The Boundary Emergence Theorem: A Constraint on Ontological Inference from Model Divergence

Singularities in classical field theories are characterized by divergence of invariants or geodesic incompleteness within a mathematical framework. Such divergence indicates breakdown of descriptive applicability, not proof of ontological origin or termination.This paper formalizes the Boundary Emergence Theorem, a minimal inference constraint stating that model divergence does not entail metaphysical boundary conditions. The theorem demonstrates that singularities mark descriptive limits of a formalism rather than ontological beginnings.The result is compatible with the Hawking–Penrose singularity theorems, the Borde–Guth–Vilenkin past-incompleteness theorem, effective field theory, and scientific realism. It introduces no new physics and asserts no metaphysical doctrine beyond a restriction on inference from formal breakdown.Version 2.0 strengthens the formal structure, engages directly with the Borde–Guth–Vilenkin theorem, clarifies compatibility with quantum gravity programs, and tightens the inferential formulation.