A One-Parameter Geometric IR-Transition Model for SPARC Rotation-Curve Phenomenology

We develop EQS/GAL as a galaxy-scale observational reduction of a geometric compression framework. The underlying variables are the scalar compression field chi = -div u, the local volume factor y = det(I + grad u), its logarithmic representation y = exp(-phi), and a conservation-like closure relation for chi. The infrared component is defined through an IR projection of the compression field. In this first paper, the inferred selection relation between the infrared quantity Q_IR and baryonic mass M_b is treated as an emergent constraint class for admissible quasi-stationary infrared configurations, rather than as a fundamental axiom or a general theorem. The resulting observational layer, GAL-7A, introduces one global galaxy-scale infrared acceleration parameter. It preserves the low-acceleration square-root enhancement while bounding the correction in the high-acceleration regime. Applied to SPARC rotation-curve phenomenology with a single global acceleration scale of approximately 10^-10 m s^-2, GAL-7A robustly improves upon the earlier GAL-5R reduction and reaches performance comparable to standard RAR/MOND-level phenomenology without galaxy-by-galaxy tuning of the acceleration parameter. The model is not claimed to be statistically superior to MOND or RAR, nor is it presented as a complete solution to the dark-matter problem. A residual baryonic Tully-Fisher normalization tension and mild galaxy-level residual systematics remain. The proportionality Q_IR to M_b has not yet been established as a universal theorem, and further validation, including the planned GAL-7E stage, is left for future work.