Minimum Virtual Proper Time and Finite Mass--Charge Matching in QED

We formulate a finite-proper-time version of QED defined by a gauge-covariant generating functional in which every complete internal virtual history carries a physical lower endpoint $s_0=\Lambda^{-2}$ that is not removed.

Closed fermion loops are defined by the heat-kernel determinant, while open fermion lines, vertices, and contact terms are derived from the corresponding open-line kernel.

Gauge covariance gives the Ward--Takahashi hierarchy and transversality of the photon functions, while a worldline bound establishes ultraviolet finiteness of connected Euclidean amplitudes at every fixed perturbative order and fixed infrared regulator.

One-loop mass and charge renormalisation are replaced by finite matching, and the anomalous magnetic moment acquires a calculable $O(m^2/\Lambda^2)$ correction.

The free propagators retain canonical unit pole residues and contain no additional poles.

Lorentzian amplitudes are defined at fixed order by analytic continuation of the Euclidean correlators in the external invariants with $s_0$ held fixed.

An amputation theorem removes the endpoint factor from real external particles and reduces the two-body virtual correction at two loops to photon-modified on-shell form factors.

The Born-level $q\bar q\to\gamma\gamma$ hard amplitude is unchanged, providing a parameter-free null test.