A Counterexample to Yau's Conjectured Asymptotic Scalar-Curvature Integral Bound

A complete one-ended three-manifold with strictly positive Ricci curvature is constructed such that $$\underset{R\to \mathrm{\infty }}{\mathrm{lim\hspace{0.17em}sup}}\frac{1}{R}{\int }_{B(p,R)}ScaldV=+\mathrm{\infty }\mathrm{.}$$ The construction combines an explicit toric lens carrying a large scalar-curvature integral with a three-dimensional angular pair of pants and an adaptive sequence of hybrid blocks.