Beiter's conjecture on the height of ternary cyclotomic polynomials

For odd primes $p<q<r$, let $A(n)$ denote the height of the cyclotomic polynomial $4\Phi_n(X)$. Beiter's conjecture.

$$A(pqr) \leq \tfrac1{2}(p+1)$$

for all odd primes $p<q<r$. The conjecture was disproved by Leher's example $A(17\cdot29\cdot41)=10>(17+1)/2$; subsequent work gives substantially different bounds for the maximal ternary height.