Quantized Proper Time and Gravity as Resynchronization: A Minimal Discrete-Time Framework for Singularities and Quantum Corrections

We propose that gravity can be reinterpreted as the resynchronization of quantum states across discrete time steps, arising naturally from quantized proper time. This paper is the third in a sequence developing that framework. Part I introduced the finite Lorentz factor from Planck-scale discretization, eliminating divergences near v = c. Part II developed vacuum stress–energy corrections and Casimir phenomenology. Here in Part III, we extend the framework to general relativity. Quantum corrections to the Einstein field equations reinterpret gravity as the resynchronization of quantum states across discrete time steps. Key predictions include Planck-suppressed photon delays (potentially testable if timing improves to about 10^ (-2) seconds over cosmological baselines), modified Casimir contributions (testable with resonator Q-factors beyond 10⁹ and cryogenic MEMS stability), and gravitational-wave phase shifts (delta phi ~ 10^ (-70) as future design targets for LISA or the Einstein Telescope). Together these define quantitative benchmarks for future falsification rather than immediate detectability. Unlike loop quantum gravity or causal set theory, the discrete-time approach discretizes only time while leaving space continuous. This minimal intervention emphasizes engineering-style tractability, preserving special relativity at low energies while yielding long-term quantitative design targets for clocks, resonators, and gravitational-wave detectors. Prototype numerical kernels are also provided, ensuring reproducibility on standard desktop hardware and defining a clear migration path toward HPC, GPU, or FPGA platforms. This emphasizes that even though the effects are far below current sensitivities, the framework is framed as falsifiable, reproducible, and aligned with long-term experimental design. Scope: Throughout, the modified dispersion relation (MDR) is applied per co-moving constituent (for example, nucleon or nucleus) rather than to a macroscopic aggregate treated as a single degree of freedom. This choice preserves standard relativistic behavior at low speeds and only impacts ultra-relativistic kinematics.