Infrared Gravity from Dimensional Relaxation: Information Geometry, Fixed Residual Running, and Bronze-Scaled Breathing Residuals This paper introduces a constrained infrared gravity framework in which the effective spatial scaling dimension is treated as a dynamical field. In this approach, the scaling dimension is expressed as n (x) = 3 + ε (x), where the dimensionless scalar deformation ε evolves with scale and relaxes toward exact three-dimensionality in the infrared limit. Importantly, the underlying spacetime remains a standard four-dimensional Lorentzian manifold; the modification applies strictly to the long-distance gravitational sector through its scale-dependent behavior, rather than altering the fundamental topological structure of spacetime. The theoretical foundation of the model rests on three core components. First, a stability principle derived from an information-geometric functional (Itakura–Saito type) selects exact three-dimensionality as a stable local attractor. Second, a minimal normalized gradient-flow completion fixes the linearized running of the dimensional deformation to dε/d ln μ = -1/9ε. This fixed running leads to a specific weak-field acceleration correction, a_ε (r), which scales approximately as r to the power of -10/9 in the infrared regime. Finally, the dimensional-relaxation sector is embedded within an effective scalar–tensor theory with universal conformal coupling, ensuring a consistent field-theoretic framework for interacting with matter. To account for diverse galactic dynamics, the framework is organized into a hierarchy of progressively refined phenomenological sectors. The Baseline Model represents the first-principles implementation of fixed dimensional running. This is supplemented by an optional Bronze-Scaled Sector, which introduces a weak logarithmic modulation ("wobble") governed by the Bronze ratio. For further refinement, a higher-order extension incorporates a radial "Breathing" Envelope and mild End Corrections to handle outer-edge deformations in galaxy profiles. Benchmark analysis against a multi-galaxy sample—including NGC 2403, NGC 3198, IC 2574, NGC 2841, F568-3, and UGC 6614—reveals a clear performance hierarchy. While the baseline model is found to be too rigid to capture the full diversity of observed rotation curves, the addition of Bronze wobble provides modest improvements. The full "Breathing plus End-Correction" extension (M2+M3) yields significantly better agreement across the sample, suggesting that the model may be sensitive to repeatable radial structures in galactic dynamics rather than isolated artifacts. This work does not propose a final, closed replacement for dark matter but instead advances a sharply testable infrared gravity program. The framework remains falsifiable through future investigations into weak gravitational lensing closure, dense-environment screening behavior, and broader empirical tests against extended galaxy datasets. Keywords: Infrared Gravity, Dimensional Relaxation, Information Geometry, Galaxy Dynamics, Modified Gravity, Dark Matter Alternatives.
Achyut Rateria (Fri,) studied this question.