The Gravitational Parameter as a Closure-Stable Observable: A QDL GM-Ledger Audit of Structural Identifiability and the Uncertainty Cost of M = μ/G

This paper develops the gravitational parameter μ = GM as a structurally identifiable and closure-stable observable within the Quantized Dimensional Ledger (QDL). In the Newtonian two-body problem, the observable trajectory depends on Newton’s gravitational constant G and the gravitating mass M only through their product μ = GM. Parameter pairs with the same product generate the same acceleration field and the same ideal two-body trajectories for the same initial data. Thus μ labels the identifiable equivalence class of gravitational parameter pairs, while G and M are not separately identifiable from orbital reconstruction without an external calibration channel. The paper proves this structural-identifiability result and then applies it as a public GM-ledger audit. The IAU nominal solar mass parameter μ⊙N = 1.3271244 × 10^20 m^3 s^-2 is an exact nominal conversion constant. Decomposing it through the CODATA value G = 6.67430(15) × 10^-11 m^3 kg^-1 s^-2 gives M⊙N = 1.9884098707 × 10^30 kg. Because this decomposition uses G, the inferred mass inherits the relative standard uncertainty of G, producing u(M⊙N) approximately 4.37 × 10^25 kg, or about 7.32 Earth masses. This is not a new measurement of the solar mass and not a new gravitational field equation. It is a structural audit of representation. The mathematical result is that orbital dynamics identifies μ = GM as the operational gravitational scale. The metrological result is that decomposing M = μ/G incurs a quantifiable uncertainty cost. The QDL interpretation is that μ = GM is a closure-stable gravitational observable with dimensional class L^3F^2, while G and M are decomposition-dependent factors unless independently constrained. The paper builds on the closure-deficit theorem by giving a concrete, numerical, source-anchored example of closure-stable representation and compensator accounting. It argues that a decomposition of a closure-stable observable is QDL-admissible only when the decomposition channel is explicitly represented. In this case, the compensator is the calibration and uncertainty status of G.