
This work develops a formal geometric and field-theoretic model of identity dynamics grounded in the exceptional Lie group E₈. Identity states are represented as stable fixed points on the E₈ weight lattice (Λ₈), while cognitive transformations—ideological conversions, trauma-driven discontinuities, developmental reorganizations—are described as Weyl reflections across the hyperplanes of the 240-root system. The framework synthesizes lattice geometry, Calogero–Moser–Sutherland (CMS) integrable systems, Toda flows, Zamolodchikov’s E₈ Ising field theory, and hyperbolic embeddings to derive a Cognitive Hamiltonian governing stability, drift, catastrophe, and recovery. Life transitions correspond to discrete symmetry actions of the Weyl group, while crisis points arise from spectral gap contraction, phase-transition analogues, and curvature spikes in the semantic manifold. The model predicts a 30-stage developmental cycle derived from the Coxeter element and identifies Golden Ratio–scaled resonances as drivers of major biographical reorganizations. This unified formalism positions identity as a quantized, symmetry-governed dynamical system with predictive structure and falsifiable signatures.
E₈ lattice; Weyl reflections; identity dynamics; phase transitions; spectral gap; Calogero-Moser system; Toda lattice; cognitive Hamiltonian; root systems; Coxeter element; hyperbolic embeddings; curvature; Golden Ratio mass spectrum; psychological phase transitions; cognitive geometry.
E₈ lattice; Weyl reflections; identity dynamics; phase transitions; spectral gap; Calogero-Moser system; Toda lattice; cognitive Hamiltonian; root systems; Coxeter element; hyperbolic embeddings; curvature; Golden Ratio mass spectrum; psychological phase transitions; cognitive geometry.
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