Cavendish Measurements in Planck Coordinates: Theory-Dependent Measurands and Exact Multivariate Uncertainty Transport

One gravitational result, four Planck coordinates: which equality is physics, and which is only notation? A torsion balance records angles, periods, geometry, calibration data, and environmental corrections. Those records first acquire a gravitational meaning through a declared apparatus and theory model. Only afterward may the inferred local response be written in Planck coordinates: \[ D {\; M\;} GCavM {\;f\;} CavM = √{{ GCavM}{c^3}}. \] The paper distinguishes the local Cavendish response, curvature-action coupling, cosmological coupling, and strong-field coupling. Their conventional length coordinates satisfy the exact identification gate \[ { _X=_Y G_X=G_Y } \] for positive couplings. A scalar-tensor countermodel shows why shared dimensions alone do not license this equality. The complete revised-SI output packet is transported as one stochastic object: \[ Y(G)= ( G, √ G/c^3, √ G/c^5, √ c/G )\! T. \] Its density, cumulative distribution, quantiles, coverage sets, moments, and cross-covariances are given in closed form. Ordinary Pearson correlations are distribution dependent; in logarithmic coordinates the packet is exactly affine in one latent variable: \[ { Cov(log Y) = Var(log G)\, a aT, a= (1,12,12,-12)\! T. } \] The framework is executed on all 16 measurements and all three published cross-correlations used in the CODATA 2022 adjustment. The independent reconstruction gives \[ { χ^2=12.8651383447, p=0.6127138552, RB=0.9261079255 } \] after reproducing CODATA's factor-3.9 uncertainty expansion. The corresponding coordinate is \[ Cav,CODATA =1.6162550244×10⁻³⁵\ { m}. \] For the final peer-reviewed 2026 NIST result, the exact central image and equal-tail 95% interval are \[ { Cav,NIST =1.6162029590×10⁻³⁵\ { m} } \] and \[ [1.6161127745,\;1.6162931385]×10⁻³⁵\ { m}. \] The reported NIST-CODATA separation is one discrepancy in two coordinates, not two independent anomalies. The release includes the paper, all public numerical inputs, the complete analysis program, transformed tables, numerical certificate, vector figures, three-round scientific audit, clean-build instructions, and SHA-256 manifest. Concept DOI: 10.5281/zenodo.21835597