Working Backward Through the Maze: A Reverse Derivation of the NeoGravity Ether Plenum From Observation, Using Newtonian Relativity Mathematics Alone

The preceding paper in this series tested three candidate foundations for the Theory of NeoGravity and reported that all three fail. This paper reverses the direction of reasoning and succeeds. Rather than beginning from the framework's postulates and searching for a formalism that reaches the observations, it begins from the observations and asks what structure the medium must possess for them to follow. The answer is a single separable first-order differential equation, and the missing ingredient proves to be neither exotic nor new: it is classical hydrostatic equilibrium, the same principle governing the density profile of a planetary atmosphere. A medium takes its structure not from the instantaneous local force but from the state into which it settles under that force, and because equilibrium integrates the force rather than reproducing it, an inverse-square load produces a profile whose exponent depends on the inverse first power of distance. Taking the inward Radiative Undertow of magnitude GM per unit mass divided by the square of the radius, imposing pressure balance with the equation of state relating pressure to mass-energy density, and integrating, gives a density profile exponential in the reciprocal radius. The equation-of-state parameter is then shown not to be free: because the medium is electromagnetic its quanta are massless, the stress-energy tensor is traceless, and the equation of state is forced to that of a radiation field. Applying the optical relation in its general form and matching the coefficient the measured solar deflection requires fixes the one remaining exponent and determines the medium completely. The result is a single expression for the refractive index of space near a mass, the exponential of twice GM divided by the product of the square of light speed and the radius, containing no free parameter and no fitted quantity beyond the one calibrated constant. From that single expression this paper obtains four classical results: solar light deflection of 1.7516 arcseconds, a round-trip Shapiro delay of 232.6 microseconds, gravitational redshift of 2.459 times ten to the minus fifteen, and Mercury's perihelion advance of 42.992 arcseconds per century. Because the expression is exact rather than a first-order approximation, it yields a falsifiable prediction: expanded in powers of the dimensionless field strength it gives a second-order coefficient of 2.00 against general relativity's exact value of 1.75, a difference of approximately 0.23 microarcseconds at the solar limb, below present astrometric precision but within proposed next-generation design targets. Every step uses Newtonian mechanics and classical fluid statics; no tensor, metric, or curvature object appears anywhere in the derivation.