No Small Observer Can Verify a Black Hole Firewall

Alice stays outside a black hole; Bob falls in. Alice never sees the interior. Bob crosses the horizon but can never signal back. Physics holds subjectively for both, yet their realities objectively contradict. This illustrating a conflict between quantum and classical mechanics. AMPS is a thought experiment about this. It asks one observer to distil a purifier of a late Hawking mode \( B \) from early radiation $R$, then compare it with the interior partner \( A \) inside a single causal patch. The hidden cost is not just computation but control. If the correct decoder depends on the black hole microstate, the observer must carry a physical selector for the decoder family. I model that selector as a finite control register bounded by the covariant entropy bound on the patch. A covering argument shows that any fixed, state-independent decoder works on at most \( 2^{\alpha_* S_{\mathrm{BH}}+c_\varepsilon} \) microstates, so the observer needs at least \( (1-\alpha_*)S_{\mathrm{BH}}-c_\varepsilon \) control bits---requiring a patch with area fraction \( \rho^2 \ge 1-\alpha_* - c_\varepsilon/S_{\mathrm{BH}} \). A time-sharing objection fails because single-observer verification requires co-instantiation, not mere sequential occurrence; serialisation creates no free room. The conclusion: a subhorizon observer generally cannot certify the AMPS contradiction. In quantum gravity, control information is physical, and single-observer certification is a capacity problem. If the contradiction can never be measured, is it real?