Consciousness as 4-Manifold Painlevé V Dynamics: From Quantum Topology to Classical Gamma Oscillations
Axioms February 6, 2026 Michel R. P. Planat 1 citation
A new mathematical framework models consciousness as a dynamical phenomenon governed by nonlinear integrable equations, specifically the Painlevé VI equation and its confluence limits. Consciousness is described as an emergent phase sustained near criticality, where coherent quantum-like structures and classical decoherence coexist in a regulated balance. The theory uses isomonodromic deformations on SL(2,C) character varieties to characterize conscious states by monodromy data. It encodes memory, attention, and transitions between conscious and unconscious phases, with confluence processes accounting for irreversible loss of coherence. A two-stage quantum-to-classical transition separates microscopic coherence from macroscopic stabilization. The framework yields universal signatures like critical slowing down and scaling laws near transition points.