Remark: Strictness is not automatic for every observation

Equation (eq:strict-detection) is observation-qualified. For example, $f=0$ makes every auxiliary pairing zero and gives ${\mathcal{C}}_{\mathrm{def}}(W;0,g)={\mathcal{C}}_{\mathrm{sol}}$. A copied existential witness cannot prove strictness for every already frozen observation and switch. By contrast, Section sec:ideal proves that ${\mathcal{C}}_W$ is proper and that the naive quotient fails for every nonempty $W$, independently of whether the chosen observation detects $\mathfrak{B}$.