What does this equation mean?

This model has an explicit conservation ceiling built in: it cannot be extended past the compass’s own total intrinsic Fisher information $F_Q^{(0)}$ = 4$\operatorname{Var}$$\hat J$/$\hbar^2$ , since no amount of radiation can reveal more about g than the original state ever carried. A tolerance $\delta$ tighter than 1/$\sqrt{F_Q^{(0)}}$ is not a slower recovery — it is a request for better precision than the compass itself possessed, which no observer, inside or outside any horizon, could ever meet. Within that ceiling, $t_G(\delta)$ grows toward the hole’s full evaporation lifetime as $\delta$ is tightened, which is a specific, checkable form of the “information remnant” Nakata, Wakakuwa, and Koashi found directly in their symmetry-constrained analysis of the Hayden-Preskill protocol: a residue that a purely logical decoder never has to wait for, because it was never entitled to it in the first place [ 8 ] .