Universal Ψ Equation Assessment of Feynman's 1948 Path-Integral Method: Variational Closure Failure, Coherence Violations, and Mathematical Inconsistencies

This technical report provides a complete variational assessment of Feynman’s 1948 path-integral formulation using the fully closed structure of the Universal Ψ Equation. The analysis shows that the path integral, while historically influential, is mathematically open and therefore incompatible with any universal variational framework. By applying the Ψ functional tests—closure, internal operator emergence, nonlinear coherence, normalization constraints, and coherence-domain restriction—we demonstrate that the Feynman action cannot be derived from a self-consistent variational functional, and that the linear superposition underlying the kernel is only an approximate computational construct. The result establishes that the 1948 formulation does not satisfy the structural requirements of a universal physical law and should be regarded as a limited, non-fundamental approximation rather than a foundational theory. The full mathematical derivations supporting this conclusion are provided in the appended Variational Inconsistency Tests.