  The largest coefficient (in absolute value) of a cyclotomic polynomial
$\Phi_n$ is called its height $A(n)$. In case $p$ is a fixed prime it turns out
that as $q$ and $r$ range over all primes satisfying $p<q<r$, the height
$A(pqr)$ assumes a maximum $M(p)$. In 1968, Sister Marion Beiter conjectured
that $M(p)\leq (p+1)/2$. In 2009, this was disproved for every $p\ge 11$ by
Yves Gallot and Pieter Moree. They proposed a Corrected Beiter Conjecture,
namely $M(p)\leq 2p/3$. In 2009, Jia Zhao and Xianke Zhang posted on the arXiv
what they thought to be a proof of this conjecture. Their work was never
accepted for publication in a journal. However, in retrospect it turns out to
be essentially correct, but rather sketchy at some points. Here we supply a lot
more details. \par The bound $M(p)\le 2p/3$ allows us to improve some bounds of
Bzd\k{e}ga from 2010 for ternary cyclotomic coefficients. It also makes it
possible to determine $M(p)$ exactly for three new primes $p$ and study the
fine structure of $A(pqr)$ for them in greater detail.
