domainCost_nonneg

The module proves eight-tick completeness: a period-8 lattice covers all $2^D=8$ binary states exactly once per cycle, and no shorter period exists. That is the structural content of the T7 octave step in the forcing chain.

The recognition cost $J$ is the unique nonnegative cost forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$ for $x>0$ (equivalently $\cosh(\log x)-1$). Upstream lemmas record $J(x)\geq 0$ for every positive $x$, proved by AM-GM or by rewriting $J$ as a square over a positive denominator.

Domain cost is the specialization of $J$ to a positive mass-energy ratio $m/e$. Nonnegativity of that specialization is the local fact needed before comparing costs to canonical thresholds in the same file.

One-line wrapper. Unfold the definition of domain cost (which is $J(m/e)$). The hypotheses $m>0$ and $e>0$ give $m/e>0$ by positivity of division, so the standard lemma $J\geq 0$ on positive reals applies directly.

Keeps domain costs inside the nonnegative cone required by any threshold comparison in the eight-tick completeness development. The module is the T7 structural theorem (period $2^3$, full coverage of the binary state space). Sibling objects such as the canonical threshold and the EightTickCompleteCert package are the natural consumers; no external used-by edges are recorded yet. The result is pure bookkeeping relative to the uniqueness of $J$ (T5) and the eight-tick forcing step, not a new physical claim.