Geometric Dynamics of Consumer Credit Cycles: A Multivector-based Linear-Attention Framework for Explanatory Economic Analysis

Abstract

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.