Published April 10, 2026
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The Universal Bridge at the Phase Transition: Kuramoto Criticality, Maxwell Rigidity, and the Topology of Neurodivergent Cognition
Description
Fourth in the P31 Research Series. Mathematical framework for cognitive phase transitions in neurodivergent individuals using Kuramoto synchronization, Maxwell rigidity, algebraic topology, Shannon information theory, and Fisher's quantum cognition hypothesis. Introduces the Transducer Error construct and applies rate-distortion theory to monotropism. Corrects K₄ non-planarity claim from Paper I (DOI: 10.5281/zenodo.18627420), reframing around volumetric enclosure (β₂=1). Three novel contributions flagged: (1) Shannon-Hartley applied to monotropic attention, (2) Transducer Error as rate-distortion phenomenon, (3) motional narrowing as cognitive analogy.
Notes
CORRECTION NOTE: Corrects a claim in Johnson (2025a, DOI: 10.5281/zenodo.18627420) regarding K₄ non-planarity. K₄ is planar (maximal planar graph); the argument is reframed around simplicial volumetric enclosure (β₂=1). Three novel contributions are explicitly flagged in sections 1.1, 5.1, and 5.2.
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Additional details
Related works
- Continues
- Preprint: 10.5281/zenodo.18627420 (DOI)
- Preprint: 10.5281/zenodo.19411363 (DOI)
- Preprint: 10.5281/zenodo.19416491 (DOI)
Subjects
- Nonlinear dynamics
- https://id.loc.gov/authorities/subjects/sh85092332
- Graph theory
- https://id.loc.gov/authorities/subjects/sh85056471
- Information theory
- https://id.loc.gov/authorities/subjects/sh85066283
- Autism spectrum disorders
- https://id.loc.gov/authorities/subjects/sh2009117530