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 $m^{4/3 - o(1)}$ time. This is the first result that conditionally rules out a near-linear time $5/3$-approximation for undirected Diameter.
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