The Omegaon Model v3.1 Emergent Curvature Regulation_Pertubative Robustness and Analytic Control of Nonsingular Gravitational Collapse

This work presents version 3.1 of the Omegaon Model, an effective geometric framework for nonsingular gravitational collapse in general relativity. The Omegaon sector is introduced as an emergent curvature-regulating response that becomes dynamically relevant at extreme spacetime curvature, preventing classical singularity formation while remaining dormant at low curvature. Version 3.1 consolidates and refines earlier numerical and analytic results, placing particular emphasis on perturbative stability, analytic control parameters, and gauge-invariant robustness. The model is formulated as a controlled effective description rather than a fundamental ultraviolet completion, in direct analogy with the historical development of general relativity itself. Key results include: · Demonstration of nonsingular collapse–bounce solutions across a finite and physically motivated region of parameter space · Gauge-invariant linear and weakly non-linear perturbation analysis, showing stability of the bounce against scalar perturbations · Identification of analytic control parameters governing collapse dynamics, curvature suppression, and failure boundaries · Numerical confirmation that the Omegaon regulator suppresses unphysical divergences without introducing ghost instabilities or fine-tuned initial conditions This version focuses primarily on isotropic and weakly anisotropic collapse regimes, establishing a solid analytic and numerical foundation for the model. Strongly anisotropic interiors, geometric universality, and Bianchi-type dynamics are treated in subsequent work. The Omegaon Model does not claim to be a fundamental theory. Instead, it provides a phenomenologically well-controlled effective sector capturing how spacetime itself may respond when pushed beyond the classical limits of general relativity. The results support the view that singularities are not inevitable features of gravitational collapse, but rather artifacts of extrapolating classical equations beyond their domain of validity. This release serves as the analytic and perturbative backbone of the Omegaon programme. A companion paper (v4.0) extends these results to anisotropic Kantowski–Sachs and Bianchi IX interiors, demonstrating geometric universality and anisotropy-driven bounce dynamics.