The Fundamental Structure of a Gravity Theory Based on Layered Time Geometry: A New Spacetime Model with Quantum Consistency

Layered time geometry is proposed as a new foundational principle for constructing gravitational dynamics. In this framework, the flow of time possesses a layered structure characterized by an intrinsic phase, and this geometric property induces a nontrivial modification of the spacetime metric without introducing additional fields or higher‑derivative terms. We derive the fundamental structure of a gravity theory based on this geometry and show that the resulting metric naturally exhibits an exponentially damped oscillatory correction while preserving the second‑order nature of Einstein’s equations. The geometric origin of the oscillatory term allows the theory to remain fully local and free of extra dynamical degrees of freedom. We analyze the constraint structure, construct the quadratic action, and demonstrate that the theory maintains quantum consistency at the perturbative level, including closure of constraints and the absence of ghosts. These results indicate that layered time geometry provides a viable route toward a quantum‑compatible modification of spacetime that does not rely on scalar fields or multi‑field extensions. This paper establishes the foundational spacetime model of the layered gravity framework. Its implications for ultraviolet behavior, cosmological dynamics, and full BRST quantization are developed in subsequent companion papers.