domainCost
plain-language theorem explainer
Domain cost assigns to a mass-energy pair the recognition cost of their ratio. Materials work on Bravais counting from configuration dimension uses it as the local scale mismatch measure. The body is a one-line wrapper of the forced J-cost on m/e.
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
The ambient module counts 3D Bravais lattices from configuration dimension (Plan v7). Status is structural: zero sorry, zero axiom. The Count Law sketch is $14=2\cdot(2^3-1)$, doubled for dual lattice structure under $D=3$.
The cost functional is the unique RS J-cost $J(x)=\frac12(x+x^{-1})-1$, forced by the Recognition Composition Law (T5). Upstream docs state it is the recognition cost of a positive ratio, nonnegative for $x>0$, and the unique cost forced by RCL. Domain cost simply evaluates that functional on the ratio of two real parameters (mass-like over energy-like scale).
Sibling lemmas in the same file prove evaluation identities, nonnegativity, a canonical threshold, and the Bravais-3 certificate that packages the lattice count.
proof idea
Pure definition: apply the imported J-cost to the quotient $m/e$. No tactics, no lemmas, no side conditions in the body. Downstream nonnegativity and threshold facts are separate theorems on this def.
why it matters
Gives the materials layer a uniform RS cost on lattice scale ratios, so crystal-structure certificates can speak the same language as cosmology and gravity modules that already import J-cost. Siblings (domainCost_nonneg, canonicalThreshold, Bravais3Cert) build the 14-lattice count on top of it. Ties directly to T5 J-uniqueness and the RCL-forced form $J(x)=\cosh(\log x)-1$. No used_by edges yet; the def is infrastructure for the structural Bravais theorem in this file.
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