No Small Observer Can Verify a Black Hole Firewall

Quantum gravity is often probed by thought experiments that assume unlimited classical control over quantum systems. The firewall paradox is one such thought experiment. It asks if one observer can decode early Hawking radiation, and then later compare with degrees of freedom behind the horizon. Here I show that this protocol is constrained by an instruction budget. If the correct decoding depends on the black hole microstate, a hidden internal configuration, then the observer must specify which decoder to use. The number of decoders needed to cover all microstates grows exponentially with the black hole entropy, so the decoder specification requires a number of bits that scales with that entropy. A covariant entropy bound limits how much information can be stored within a bounded causal patch. This enforces a horizon-scale lower bound on the region required for single-observer verification, even when computational complexity is ignored. More broadly, the result highlights a principle for quantum gravity experiments. Control information is physical, and bounds on storage can decide what is testable.