Integrated energy comparison is safer than an unsupported derivative

A bound on energy values alone does not bound their derivatives: an error $\eta \sin (\Omega t)$ has amplitude $\eta$ but derivative amplitude $\eta \Omega$. Thus a claimed pointwise remainder ${\mathcal{R}}_E(t)$ needs derivative control. For the autonomous model, a natural exact stored-energy convention is $E_{\mathrm{mic}}=E_S+E_I$, whose loss equals the full reservoir energy gain. Identifying that gain with collected outgoing physical flux is a separate comparison.