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