Monetary Entropy and the Epistemic Limits of Economic Coordination: An Information-Theoretic Analysis

This paper presents FAURAS framework (Formal Analytical Unified Restriction on Ac-cess to Simultaneity) that demonstrates how informational entropy creates fundamental epistemic barriers to economic coordination by imposing intrinsic limits on the simulta-neous processing and aggregation of dispersed information necessary for market clearing. We provide mathematically rigorous definitions of monetary entropy based on volatility distributions and derive the entropy-cognitive capacity relationship from infor-mation-theoretic principles, with complete formal verification in Lean 4 proof assistant ensuring mathematical soundness. Our theoretical framework proves that General Equi-librium becomes epistemically unattainable when entropy exceeds critical thresholds de-termined by system complexity, with formal impossibility theorems verified computa-tionally through theorem proving. Using entropy measures applied to comprehensive daily financial market data (2000-2023, n=8,309 daily observations), we validate theoreti-cal predictions through multi-dimensional entropy analysis capturing sectoral disper-sion, yield curve dynamics, and stress indicator alignment. The framework reveals en-hanced empirical support with theoretically grounded thresholds at H* = 0.5×ln(M) and H** = ln(M), where M represents market complexity. Our optimal entropy combination achieves predictive power for market stress with Granger-causal relationships extending 1-5 days ahead (p< 0.001). The cognitive capacity degradation follows K(t)=C·e(-λH(t)), where λ=ln(2)/Hcritical, providing precise quantification of information processing limitations with formal proofs establishing monotonicity, impossibility conditions, and critical threshold properties. These findings establish entropy monitoring as a scientifically grounded tool for systemic risk assessment, with immediate applications for central bank communica-tion strategies and financial stability policy, supported by rigorous mathematical founda-tions verified through computational theorem proving.