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We prove an $L^2\times L^2\to L^q_tL^r_x$ bilinear adjoint Fourierrestriction estimate for $n$-dimensional elliptic paraboloids, with $n\ge 2$and $1\le q \le \infty$, $1\le r\le 2$ being on the endline$\frac{1}{q}=\frac{n+1}{2}\bigl(1-\frac{1}{r}\bigr)$ except for the criticalindex. This includes the endpoint case when $q=r=\frac{n+3}{n+1}$, a questionleft unsettled in Tao \cite{TaoGFA}. Apart from the critical index, it improvesthe sharp non-endline result of Lee-Vargas \cite{LeeVargas} to the full range,confirming a conjecture in the spirit of Foschi and Klainerman \cite{FoKl} onthe elliptic paraboloid. Our proof is accomplished by uniting the\emph{profound} induction-on-scale tactics based on the wave-table theory andthe method of descent both stemming from \cite{TaoMZ}.

An endline bilinear restriction estimate for paraboloids