= Particle-hole equality of tetragonal extremal orbit areas
{title2=$A_e=A_h$}
At half filling the nearest-neighbor band $E-E_0=-2t(\cos x+\cos y)-t\cos z$ has an electron contour at $z=\pi$ and a hole contour at $z=0$. Translation $(x,y)\mapsto(x+\pi,y+\pi)$ maps the enclosed pockets into each other, proving equal regular Onsager frequencies for a field along $z$. Comparing an occupied slice with the complement of a hole orbit is not a comparison of two different enclosed planar orbits. Additional band terms or changed filling can lift this equality.
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