Before revision:  Our index locates path occurrences in constant time each and takes 2n + o(n) + O(r \log n) \leq 2n + o(n) + O( \mathcal H ^{wc_k\log }  n) bits of space: the reporting time is optimal and the locate machinery fits within compressed space on top of the tree's topology.
After revision:  Our index locates path occurrences in constant time each and takes 2n + o(n) + O(r \log n) \leq 2n + o(n) + O( _k\log } n) bits of space: the reporting time is optimal and the locate machinery fits within compressed space on top of the tree's topology.