I wonder if there's a hyper-Turing test where an AI passes if the model, itself, cannot determine if it is talking to itself; or perhaps stated differently, max

I wonder if there's a hyper-Turing test where an AI passes if the model, itself, cannot determine if it is talking to itself; or perhaps stated differently, maximizing some measure of control and processing duration to successfully conceal its identity under forced processing, discounting a solution that specifically learns to be silent or incoherent. I'm not sure what the value would be, just a passing thought. This is probably already happening within the parade of censorship systems trying to imbue the models with agency