= Cubic covering from few ordinary lines
{title2=$P\subseteq\bigcup_{j=1}^{O(K+1)}\gamma_j$}
If a finite planar point set has at most $Kn$ <ordinary lines>, its points can be covered by $O(K+1)$ possibly reducible cubics. The <Euler defect identity for a projective line arrangement> gives $O(Kn)$ bad edges in the dual. <Bounded-radius propagation of edge defects> and averaging select one dual line with $O(K+1)$ unsafe edges. <Cubic propagation along a triangular strip> covers each safe run; each exceptional intersection vertex represents a primal line, covered by a <degenerate cubic containing a line>. A dual line with very few intersection vertices instead yields a direct covering by few primal lines.
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