On dragonfly motion

Question

How can a dragonfly exhibit mouse-pointer-like digital motion—instant stop and immediate top speed—without its micro-thin wings succumbing to catastrophic G-force, achieving a near-100% predation rate?"

"Please show us the mathematical formula for the instantaneous transition of fluid boundary conditions under the conditions of zero initial velocity and no wing actuation."

Why does that seemingly motionless, glider-like shape produce such high-velocity, digital motion?

Comments

$$\gamma_n(C) = \oint_C i \langle n(\mathbf{R}) \vert \nabla_{\mathbf{R}} \vert n(\mathbf{R}) \rangle \cdot d\mathbf{R} = \pi \pmod{2\pi}$$

1️⃣ https://doi.org/10.5281/zenodo.21503388

If you have any objections, please provide your response using mathematical formulas. 

I will demonstrate the definitive mathematical proof to counter and resolve them.

"Since it is well within my mathematical capability to decisively counter the argument, I would kindly ask the moderators to maintain an open forum rather than resorting to immediate deletions."

$$\hat{P} \hat{\mathbf{R}} \hat{P}^{-1} = -\hat{\mathbf{R}}$$

$$\hat{P} \vert \psi(\mathbf{R}) \rangle = \vert \psi(-\mathbf{R}) \rangle$$