Phase-Wave Differential Calculus: Neural Tuning, Variability Tokens, and Taylor-Sequence Approximation in Oscillatory Neural Networks

The same neural event can matter differently depending on what a receiving cell or population is already doing. Existing accounts measure important parts of that problem-rate, phase, joint phase-rate, prediction error, phase response, plasticity, waveform shape, or nonlinear history-but they do not by themselves specify one typed record that joins the departure, its receiver, its physical route, and the receiver's subsequent change. This paper defines a phase-wave differential (PWD) as that bounded, receiver-relative record. Its candidate components are phase, event rate, amplitude, duration, transmitted quantity, variability, and declared spatial or network context, each measured against a frozen tonic reference. A measured difference qualifies as a candidate biological token only if a named receiver preserves or transforms it, a selective perturbation changes the predicted consequence, and the representation adds held-out value beyond matched alternatives. Its conclusions are limited to the assumptions, evidence, and testing conditions stated in the manuscript. It belongs to the Self-Aware Networks neuroscience and consciousness research program. This is a corrected preprint edition released under the Creative Commons Attribution 4.0 license.