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 the
Cohesion Unified Field Theory recursion dynamics. This paper establishes the complementary result: the Schr¨odinger equation is the non-relativistic, low-energy limit of
a 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 of
Klein-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 field
propagation speed) removes the second time derivative, producing the free Schr¨odinger
equation. Fourth, spatial variation in the recursion resistance R(Dst) introduces the
potential energy term. The mechanical origin of each term is identified: iℏ ∂/∂t from
the structural time evolution of the recursion phase; −(ℏ
2/2m)∇2
from the kinetic
energy of the slowly-propagating trapped recursion; and V (x) from the local recursion
rate deficit relative to the background. This derivation closes Open Problem 1 of the
Born rule paper and establishes quantum mechanics as a density-regime consequence of
the 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 the
primary remaining open problem.