the definition:

$$\label{braking_index}
n = \frac{f\ddot{f}}{\dot{f}^{2}}.$$

Assuming a braking index $n$ between 2 and 7 covers most accepted neutron star models ($n=5$, the neutron star radiating all energy as gravitational waves via the mass quadrupole, is used to obtain the indirect limit). We allow the braking indices in these expressions to range from 2 to 7 independently, to reflect the fact that in general multiple processes are operating and $\dot{f}$ is not a simple power law. This constraint on the braking indices then produces limits on the frequency derivatives given by [@Wette2008]

$$\label{spindown range}
\frac{f} {\tau } \leq -\dot{f} \leq \frac{f} {6\tau}$$

for the spindown at each frequency and

$$\label{second spindown range}
\frac{2 \dot{f}^2} {f} \leq \ddot{f} \leq \frac{7 \dot{f}^2} {f}$$

for the second spindown at each $(f,\dot{f})$. The step sizes for frequency and its derivatives are given by the equations [@WhitbeckThesis2006; @PatelThesis; @ReinhardStep]

$$\label{freqstep}
df = \frac{2\sqrt{3m}}{\pi }\frac{1}{T_\mathrm{data}},$$

$$\label{fdotstep}
d\dot{f} = \frac{12\sqrt{5m}}{\pi }\frac{1}{T^{2}_\mathrm{data}},$$

and

$$\label{fddotstep}
d\ddot{f} = \frac{20\sqrt{7m}}{\pi }\frac{1}{T^{3}_\mathrm{data}}.$$

where $m$ is the mismatch parameter, the maximum loss of $2\mathcal{F}$ due to discretization of the frequency and derivatives [@Owen1996; @Brady1998]. This search used a mismatch parameter $m = 0.2$.

From these relations the total number of templates (points in 