Proposition: The finite-fit interface

Let an explicitly parameterized subfamily of the declared stress class produce

Then a candidate with complete vanishing exists exactly when

For a particular candidate, complete vanishing is equivalent to $w_0+N\theta =0$.

Proof. Membership in the actual image of $N$ is equivalent to solving the displayed finite linear equation. Theorem thm:coverage then converts that solution into complete residual vanishing in the declared class.