Suppose I have three points $O_1, O_2, O_3$ floating in a universe that obeys galilean relativity
$O_2$ is located 10 metres east of $O_1$ (just pick a direction vector of your choice and call it east)
$O_3$ is located 20 metres east of $O_1$.
It is correct to say, $O_1$ would report that from $O_1$'s frame of reference $O_3$ is 10 metres east of $O_2$.
Now suppose we enter the world of special relativity and set up the same 3 points with these initial conditions when they are not moving with respect to each other.
Suppose now that $O_2, O_3$ are moving with velocity $v$ east relative to $O_1$ with the same starting positions. If we treat $O_2, O_3$ as single system it should undergo length contraction meaning that $O_1$ would report the relative distance between $O_2$ and $O_3$ as $10 \sqrt{1 - \frac{v^2}{c^2}} $
Is this a valid interpretation of length contraction?