Deterministic Topology of Market Microstructure: H-infinity Robust Portfolio Decoupling and Liquidity Phase Transitions in Discrete Tensor Spaces

Abstract

Classical financial mathematics traditionally utilizes continuous stochastic differential equations and historical covariance matrices, which often encounter structural limits during systemic liquidity constraints when asset correlations converge toward unity. This paper introduces the Chrysene Formalism to quantitative finance, cooperatively advancing risk management from probabilistic estimation to deterministic spatial geometry. By mapping financial networks into a discrete, non-commutative fibrated manifold, we formulate portfolio optimization as a spatial min-max H-infinity robust control problem. Utilizing L-infinity topological boundary normalization and L2 geometric overlap, we demonstrate that systemic liquidity events can be rigorously parameterized as deterministic phase transitions governed by invariant thermodynamic limits. Empirical evaluation of the 2008 and 2020 macroeconomic transitions validates this deterministic topological load parameter as a leading structural indicator compared to classical stochastic volatility (VIX), providing a computable framework for absolute orthogonal portfolio insulation.