4 vs 7 sparse undirected unweighted Diameter is SETH-hard at time $n^{4\mathrm{/}3}$

We show, assuming the Strong Exponential Time Hypothesis, that for every $\epsilon >0$, approximating undirected unweighted Diameter on $n$-vertex $n^{1+o(1)}$-edge graphs within ratio $7\mathrm{/}4-\epsilon$ requires $n^{4/3 - o(1)}$ time. This is the first result that conditionally rules out a near-linear time $5\mathrm{/}3$-approximation for undirected Diameter.