Within AdS/CFT, focusing on the AdS-Rindler wedge, we show that when N is large but finite, correlation functions of reconstructed bulk operators grow exponentially with bulk momentum, overwhelming the usual 1/N suppression. The growth starts when the smeared operator’s ultraviolet scale goes beyond a critical value \( {\Lambda}_{\mathrm{crit}}=\frac{2}{\pi}\ln N \) , which is far below the Planck scale. Above this logarithmic threshold, the large N expansion ceases to be reliable, and the would-be bulk operators cannot be consistently defined as observables in the full quantum gravity theory. Since the AdS-Rindler wedge describes the near-horizon region of black holes, this result implies a sharp ln N cutoff for reconstructing bulk operators across horizons. This has a direct impact on whether and how information from the black hole interior is encoded — a central question in the black hole information paradox.
