BU51 Minimal Structure and Minimal Variation under B_U Ontic Audit, Appearance-Side Readout, and the Disqualification of Formal Shadow Substitution

This paper develops BU51 as a structural clarification of the distinction between minimal structure and minimal variation under Single-Universe Boundary Consistency, B_U. Its central claim is that minimal structure is the stake, while minimal variation is the shadow. The appearance-side minimal structure is the first lawful nonzero standing obtained after B_U, B_0, D(M), microscopic zeroing, fast-slow orthogonality, finite projection, coherence audit, and settlement. Minimal variation, by contrast, is only the ex-post differential readout of that already established structure inside the projection stratum. The paper separates three levels that are often conflated in backward-mirror formal systems: zeroing, structure, and variation. Microscopic zeroing is a necessary audit threshold; it clears the background but does not yet generate structure. Minimal structure is the sufficient appearance-side landing point; it writes the first lawful nonzero retained item into the reality ledger. Minimal variation is a subsequent descriptive reading; it records how the established structure moves, changes, or minimizes cost inside a finite observational window. BU51 further reclassifies a broader cluster of formal concepts, including least action, variational calculus, Lagrangians, path integrals, geodesics, low-cost paths, optimization, minimal differentials, and effective-theory closure. These concepts are classified as projection-level shadows of already audited structures. They may describe lawful motion, stability, or closure, but they do not possess ontic audit power. Audit authority belongs to B_U, B_0, and D(M), through boundary consistency, microscopic zeroing, covariance cancellation, information-update cost, and settlement predicates. The final judgment is that formal elegance cannot replace ontic permission. Structure obtains standing first; formal readout appears afterward. BU51 therefore blocks the substitution of symbolic shadow for physical stake.