domainCost
plain-language theorem explainer
Defines the recognition cost of a mass-to-energy ratio as the J-cost of that ratio. Structural Physics certificate work at rung 36 cites it as the domain-level cost functional. The body is a one-line abbreviation of the forced cost J applied to m/e.
Claim. For real $m$ and $e$, the domain cost is $J(m/e)$, where $J(x)=\frac{1}{2}(x+x^{-1})-1$ is the Recognition Science cost of a positive ratio.
background
Recognition Science forces a unique nonnegative cost on positive ratios: $J(x)=\frac12(x+x^{-1})-1$, equivalently $\cosh(\log x)-1$. Upstream modules record the same functional as the unique solution of the Recognition Composition Law (T5 in the forcing chain). Any genuine distinction ($x\neq 1$) has strictly positive cost.
This module is the structural Physics certificate at recognition rung 36 (Plan v7, 120th pass): a zero-sorry, zero-axiom structural prediction for the Physics domain. The local cost of a mass-energy pair is obtained by feeding the ratio $m/e$ into $J$.
proof idea
Pure definitional abbreviation: domainCost m e is definitionally equal to Jcost (m / e). No tactics or lemmas; the mathematical content is inherited entirely from the upstream $J$-cost definition.
why it matters
Gives the Physics-domain instance of the forced cost functional used by the structural certificate at rung 36. Sibling lemmas (nonnegativity, evaluation identities, the canonical threshold, and the inhabited certificate) build on this abbreviation. It ties the Physics structural prediction to T5 $J$-uniqueness and the Recognition Composition Law without introducing a new free functional. Downstream certificate packaging (StructPhysicsM36Cert) treats this as the domain cost entry point.
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