Integration vs State Update: Architectural Conditions for Consciousness-Relevant Re-Entry

Integration² (I²) proposes that phenomenal consciousness is identical with the recursive loop formed when an integration process takes its own output as input, producing a recursive loop. This raises an immediate question: what distinguishes genuine integration-bearing re-entry from ordinary recurrent state update? A vanilla recurrent network has reflexive structure (its output influences its next input) but is not, on most accounts, conscious. We argue that the confusion arises from treating integration and state update as positions on a shared continuum, when they are in fact distinct operations that can compose. State update is a temporal operation: sequential replacement of one state with another. Integration is a binding operation: the combining of multiple heterogeneous signals into a joint representation. The two are independent, and a system can exhibit both at once. The paper's aim is not to re-establish the I² consciousness claim but to draw this distinction cleanly, so that the I² re-entry criterion can be stated precisely against it. We proceed in three stages. First, we define the two operations and show how they compose. Second, we specify three criteria for genuine re-entry that any candidate loop must satisfy: preservation and functionally diverse transformation of the integrated representation, temporal separation with intervening transformation, and re-entry into the same integration process. Third, we propose a Loop Parameter Framework comprising six parameters whose joint product determines whether a topologically adequate loop reaches ignition. The framework cuts against substrate-based arguments about machine consciousness, identifies a tractable experimental programme, and offers a way to reframe the unity-of-consciousness problem.