The scientific study of consciousness is currently undergoing a critical transition in the form of a rapidly evolving scientific debate regarding whether or not currently proposed theories can be assessed for their scientific validity. At the forefront of this debate is Integrated Information Theory (IIT), widely regarded as the preeminent theory of consciousness because of its quantification of consciousness in terms a scalar mathematical measure called $Φ$ that is, in principle, measurable. Epistemological issues in the form of the "unfolding argument" have provided a refutation of IIT by demonstrating how it permits functionally identical systems to have differences in their predicted consciousness. The implication is that IIT and any other proposed theory based on a system's causal structure may already be falsified even in the absence of experimental refutation. However, so far the arguments surrounding the issue of falsification of theories of consciousness are too abstract to readily determine the scope of their validity. Here, we make these abstract arguments concrete by providing a simple example of functionally equivalent machines realizable with table-top electronics that take the form of isomorphic digital circuits with and without feedback. This allows us to explicitly demonstrate the different levels of abstraction at which a theory of consciousness can be assessed. Within this computational hierarchy, we show how IIT is simultaneously falsified at the finite-state automaton (FSA) level and unfalsifiable at the combinatorial state automaton (CSA) level. We use this example to illustrate a more general set of criteria for theories of consciousness: to avoid being unfalsifiable or already falsified scientific theories of consciousness must be invariant with respect to changes that leave the inference procedure fixed at a given level in a computational hierarchy.