A Closure-Deficit Theorem for Dimensionally Homogeneous Physical Models: Dimensional Persistence, Compensator Completeness, and Model Admissibility in the Quantized Dimensional Ledger

This paper formulates a closure-deficit theorem within the Quantized Dimensional Ledger (QDL), a structural-admissibility framework for distinguishing ordinary dimensional homogeneity from stronger closure admissibility. Dimensional homogeneity remains a necessary condition for physical representation: equations must be locally well typed. The central claim developed here is that dimensional homogeneity is not sufficient for QDL admissibility. A relation, model term, transformation, truncation, or parameter decomposition may preserve ordinary dimensional type while producing a nonzero closure deficit relative to a declared QDL closure condition. The formal scaffold treats ledger space as an additive abelian group. Ordinary dimensional homogeneity is represented by a dimensional typing map D, while QDL closure is represented by a closure functional C. The mathematically decisive condition is that dimensional and closure admissibility diverge for at least one ledger relation v with D(v) = 0 but C(v) ≠ 0. Under this condition, there exist dimensionally homogeneous relations that are not closure-admissible. The closure-deficit theorem states that a transformation, truncation, decomposition, or role transition that preserves dimensional type but produces a nonzero closure deficit is structurally inadmissible, with respect to the declared QDL closure condition, unless an explicit compensator is included in the model. The paper develops the theorem through a toy closure lattice, an effective-truncation example, and two conservative physical anchors. The Compton–gravity threshold is treated as a closure transition between stored quantum recurrence and gravitational scale recurrence, yielding the standard threshold m* = mP/√2 from the equality of the reduced Compton wavelength and Schwarzschild radius. The gravitational parameter μ = GM is analyzed as a closure-stable observable with dimensional class L³F². In many orbital reconstructions, μ is directly identifiable through μ = a³n² or μ = 4π²a³/P², whereas the inferred decomposition M = μ/G imports the uncertainty and operational status of G. The contribution of the paper is not the discovery of the standard physical relations used as anchors. Rather, the contribution is the formal category of closure deficit: a structurally meaningful failure mode that can occur even when ordinary dimensional homogeneity is satisfied. The result clarifies the distinction between dimensional consistency, closure persistence, compensator completeness, and full physical admissibility, while explicitly limiting the claim to structural admissibility rather than empirical truth or dynamical derivation.