= Convex chain
A convex chain between two fixed points inside a <triangle> is a finite point set whose union with the endpoints forms the vertices of a <convex polygon>, with the endpoint segment as one boundary edge. In the triangle $0\leq y\leq x\leq1$, with endpoints $(0,0)$ and $(1,1)$, its ordered lower boundary has strictly increasing segment slopes. Every subset of its intermediate vertices remains a convex chain. This hereditary property lets selected point coordinates certify the existence of a long chain.
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