The Residuum of the Possible: Result-Blind Generation of Single- and Double-Slit Structure from a Constraint Cascade

A benchmark, not a new theory of diffraction. The propagation mathematics used here is established scalar wave optics. What is tested is an architectural question: which information must be present in a solver before the slit pattern can exist? The generator receives a device class, one invariant free-space evolution operator, a binary geometric admissibility mask, and one square-law detector. It does not receive the single-slit minimum formula, the double-slit path-difference relation, the fringe spacing, or a target intensity profile. Only the aperture mask changes between runs. Analytic diffraction formulas are isolated in a separate process that executes after the raw detector profiles have been written to disk. The feature detector that reads those profiles is scale-free and uses one threshold pair, unchanged across every aperture; its isolation from the device parameters is enforced by test rather than asserted in prose. Writing the cascade as R_B = D[U2 C_B U1 psi_P], the observed pattern is the detector-visible residuum of a state space restricted by device geometry and evolved by an invariant free-space law. Results Single slit, 30 µm: first four blind minima agree with post-hoc finite-angle Fraunhofer controls to a maximum relative position error of 0.00953 %. Blind width change to 17 µm, with propagator, detector, feature detector and thresholds all frozen: maximum error 0.00176 %. The detected first-minimum scaling ratio is 1.765138 against an inverse-width prediction of 30/17 = 1.764706. Double slit, 30/150 µm: complex-field propagation is linear to 4.17e-16 relative error, while square-law detection yields a centre coherent-to-incoherent intensity ratio of 1.99999984 and a full normalised profile matching the post-hoc control over ±20 mm with RMSE 6.14e-5. An independent direct-space Rayleigh-Sommerfeld solver, sharing no code path with the angular-spectrum generator, reproduces the same minima to within 1.4 µm. This supplies the validator that the projector-illuminated case lacks, since that case has no closed form: the 66 µm shift of the first minimum under non-uniform upstream illumination exceeds the inter-method disagreement by a factor of 48. Eleven automated tests pass in the reference run. The claim, and its failure condition The contribution is a separation rather than a physical result. The generative content of scalar diffraction admits an exhaustive partition into four individually phenomenon-independent components, and the analytic result laws occupy none of them. That completeness is the claim. It fails visibly if a new aperture geometry within the scalar regime requires a phenomenon-specific change to the evolution operator or the detector. The paper deliberately does not claim that quantum mechanics is unnecessary for interference: in the scalar regime tested, that statement would be uncontroversial rather than bold. The generator does contain physics, and the square-law detector is a postulate, not a theorem. The broader hypothesis about constrained joint state spaces is stated as a research programme and reserved for a subsequent tensor-space test. Contents Complete Python package, both executable stages plus the cross-implementation control, raw profiles, JSON results, all figures as PDF and PNG, eleven pytest acceptance tests, the LaTeX source and compiled PDF, a prior-art note, and a SHA-256 manifest of every file. Reproduce with: python scripts/run_all.py Software in the archive is released under the MIT License; the paper and figures are released under CC BY 4.0.