing chain T5 (J-uniqueness) through T8 (D=3), with status structural theorem (zero sorry, zero axiom). Domain cost specializes J to a mass-over-energy ratio, the natural dimensionless input when particle masses sit against an energy yardstick.
proof idea
Pure definition: no proof obligations. The body applies the shared J-cost functional to the single ratio $m/e$. Sibling lemmas (nonnegativity, evaluation identities) discharge analytic properties separately.
why it matters
Gives the Standard Model layer a named cost on mass-to-energy ratios so structural certificates can talk about thresholds without reopening the T5 uniqueness argument. The module sits on the RS forcing chain after phi is fixed and the eight-tick octave and D=3 are forced. Downstream siblings in the same file (domainCost_nonneg, canonicalThreshold, the RSSTDStructural009 certificate) are the immediate consumers; used_by is empty at graph export time, so this is infrastructure for those local claims rather than a widely reused lemma yet.
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