Scalar Finite-Proper-Time Field Theory as Spectral Operator Calculus
This paper formulates a finite-proper-time construction for Euclidean scalar theory using a spectral operator calculus and complete-history diagrammatics, demonstrating that the retained endpoint scale yields a finite, momentum-dependent remainder in the one-loop four-point function that cannot be eliminated by standard renormalization or field redefinitions, thereby distinguishing it from arbitrary cutoff prescriptions.