Physics is often described as moving between experiment and model. That picture is indispensable but incomplete. In several episodes since the rise of mathematical physics, investigators have also proceeded by fixing a class of possible representations and progressively restricting it through conservation, covariance, locality, isotropy, variational, and constitutive requirements. The result is sometimes not merely compatibility but rigidity: within a stated model class, few law-forms—and occasionally only one up to empirical parameters—remain admissible. I call the resulting conditional status structural necessity. The term names no new species of metaphysical necessity: it denotes the degree to which an empirical law-form is fixed by an explicit package of constraints relative to a model class. This article develops an operational test based on nested admissible sets and constraint ablation. A modern reconstruction of Fourier heat conduction supplies the principal case; Fermat’s derivation of refraction and Noether’s theorems show two different yields of constraint reasoning. I then retain the "structural demon" in a deflated, historically useful role: not as a personification of logical closure, but as an ideal reasoner restricted to the concepts, mathematics, evidence, and computational resources available at a given time. Comparing the earliest defensible derivability window with actual discovery yields a measure of derivational latency. This framework supports a historiography of the constraint turn without making discovery inevitable, erasing empirical input, or collapsing constraints into laws.