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ZENODO
Preprint . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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Cognitive Phase Transitions on the E₈ Weight Lattice: A Unified Field Theory of Identity Structure and Dynamics

Authors: Slade, Trent;

Cognitive Phase Transitions on the E₈ Weight Lattice: A Unified Field Theory of Identity Structure and Dynamics

Abstract

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.

Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green