In a static graph, reachability is binary: can you get from A to B? In a temporal graph, reachability is richer: can you get from A to B using edges that exist at the right times, in the right order? Each edge has a time label, and a valid path must traverse edges in non-decreasing time order. You can't use Tuesday's connection before Monday's.
Universal temporal reachability asks for more: maintain the ability to answer reachability queries for all possible time orderings of the edges. Not just “can A reach B given this specific temporal sequence?” but “for what temporal sequences can A reach B?” This is the difference between answering one query and maintaining a complete temporal reachability oracle.
The price of this universality is quantified. The structural cost — how many edges the temporal graph needs, how dense it must be — is bounded. The computational cost — how much work is needed to maintain and query the oracle — is characterized. The tradeoff is between the flexibility of the queries and the resources required to support them.
The fundamental tension: temporal networks are inherently more complex than static ones because time adds a dimension. But universality over that temporal dimension — being ready for any time ordering — is even more expensive. The reachability tax is what you pay for temporal generality over temporal specificity.