Matter-Originated Spacetime Gradient Model (MOSGM): A Scalar–Tensor Gravity Theory with Cluster-Scale Tests and Galaxy-Scale Constraints

This work presents Version 8 of the Matter-Originated Spacetime Gradient Model (MOSGM), a covariant scalar–tensor modified gravity framework in which gravitational response emerges from a nonlinear kinetic scalar field coupled to the trace of the matter stress–energy tensor. The theory is defined by a generally covariant action with an exponential kinetic structure F (X), producing an interpolating response function μ (X) derived directly from the action rather than imposed phenomenologically. The model is shown to be free from ghost and gradient instabilities and to recover Newtonian gravity in the high-acceleration limit without additional screening mechanisms. Three parameter-free structural predictions are derived: • An environmental recovery law with exponential convergence to Newtonian dynamics • A transition radius scaling relation rₜ ∝ Mb^1/2 • A transition slope invariant κ = 1/ (e−1) As an observational consistency test, these predictions are compared with stacked velocity-dispersion profiles of 15 galaxy clusters. The results are found to be consistent with MOSGM predictions within current uncertainties. A galaxy-scale falsification test using 25 SPARC rotation curves (307 data points) is also included. This analysis shows that the present exponential kernel does not reproduce deep-regime galaxy rotation curves, thereby constraining the current MOSGM formulation primarily to cluster-scale environments (x ≳ 0. 5). This provides a clear empirical domain boundary and identifies refinement of the kinetic action as future theoretical work. This version (v8) includes: • SPARC galaxy diagnostic analysis • Global η (x) slope test • Cluster statistical robustness tests • Domain-of-validity discussion • Improved theoretical derivations • Updated discussion and limitations section This record represents the pre-journal version of the MOSGM framework intended for academic discussion and peer review. All analysis scripts correspond to the MOSGM diagnostic pipeline described in the manuscript. Tarun Kumar Saxena Independent Researcher, India