The Global Convergence Theorem shows convergence behavior in admissibility systems, indicating possible states like stability and oscillation.
This paper formalises the Global Convergence Theorem within the Paton System. It demonstrates that any system governed by admissibility constraints, bounded tolerance, and finite operator composition cannot diverge indefinitely. Such systems must converge to one of three states: stability, bounded oscillation, or termination. This theorem establishes formal closure of admissibility-governed operator frameworks and confirms structural completeness.
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Andrew John Paton (2026) studied this question.
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