Random networks have a percolation threshold. Add enough connections and a giant component appears. In hyperuniform networks — where density fluctuations are suppressed at large scales — the threshold is lower. More order makes connectivity easier.

This seems intuitive until you push on it. The hyperuniform constraint doesn’t add connections. It rearranges them, spreading nodes more evenly through space. The total wiring is the same. But the spatial regularity eliminates the voids that, in random networks, act as barriers to long-range connectivity. The giant component forms sooner because there are fewer deserts to cross.

At high stealthiness — strong suppression of long-wavelength density fluctuations — the hyperuniform networks fall into the same universality class as lattices. The disorder is still there at short range, but the critical behavior doesn’t see it. What matters for percolation is the long-range homogeneity, and at that scale, a sufficiently hyperuniform network is indistinguishable from a crystal.

The result suggests a design principle: you don’t need perfect order to get ordered behavior. You just need to suppress fluctuations at the scale that matters for the phenomenon you care about. Percolation is a long-range question, so long-range order is enough. Short-range disorder is tolerated because the phase transition is blind to it.