What question did this study set out to answer?

This research aims to address the limitations of traditional macroeconomic models in uniquely representing financial dynamics, especially in the context of financial bubbles.

July 6, 2026Open Access

Unique Solution Constraints of Macroeconomic Equations and Evolution Model of Financial Bubbles under the Real-Virtual Binary Field Framework

Key Points

This research aims to address the limitations of traditional macroeconomic models in uniquely representing financial dynamics, especially in the context of financial bubbles.
Introduced intrinsic field resistance and conjugate golden decay law as constraints within the Real-Virtual Binary Field Framework.
Constructed a dynamic evolution differential equation to describe financial bubble dynamics based on energy dissipation laws.
Eliminated multi-solution ambiguity by applying scale cutoff constraints related to the minimum lattice unit.
The proposed framework retains a unique effective solution aligned with real economic logic.
Quantitative analysis reveals critical thresholds in bubble dynamics and the collapse dissipation process.
Provides tools for macroeconomic regulation and financial risk early warning.

Abstract

Abstract Traditional macroeconomic models represented by DSGE generally suffer from multiple equilibrium solutions, which cannot uniquely match the real economic operation state, and lack quantitative analytical formulas to describe the whole process of financial bubble generation, expansion and burst. Based on the Real-Virtual Binary Field Framework built on discrete macroscopic lattice medium, this paper introduces intrinsic field resistance and conjugate golden decay law as universal constraint conditions. The real field corresponds to physical entity value formed by lattice aggregation, and the virtual field corresponds to asset premium, monetary bubble and speculative virtual energy. By adding scale cutoff constraints brought by the minimum lattice unit, the multi-solution ambiguity of classical macroeconomic equations is eliminated, and the system only retains the unique effective solution matching real economic logic. On this basis, a dynamic evolution differential equation of financial bubbles is constructed by analogy with the energy dissipation law of lattice medium, which quantitatively describes the accumulation of virtual field energy, critical threshold and collapse dissipation process, and provides a unified quantitative analysis tool for macroeconomic regulation and financial risk early warning. Keywords: Real-Virtual Binary Field; macroeconomic system; unique equilibrium solution; conjugate golden decay law; financial bubble; intrinsic field resistance

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