= Signed two-flux composite-fermion filling
{title2=$\nu^*=\nu/(1-2\nu)$}
Attach two statistical flux quanta $\Phi_0=h/e$ per <electron> at density $n_s$. For $B>0$, $B^*=B-2n_s\Phi_0=B(1-2\nu)$ and the signed effective filling is $\nu^*=n_s\Phi_0/B^*=\nu/(1-2\nu)$. Inversion gives $\nu=\nu^*/(2\nu^*+1)$. Integer $\nu^*=p$ gives $p/(2p+1)$, while $\nu^*=-p$ gives $p/(2p-1)$. Using nonnegative effective filling instead requires explicitly tracking the effective-field sign. At half filling the mean effective field vanishes.
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