The Structural Conditions of Consciousness II — Structural Knot Theory — Mathematical Identification and Theory Construction (Repositioning State-Based Theories of Consciousness: IIT, GNW, HOT, Predictive Processing, RPT, and Epiphenomenalism)

This paper addresses the hard problem of consciousness—commonly formulated within state-based frameworks such as Integrated Information Theory (IIT), Global Neuronal Workspace (GNW), Higher-Order Thought (HOT), Predictive Processing, Recurrent Processing Theory (RPT), and epiphenomenalism—by shifting the explanatory target from state generation to the structural localization of irreversible determination. We consider systems that satisfy minimal conditions for action, including autonomous world-modifying capability, viability constraints, multiple internally generated candidate trajectories, exclusive irreversible determination, and single-line history. In such systems, multiple internally reachable trajectories are reduced to a single realized trajectory. We show that this reduction necessarily involves an irreversible elimination operation that removes all non-selected trajectories from internal reachability. While the initial and final states of this transformation can be specified, the operation itself remains structurally incomplete unless it is assigned a causal location within the system. Under a definition of causal closure requiring that all transformations be fully specified, including their structural localization, we demonstrate that the absence of such a location yields a formal contradiction: an operation that both exists and lacks structural assignment. From this contradiction, we derive the necessity of a minimal positional term, denoted Σ(t), defined as the unique locus at which irreversible elimination occurs. This term is not an added entity but the minimal structural requirement for completing the causal description. Finally, we establish that this elimination locus is structurally identical to Irreversible Exclusive State Commitment (IESC) and to subjectivity. Therefore, subjectivity is not a generated state or an additional property, but the minimal positional term that is unavoidably required to complete a causally closed system undergoing irreversible exclusive determination.