  Hypertranslations and hyperrotations are asymptotic symmetries of flat space,
on top of the familiar supertranslations and superrotations. They were
discovered in arXiv:2205.01422 by working in the Special Double Null (SDN)
gauge, where $\mathscr{I}^{+}$ and $\mathscr{I}^{-}$ are approached along
$null$ directions. It was observed there that while the hair degrees of freedom
associated to these diffeomorphisms show up in the covariant surfaces charges,
the diffeomorphisms themselves do not. This made their status intermediate in
some ways between global symmetries and trivial gauge transformations, making
interpretation ambiguous. In this paper, we revisit the fall-offs considered in
arXiv:2205.01422 which were strictly subleading to Minkowski in conventional
double null coordinates. We identify a new class of fall-offs where this
assumption is relaxed, but whose charges nonetheless remain finite. Remarkably,
the leading behavior is still Riemann flat, indicating that these are soft
modes. With this more refined definition of asymptotic flatness, we show that
leading hypertranslations and leading hyperrotations explicitly show up in the
charges. This makes them genuine global symmetries of asymptotically flat
Einstein gravity in the SDN gauge. We write down the new algebra of asymptotic
Killing vectors that subsumes the BMS algebra.
