Toward a Correlative Topology of Geopolitics: A CST-Based Spectral Framework for International Stability

We propose a structural reformulation of geopolitics based on Correlative Structure Theory (CST), in which international systems are modeled as non-factorizable networks encoded by a positive semi-definite correlation operator. Geopolitical stability is defined as the preservation of the dimension of accessible correlation modes, quantified by the rank of this operator. We establish a minimal and invariant criterion: Instability ⇔ rank loss i.e., the loss of independent modes of coordination. This framework replaces force-based interpretations with a topology of correlations and provides measurable indicators for systemic robustness.