Deterministic Navigation of Algorithmic Stablecoin Devaluations: An H-infinity Robust Control Framework over the Tc Liquidity Manifold

Abstract

Classical quantitative finance has traditionally modeled systemic liquidity through stochastic approximations. During periods of supercritical stress, these continuous probability distributions can encounter structural limitations, behaving more like a deterministic topological manifold (Tc) governed by rigid boundary conditions. This paper introduces a complementary deterministic framework treating algorithmic stablecoins as dynamical systems under active feedback control. Specifically, we introduce a deterministic threshold, the Kinematic Tether Limit, that marks the point at which an algorithmic stablecoin's peg-defense capacity is mathematically exhausted. We then derive three operational strategies for traders and protocols to navigate or contain the resulting structural transition: (I) executing directional short positions within the metastable phase strictly prior to the stablecoin's recursive devaluation, (II) achieving microeconomic resilience by engineering Kolmogorov-Arnold-Moser (KAM) invariant portfolio tori governed by Hamiltonian mechanics, and (III) deploying the Topological Scission Operator as an autonomic systemic firewall to quarantine strain and preserve macroeconomic homeostasis.