Geometric Dynamics of Consumer Credit Cycles: A Multivector-based Linear-Attention Framework for Explanatory Economic Analysis
This work addresses the problem of understanding systemic economic crises for economists and policymakers, though it appears incremental as it applies a known mathematical framework to a specific domain.
The study tackled the problem of analyzing consumer credit cycles by introducing geometric algebra to decompose credit system relationships into projective and rotational components, revealing that when unemployment and credit contraction enter feedback loops, their geometric relationship shifts to dangerous rotational dynamics characteristic of systemic crises.
This study introduces geometric algebra to decompose credit system relationships into their projective (correlation-like) and rotational (feedback-spiral) components. We represent economic states as multi-vectors in Clifford algebra, where bivector elements capture the rotational coupling between unemployment, consumption, savings, and credit utilization. This mathematical framework reveals interaction patterns invisible to conventional analysis: when unemployment and credit contraction enter simultaneous feedback loops, their geometric relationship shifts from simple correlation to dangerous rotational dynamics that characterize systemic crises.