Seven Operators of Neural Dynamics: A Spectral Nod Theory Approach to Consciousness and Behavior – Numerical Simulations of the C. elegans Connectome

The quest to understand consciousness and brain function has advanced through detailed connectomics and phenomenological theories like Integrated Information Theory (IIT). Yet a fundamental challenge remains: even with complete wiring diagrams, we lack a dynamical framework that captures the transitions between cognitive states, the emergence of qualia, and the homeostatic mechanisms that sustain neural activity. This paper introduces a novel operator-based formalism derived from Spectral Nod Theory (SNT) to model neural dynamics at multiple scales. Seven fundamental operators—fluctuating equivalence (), cyclic equivalence (), phase nexter (), phase reverser (), liminal projection (), irreversible loss (), and subspace mapping () —are each mapped to a distinct class of neural processes: stochastic fluctuations, refractory reset, phase transitions, reversal dynamics, threshold activation, synaptic pruning, and neuroplasticity. We present the first numerical simulations of a 302-neuron C. elegans network under full seven-operator dynamics. Using a biologically realistic connectome with 20\% inhibitory and 80\% excitatory neurons, we demonstrate that the operator framework generates rich, plausible network behavior from just seven global parameters—a drastic reduction from the hundreds of parameters required by traditional Hodgkin–Huxley models. Our simulations reveal five key findings: 1. Spontaneous activation cascades driven by the Liminal operator, accurately modeling spike initiation and wave propagation. 2. Distinct temporal phases where each operator dominates (Liminal early, Cyclic Reset mid, Fluctuation late), confirming the non-redundant functional roles of all seven operators. 3. Low-dimensional attractor dynamics revealed by PCA, with the 302-dimensional state space collapsing onto a 2-3 dimensional manifold—consistent with empirical C. elegans locomotion studies. 4. A peak in integrated information precisely when all seven operators are simultaneously active (t 5. 8), supporting the theoretical claim that consciousness-like integration emerges from balanced multi-operator interplay, not from any single mechanism. 5. Heterogeneous neuronal recruitment reflecting hub structure in the connectome, with specific neuron groups (60-120, 200-260) showing disproportionately high activation—patterns that align with known sensory, interneuron, and motor neuron classifications. These results demonstrate that the seven-operator SNT framework is not merely a theoretical abstraction but a computationally viable, biologically grounded model of neural dynamics. By reducing the complexity of brain function to seven fundamental operations, the framework offers a parsimonious alternative to traditional biophysical models, provides a dynamical extension to IIT's static measure of consciousness, and opens new pathways for understanding consciousness, behavior, and the design of truly adaptive artificial intelligence. The simulation code and results are made available open source to facilitate replication and extension.