  We investigate global solutions to the Euler-alignment system in $d$
dimensions with unidirectional flows and strongly singular communication
protocols $\phi(x) = |x|^{-(d+\alpha)}$ for $\alpha \in (0,2)$. Our paper
establishes global regularity results in both the subcritical regime
$1<\alpha<2$ and the critical regime $\alpha=1$. Notably, when $\alpha=1$, the
system exhibits a critical scaling similar to the critical quasi-geostrophic
equation. To achieve global well-posedness, we employ a novel method based on
propagating the modulus of continuity. Our approach introduces the concept of
simultaneously propagating multiple moduli of continuity, which allows us to
effectively handle the system of two equations with critical scaling.
Additionally, we improve the regularity criteria for solutions to this system
in the supercritical regime $0<\alpha<1$.
