Relational Attribution of Model Preference

The change in model preference produced by a new dataset depends on the inference context in which it is evaluated. This preprint gives an auditable account of that dependence. An exact finite-update identity ΔG = D + R₁ − R₀ separates the incoming conditional likelihood evaluated at the previous fit from the gain due to reoptimization; a path integral of score–inverse-Hessian contractions describes the latter exactly, and a finite-face identity separates explicit nonadditivity from adaptation through shared parameters, with a Bayesian counterpart based on posterior covariance. Complete tables of coalition optima do not determine the update decomposition. In a shared-mean Gaussian model every higher-order Möbius interaction has an explicit nonzero sampling law and is blind to a common signal; the blindness extends to model-space signals in weighted linear regression with a fixed null. New in version 1.0: exact null laws for anchored data-combination faces K = G(DCX) − G(DC) − G(DX) + G(D). In nested linear-Gaussian models every signed coalition contrast is a generalized chi-square variable whose mean is the alternating sum of identified ranks; anchored faces with an identifying baseline have mean zero. In an orthogonal reference model the face is exactly √(f_C f_X)·(A − B) with A, B independent χ²_k, where f_C, f_X are the information fractions added by C and X; its law does not depend on the true values of the extra parameters, so the face is a consistency diagnostic, not signal evidence. The published DESI DR2 faces are then calibrated from public inputs: the DESI DR2 BAO data vector and full covariance, the DESI compressed CMB prior on (θ*, ω_b, ω_bc) (DESI DR2, App. A), and supernova Fisher surrogates calibrated to the published DESI+CMB+SN constraints. The exact null law gives standard deviations of 2.4–3.1; the observed contrasts −2.0 (Pantheon+), −0.5 (Union3) and −0.4 (DES-Y5) lie at 0.84–0.98σ, 0.30–0.43σ and 0.24–0.31σ across 30 surrogate variants per branch. The sign change of the Pantheon+ increment between the DESI and DESI+CMB contexts is statistically ordinary in the linear-Gaussian approximation. The work is related to, and distinguished from, the concordance estimators of Raveri & Hu (2019). No new cosmological fit, tension significance or dark-energy detection is claimed. The unchanged v0.1 audit (29 test groups) and a v1.0 extension audit are embedded in the PDF and uploaded separately.