Axiomatic Curvature Saturation: A Formal Framework for Non-Singular Spacetimes (The ΨO Model v1.2)

The ΨO-Framework (Version 1.2) introduces a novel mathematical formalism for resolving gravitational singularities. At its core, the work defines an axiomatic saturation operator 𝒮̂ that regulates physical curvature scalars at the Planck scale. Unlike classical models, this approach avoids geodesic incompleteness and preserves the functional integrity of spacetime geometry. By deriving a modified Schwarzschild metric free of point-like singularities, the model provides a consistent foundation for investigating compact objects and bridging the gap between General Relativity and effective quantum field theories.