The Tectonic Manifold: Predicting Topological Singularities through Metric Tension, Spectral Triads, and the Folding Operator

This paper presents a novel topological framework for geophysical forecasting, redefining global seismicity as a synchronized, continuous energy manifold rather than a series of isolated tectonic failures. This study identifies a "Folding Operator" that governs the structural integrity and recursive memory of the Earth's crust. Through the analysis of a 1950–2026 dataset, the authors demonstrate how metric contraction and spectral coherence in "Pinch Points" signal imminent Topological Singularities. Ultimately, the paper argues that seismic events are deterministic manifold realignments that can be predicted by monitoring the transition from coherent harmonic oscillations to decoherent folds.