= Rich-bisector deletion bound
{title2=$\#\{\text{arcs with multiplicity at least }k\}=O(tn^2/k^2+tn\log n)$}
Every supporting centre of an arc between fixed endpoints lies on their <perpendicular bisector>. Multiplicity at least $k$ therefore makes that <line> contain at least $k$ of the original points. For each such <line> containing $s$ points, its $s$ centres each support at most $t$ <circles>; on one <circle> at most two consecutive-point arcs have that symmetry axis. The <rich line bound> summed over dyadic occupancies gives the displayed bound.
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