Institutional Renewal and the Meta-Nyquist Problem: A Theory of When Societies Can Replace Failing Institutions

This paper develops a formal theory of institutional renewal — the process by which a society diagnoses failing institutions and replaces them before systemic collapse. Building on the Nyquist boundary framework for institutional inference, it models a society as a birth–death process on a portfolio of N institutions, each characterized by a Nyquist gap measuring the margin between oversight (witness) capacity and strategic obfuscation capacity. The central contribution is the Portfolio Nyquist Theorem: the society's ability to diagnose institutional failure is itself governed by a meta-level Nyquist condition on aggregate oversight capacity. When this meta-gap crosses zero, the society enters a renewal trap — an absorbing failure mode in which failed institutions cannot be identified and replaced. The paper characterizes the accomplishment window (conditions under which sustained institutional creation is possible), proves that friction-based reforms (term limits, sunset clauses, mandatory review) are structurally ineffective when the meta-gap is negative, and shows that incumbents within failing institutions optimally target oversight infrastructure rather than improving performance. The framework is validated against the V-Dem v15 panel (181 countries, 1789–2024) and applied to New Deal America, democratic backsliding, modern China, and AI governance. The results complete a conservation law across the full Bateson/Nyquist program: the impossibility of overcoming strategic frame manipulation migrates from individual cognition through institutional inference to meta-institutional renewal, preserving the same geometric structure at each level.