The Schr¨odinger Equation as a Limit Case of Cohesion UFT Recursion Dynamics

General relativity has been established as the high-density, low-gradient limit of theCohesion Unified Field Theory recursion dynamics. This paper establishes the complementary result: the Schr¨odinger equation is the non-relativistic, low-energy limit ofa massive recursion field in the Cohesion UFT. The derivation proceeds in four steps.First, the recursion field for a massive trapped recursion satisfies a wave equation ofKlein-Gordon type, with a mass term arising from the recursion rate deficit. Second,factoring out the rest-energy phase oscillation yields a slowly-varying envelope equation.Third, the non-relativistic approximation (particle speed much less than the local fieldpropagation speed) removes the second time derivative, producing the free Schr¨odingerequation. Fourth, spatial variation in the recursion resistance R(Dst) introduces thepotential energy term. The mechanical origin of each term is identified: iℏ ∂/∂t fromthe structural time evolution of the recursion phase; −(ℏ2/2m)∇2from the kineticenergy of the slowly-propagating trapped recursion; and V (x) from the local recursionrate deficit relative to the background. This derivation closes Open Problem 1 of theBorn rule paper and establishes quantum mechanics as a density-regime consequence ofthe same recursion field that produces general relativity at a different density regime.The connection between ℏ and the minimal torsion cycle action is identified as theprimary remaining open problem.