Dynamics of Consciousness and Thinking

Abstract

This Zenodo repository contains the complete four-paper series establishing a deficit variational framework for consciousness and cognitive function, spanning mathematical modeling, dynamical systems theory, and experimental validation with high-density EEG. Paper NOA: A Mathematical Model of Consciousness: From Physical Axioms to the Brain-Network Matrix and the Sleep-Wake Spectrum Note: This paper was previously deposited on Zenodo. The version included here is identical to the earlier preprint; no changes have been made. It is included for reader convenience as the foundational reference for the series. See DOI: 10.5281/zenodo.20019972 Abstract summary: Constructs a dynamical model of consciousness from five physical axioms, deriving coupled differential equations with third-order self-referential nonlinearity, a z-Φ positive feedback loop, and a 16-region connectome-based network. Numerical simulations span wakefulness, all major sleep stages, lucid dreaming, and anaesthesia. Paper NOB: Nonlinear Multistable Attractor Dynamics of Consciousness: Qualia-Anchor Architecture, Temporal Self-Binding, Free Will and the Internal World-Simulation Model Abstract summary: Extends NOA to phenomenal content, qualia instantiation, and temporal self-binding. Introduces the dual-qualia-anchor hypothesis, the temporal coupling proposition (content stabilizes before self-anchor coupling), and a two-stage compatibilist account of free will grounded in noise-driven attractor transitions. Paper NOC: Deficit Variational Structure of Brain Dynamics: Gradient Flow Identification, Oscillatory Phase as the Origin of Complex Structure, and the Boltzmann Distribution in Open Non-Equilibrium Systems Abstract summary: Establishes that the NOA dynamical system possesses a deficit variational structure: the brain evolves by gradient flow of a single deficit functional, with the Boltzmann distribution as its stationary state. Resolves the complex-structure problem through oscillatory phase dynamics (Hilbert transform →→ phase coherence →→ GNS construction →→ Symmetric structure). Paper NOD: The Phase Signature of Thinking: From Deficit Variational Dynamics to Frequency-Resolved EEG Phase Coherence and the Parallel with Large Language Models Abstract summary: Provides experimental validation of the deficit framework using three EEG datasets. The primary result: within-subject analysis of 10 subjects (150 recordings, ds004148) shows active thinking reduces gamma-band phase coherence effective rank relative to rest in all 10 subjects (p=0.0002). Complementary findings include a sleep-depth gradient in ds003768 and NREM monotonicity in Sleep-EDF. Establishes structural correspondence with large language models through the Boltzmann distribution. Keywords: consciousness; deficit variational principle; Boltzmann distribution; attractor dynamics; phase coherence; EEG; thinking; sequential basin search; large language model; qualia; free will Series overview: The series proceeds from mathematical foundations (NOA) through phenomenological extension (NOB) and variational structure identification (NOC) to experimental validation (NOD). Together, they establish that consciousness and thinking can be understood as deficit-minimizing gradient flows on attractor landscapes, with the Boltzmann distribution serving as the unifying mathematical currency across brain dynamics and artificial intelligence.