A Limit Criterion for Scientific Validity

Building on a Lyapunov-like descent principle for structural incompleteness established in prior work, this paper proposes a limit-based criterion for scientific validity defined on differentiable theory-space. While local admissible refinement ensures non-increase of a bounded completeness functional, such monotonicity does not guarantee convergence to structural adequacy. Scientific validity is therefore characterized by an existential condition: a theory is admissible if and only if there exists at least one admissible refinement trajectory along which aggregate incompleteness asymptotically approaches its infimum. The analysis distinguishes empirical stagnation from structural stagnation across independently defined invariants governing predictive adequacy, regime coverage, symmetry realization, and multiscale coherence. Bayesian updating is shown to reduce only the empirical component of incompleteness via Kullback–Leibler contraction and is therefore insufficient for global structural reducibility. The resulting framework separates local stability from global convergence and reframes scientific admissibility as asymptotic reducibility within structured theory-space rather than as mere testability or probabilistic coherence. The criterion is structural rather than teleological: it concerns existence of refinement paths, not inevitability of convergence.