  We study a random system of cn linear equations over n variables in GF(2),
where each equation contains exactly r variables; this is equivalent to
r-XORSAT. Previous work has established a clustering threshold, c^*_r for this
model: if c=c_r^*-\epsilon for any constant \epsilon>0 then with high
probability all solutions form a well-connected cluster; whereas if
c=c^*_r+\epsilon, then with high probability the solutions partition into
well-connected, well-separated clusters (with probability tending to 1 as n
goes to infinity). This is part of a general clustering phenomenon which is
hypothesized to arise in most of the commonly studied models of random
constraint satisfaction problems, via sophisticated but mostly non-rigorous
techniques from statistical physics. We extend that study to the range
c=c^*_r+o(1), and prove that the connectivity parameters of the r-XORSAT
clusters undergo a smooth transition around the clustering threshold.
