The apparent contradiction dissolves. An observable universe about 93 billion light-years across does not require light to have traveled for 46.5 billion years, because the space through which it traveled has expanded throughout its journey. Distance has a history. The universe's age, about 13.8 billion years, measures elapsed time; its quoted diameter measures how far apart its observable boundaries are now.
The tempting arithmetic fails. Multiplying cosmic age by light speed would give the observable radius only if space had remained unchanged, whereas cosmological expansion has increased the separation between us and distant matter while its light approached. The distinction changes everything. Light arriving from remote regions began its journey when those regions were much closer, and the matter associated with the earliest signals is now vastly farther away than a simple travel-time calculation suggests. No speed limit breaks. Relativity limits motion through nearby space, but it does not impose that same limit on the growth of distances across an expanding universe.
The boundary needs care. The particle horizon, whose present radius is approximately 46.5 billion light-years in the standard cosmological model, marks the greatest distance from which signals could have reached us since the universe began. It is no wall. Nor does the observable universe necessarily encompass everything that exists, since regions beyond that horizon may simply be too distant for their signals to have arrived. Observation supplies the limit. Beyond the oldest arriving light, existence need not end; only the evidence reaching this particular patch of space runs out.
