domainCost

Recognition Science measures mismatch of positive ratios by the J-cost $J(x)=\frac12(x+x^{-1})-1$. It vanishes only at $x=1$, is nonnegative for $x>0$, and is the unique continuous solution of the Recognition Composition Law forced at T5 of the unified forcing chain.

This module (Foundation RS Module 12) records dimensionless identities around the golden ratio: in particular $J(\varphi)=\varphi-3/2$ exactly (numerically $\approx 0.11803$). The local setting is structural: zero sorry, zero axioms.

Upstream, Jcost is the shared definition of that functional across Cost, Cosmology, and Gravity. Domain cost simply specializes it to a mass-over-energy (or any two-scale) ratio, so later lemmas can talk about thresholds and nonnegativity without repeating the formula.

Pure definition: one-line abbreviation that applies the upstream J-cost to the quotient $m/e$. No proof obligations; no tactics.

Gives the module a named handle for the dimensionless cost of two real scales, which siblings then use for equality-at-identity and nonnegativity facts, and for the canonical threshold that sits next to the $J(\varphi)=\varphi-3/2$ identity. In the broader RS picture it is the local instance of the T5 J-functional on a mass–energy (or analogous) ratio, feeding the dimensionless bookkeeping of the forcing chain without introducing new structure. Downstream use count on this page is empty; the immediate consumers are the sibling lemmas in the same module (domainCost_at_eq, domainCost_nonneg, threshold certificates).