= Self-paired spinless fermion mode
{title2=$k\equiv-k\pmod{2\pi}$}
In a unit-spacing periodic spinless chain, self-paired <momenta> are $k=0$ and, when available, $k=\pi$. An anomalous pair of the same <creation operator> vanishes by the <canonical anticommutation relations>. Such a mode is a single normal number level, filled or empty according to its energy sign, rather than a two-distinct-mode <Bogoliubov transformation>. This excludes the paired-angle construction at those special <momenta>.
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