Inflection Point and Field Jerk

The inflection point in the acceleration of a single charge — the sprit (σ)— is a moment of maximum rate of change of acceleration, also known as jerk. This initiates the emission of structured energy into the surrounding field.

Mathematical Formulation

Let $\vec{a}(t)$ be the acceleration vector of a charge. The inflection event is defined by the second derivative of acceleration:

$\left. \frac{d^2\vec{a}}{dt^2} \right|_{t = t_0} \rightarrow \text{Field impulse strength}$

This quantity corresponds to the magnitude of energy injected into the field structure — an initiating condition for lattice deformation. In the CA model, this deformation modifies the local admittance tensor $\Xi(\vec{r}, t)$ , ultimately leading to coherent wave emission.

Physical Implication

The “jerk” is more than a derivative — it acts as a structuring operator in CA physics. The rate at which a charge alters its acceleration determines the initial disturbance pattern that builds phase curvature in the $\vec{B}$ field and ultimately results in propagation of energy through the Ξ-lattice.