4D Projection-Limit Geometric Formulation

The unification of general relativity and quantum mechanics remains a central challenge of modern physics. Here, a four-dimensional projection-limit geometric formulation, PLG, is developed in which physical configurations are represented as fixed geometries embedded in a higher-dimensional Euclidean space, while observable dynamics arise from their projection into an observer-defined three-dimensional subspace. The formulation introduces a Reality Plane associated with the observer and a projection gradient that governs how higher-dimensional structures appear within this plane. Temporal ordering arises as an effective consequence of geometric rescaling along the fourth spatial dimension, rather than as an independent coordinate. Within this framework, projection-limit configurations arise naturally, yielding null-duration intervals on projection. More general rescaling configurations lead to effective kinematic relations within the observational subspace. The internal consistency of the formulation is developed mathematically, and its application to both localized and extended systems is examined as an illustration of the geometric construction. Possible physical implications are briefly discussed in the concluding section.