Spectral Rigidity and Topological Phase Transitions in Stressed Financial Networks

This research investigates the fundamental physical mechanisms underlying systemic collapses in complex networks. By defining the Liquidity Mask as a strictly lower-triangular directional operator, we demonstrate that the algebraic connectivity converges to an asymptotic geometric boundary of exactly 0.5 under causal confinement. We map an Anderson-like localization transition of the Fiedler vector via a multifractal Inverse Participation Ratio (IPR) equation of state. The methodology employs a Computational Adversarial Research Framework, using a multi-agent system of Generative, Analytical, and Adversarial nodes to perform iterative falsification and minimize single-agent cognitive bias. The analytical results are validated via a Circular Block Bootstrap (CBB) null model, rejecting the hypothesis of isotropic fluctuations (\(p < 0.001\)). This study establishes systemic crashes as topological phase transitions characterized by the collapse of bidirectional dynamics into unidirectional forced liquidations. The repository includes: Academic Manuscript: Detailed mathematical derivations of the Causal Limit Theorem and the Anderson Localization mapping. MÖBIUS-SPECTRA v5.1.2 Computational Engine: Production-ready Python script (mobius_spectra_v512.py) for spectral signature extraction and CBB statistical validation.