Proximity information is not taken into account at all, e.g.
aSR lattices do have much better WER -in our case the 1-best WER was 55% whereas the lattice WER was 30% -but the position information is not readily available: it is easy to evaluate whether two words are adjacent but questions about the distance in number of links between the occurrences of two query words in the lattice are very hard to answer.