domainCost_nonneg

Module 10 of the Foundation RS forcing chain treats RS calibration: $E_{\mathrm{coh}}$ is the single free parameter, fixed by the electron mass at rung 3. Status is structural (no sorry, no axiom).

The Recognition cost $J$ (also written $J_{\mathrm{cost}}$) is the unique nonnegative generator forced by the Recognition Composition Law; on positives it equals $(x+x^{-1})/2-1$, equivalently $(x-1)^2/(2x)$. Upstream, Jcost_nonneg records $J(x)\ge 0$ for $x>0$ via AM-GM (or the squared form).

Domain cost is the local name for applying that $J$ to a mass-to-energy ratio $m/e$. Nonnegativity of the ratio under $m,e>0$ is elementary, so the bound reduces to the standard $J$ inequality.

One-line wrapper. Unfold the definition of domain cost (so the goal becomes nonnegativity of $J(m/e)$). Discharge the positivity hypothesis of the upstream lemma by div_pos on $m>0$ and $e>0$, then apply Jcost_nonneg.

Keeps the Module 10 calibration ledger honest: every place that scores a mass-energy pair by domain cost inherits a free nonnegativity certificate from the T5 $J$-uniqueness layer. No downstream consumers are wired yet in the graph, so the lemma is presently a local structural fact rather than a bridge into a named parent theorem. It sits beside the module's canonical-threshold positivity and the RSForcingChain010 certificate as part of the zero-sorry calibration package around $E_{\mathrm{coh}}$ and the electron rung.