= Stationary no-runaway response and preacceleration
For positive $\varepsilon$, the real-axis frequency response of the <radiation-reaction oscillator pole structure> excludes future runaway growth but retains an upper-half-plane pole. Closing its inverse <Fourier transform> upward at $t<0$ gives a nonzero response before the force. The fast pole contributes approximately $\varepsilon e^{t/\varepsilon}$ for negative $t$. A strictly causal retarded prescription instead includes an exponentially growing term for positive $t$ and requires a <Laplace transform> contour. The pre-response is a consequence of imposing boundedness at future infinity, not an unavoidable property of all initial-value solutions of the differential equation.
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