On Celestial Dynamics III: A Simplified Computational Model for Dark-Matter Phenomenology

We develop a finite computational model of galactic response within the framework of Papers I and II. A causal kernel dictionary yields a finite coefficient problem and an explicit field calculation. We establish existence, conditional stability, and error propagation. Four single-galaxy applications give full-data mean absolute relative speed errors of 1.42–6.85 percent, whereas outer-region holdout errors range from 1.07 to 17.16 percent. Mass-conserving central redistribution tests source sensitivity. The results distinguish reconstruction from prediction and motivate resolved simulations of tractable coupled systems as benchmarks for reduced models. Historical enhancement is positive and significant only under specified response and error conditions. The same forward operators support constrained inference of baryonic geometry from kinematic and photometric data. The framework provides computational tools for testing a historical gravitational mechanism; the examples do not establish its unique physical origin or remove the need for independently constrained geometry and dynamics. Keywords Galactic dynamics; rotation curves; finite mass distributions; retarded Green functions; causal response; kernel inference; finite-data extension; dark-matter phenomenology.