Calculating CPTG Galaxy Rotation Curves

Abstract

This tutorial presents a step-by-step calculation of the Curvature Polarization Transport Gravity (CPTG) galaxy-limit equation using three worked rotation-curve examples: DDO-154, NGC-3198, and NGC-7814. Starting from SPARC-style rotation-curve inputs, the calculation converts the observed radius and velocity columns into physical acceleration fields, builds the CPTG baryonic source field, infers the object-dependent structural acceleration scale a⋆, derives the structural transport scale, computes the transport remnant, solves the implicit nonlinear acceleration equation, and recovers the model rotation curve. The three galaxies are treated separately. DDO-154 is a gas-rich dwarf system and a classic low-acceleration test case for dark matter and modified-gravity theories. NGC-3198 is a large spiral galaxy with an extended, nearly flat H I rotation curve and has long served as a standard reference case for disk-galaxy mass discrepancies. NGC-7814 is an edge-on, bulge-dominated spiral whose rotation-curve decomposition includes a large stellar bulge contribution. Together, the three examples show how the same locked CPTG galaxy calculation is carried through a low-mass dwarf, an extended disk, and a centrally concentrated bulge system. A fixed-a0, unit-source MOND/RAR-form calculation is retained as a quantitative contrast so that the different source mapping, acceleration law, predicted curve, and residual diagnostics can be followed from the same SPARC component inputs. The purpose of the paper is instructional: to make the CPTG rotation-curve calculation reproducible step by step.