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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 anear-linear time $5/3$-approximation for undirected Diameter.

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