The Exact Solution for R(Dst) from the Classical Recursion Field

The previous paper in this series estimated the exponent n in the approximate logisticsolution for R(Dst) from the Hubble tension, and identified it as a mode-sum integralrequiring quantum field theory in curved spacetime to compute. This paper showsthat no quantum field theory is required. The recursion field in the Cohesion UFTis a classical complex scalar field. Its equation of state w = (1 − 2R4)/(1 + 2R4) isderived directly from the classical energy and pressure of the recursion Lagrangian inthe curved background. The resulting ODE dR/dDst = R(1 + 2R4)/(6Dst) is separableand integrates to the exact implicit solution:R(1 + 2R4)1/4= C · D1/6st .This is a complete, closed-form result derived from the recursion Lagrangian and theasymptote theorem alone. No quantum field theory, no mode-sum integral, and noBogoliubov transformation are required. The approximate logistic form used in theprevious paper has n = 1/6 exactly, derived rather than estimated. The asymptoteR0 → 0 as Dst → 0 confirms that the early universe had arbitrarily fast propagation —inflation is the Dst → 0 limit of the exact solution. The finite observed R0 > 0 comesfrom the fact that the real universe always has Dst > 0 (asymptote theorem). OpenProblem 1 advances to 90% complete.