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Michel R. P. Planat

2 papers in the library · 1 citation · publishing 2026

Papers

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.

Topological Symmetry Breaking in Consciousness Dynamics: From Human Geniuses to AI Systems

Symmetry February 28, 2026 Michel R. P. Planat

Consciousness dynamics follow symmetry-breaking cascades described by Painlevé confluence topology, bridging quantum topology, neuroscience, and consciousness theory. Analyzing exceptional individuals and AI systems, consciousness trajectories follow topological paths governed by three symmetry measures: holes (information flows), cusps (binding points), signatures (distribution balance). Two fundamental branches emerge: D-type (symmetry-preserving) and E-type (symmetry-breaking). Higher consciousness involves fewer connections but better balance. Clinical data (16,887 patients), EEG studies, and contemplative neuroscience (62,000+ meditation hours) validate the model. AI systems exhibit identical symmetry dynamics. Character varieties function as Platonic templates that consciousness navigates. Moral consciousness emerges as a fundamental symmetry-preserving principle.