DAG reachability with O(n log n) space and O(log n)-time queries? For a directed acyclic graph ${\langle}V,E{\rangle}$, is there a data structure that allows for reachability queries without requiring quadratic space or linear time?  Ideally I seek an algorithm using only O(log n) space per vertex and logarithmic time where $n=|V|+|E|$.

It seemed intuitively obvious to me that a data structure like this ought to exist, based on some generalization of standard sorting algorithms.  But I was surprised that I couldn't find any.  Everything I came across either made assumptions about the graph (e.g. planarity) or solved a harder problem in quadratic time/space (e.g. queries interleaved with graph modifications).

The Wikipedia page on Reachability only covers one general algorithm (Floyd-Warshall); the rest of the page deals with special cases involving assumptions like the graph being planar (it isn't).

The most commonly cited paper in this space appears to be Amortized efficiency of a path retrieval data structure, but this and all the papers it cites involve either O(n^2) space or else O(n^2) time in order to allow updates to the graph interleaved with the queries (i.e. no preprocessing).

This question wasn't answered, but it deals with the harder problem of allowing edge insertions interleaved with queries.

This question asked for a persistent (pure functional) data structure, which isn't required here.  The "Succinct Posets" paper needs $O(n^2)$ space but it achieves $O(1)$-time queries; I seek a worse-time, better-space algorithm.

Mostly looking for a foothold in the literature here.  If there's a survey paper on graph reachability that doesn't spend 99% of its time on the planar-graph case, that would help.
See "interval labeling" and "2-hop labeling" which are apparently quite efficient in practice, both in time and space, and may give you what you want. In general there's quite a bunch of "reachability indexing" schemes for DAGs.