用几何代数解析信贷周期，揭示失业与信贷收缩的危险旋转耦合。
Geometric Dynamics of Consumer Credit Cycles: A Multivector-based Linear-Attention Framework for Explanatory Economic Analysis
- 用多向量建模经济状态，分离相关性与反馈螺旋两种关系。
- 发现失业与信贷收缩同步反馈时呈现危险旋转动态，预示系统危机。
- 适合研究宏观经济波动、金融风险预警的研究者参考。
本研究引入几何代数，将信贷系统关系分解为投影（类似相关性）和旋转（反馈螺旋）两部分。我们将经济状态表示为克利福德代数中的多向量，其中双向量元素捕捉失业、消费、储蓄与信贷使用之间的旋转耦合。该数学框架揭示了传统分析无法察觉的互动模式：当失业与信贷收缩进入同步反馈回路时，其几何关系从简单相关性转变为危险的旋转动力学，标志着系统性危机的特征。
原文摘要 · Abstract (English)
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.
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