Equation 109 · The Bit Comes Back Before the Bearing
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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, grows toward the hole’s full evaporation lifetime as 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 ] .
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