SNT Seven-Operator Framework for Neural Dynamics: Simulation, Calibration, and Empirical Validation

We present the Spectral Nod Theory (SNT) Seven-Operator Framework, a parsimonious dynamical model of neural computation applied to the fully empirical C. elegans connectome of Cook et al. (2019). Seven fundamental operators — fluctuation, refractory reset, phase transition, reversal, threshold activation, synaptic pruning, and neuroplasticity — are each grounded in identified biological mechanisms and applied to 300 neurons with 3, 707 empirical chemical synapses. The framework produces three results that, to our knowledge, have not been simultaneously demonstrated by any prior neural dynamics model. First, the Balanced SNT Kernel achieves a variance spectrum correlation of r = 0. 986 against the Kato et al. (2015) whole-brain calcium imaging dataset using only 7 global parameters — exceeding the Wilson-Cowan rate model (r = 0. 937) while requiring 86 times fewer parameters relative to its full neuron-specific capacity. Second, adding a single motor-command operator driven by the Kato locomotion pattern increases PC1 variance from 42. 3% to 80. 8%, demonstrating that the dominant axis of C. elegans brain dynamics — the forward–reversal locomotion command — is captured by one SNT operator with zero fitted circuit parameters. Circuit specificity is confirmed: AVB interneurons (forward command) correlate with the motor signal at r = +0. 857; AVA interneurons (reversal command) at r = -0. 700, both with the correct sign. Third, numerical analysis of the linearised operator commutators on the empirical connectome shows that the 7-element basis I, B, C, W, W, B, W, C, B, C forms a closed Lie algebra at machine precision (4. 82 10^-15), providing a network-theoretic answer to the question of why seven operators arise from the C. elegans wiring diagram. The 4-element basis I, B, C, W does not close (residual > 0. 99), confirming all three commutators are necessary generators. Limitations are reported transparently: the integrated information proxy remains statistically non-significant (p = 0. 332) ; the motor signal was derived from the Kato locomotion pattern rather than generated endogenously; and AVB suppression magnitude (-5. 4%) is weaker than electrophysiologically expected. These define the three highest-priority directions for future work.