A Discrete Lattice Approach to Spacetime Phase Transitions and the Resolution of Gravitational Singularities

Gravitational singularities in General Relativity represent a fundamental breakdown of the continuous manifold approximation at terminal energy densities. We propose a non-perturbative alternative, Vortical Lattice Dynamics (VLD), which models spacetime as a discrete manifold characterized by an Intrinsic Stiffness. By applying a local metric constraint termed the Probability Invariance Identity, we demonstrate that linear temporal flux is reallocated into localized vortical resonance to maintain manifold integrity. We define a dimensionless Lattice Stress Identity to quantify the structural load on the manifold, deriving a critical saturation density. At this limit X=1, the lattice prohibits further radial contraction, triggering a topological phase transition into a 3D Resonant Torus. This geometry facilitates the formation of a Vortical Void—a region of central restitution where ground-state stiffness and temporal flux are fully restored, effectively replacing the divergent 1/r singularity. Furthermore, we establish the 1:1 Resonant Identity, which identifies the 10M limit as a structural ceiling for stellar-origin black holes. By mapping the Lattice Strain Tensor to the Einstein Tensor, this framework resolves the Information Paradox via topological preservation and provides a mechanical solution to the vacuum energy discrepancy through the Inverse-Feedback Law of lattice damping.