Selecting and Tracking Conscious Subjects: Symmetry, Monodromy, and an IIT 4.0 Case Study

Theories of consciousness that associate subjects with physical systems face an individuation problem in addition to the problem of assigning phenomenal structure: when several physical systems are plausible subject candidates, which one is the subject, and how is that subject tracked through physical change? We formulate this as a combined selection-and-tracking problem over physical state space. At a symmetric state, an equivariant deterministic selector can choose a candidate only if that candidate is fixed by the state's stabilizer. We distinguish this local obstruction from a global monodromy obstruction that can arise even when all local candidate branches are regular. The distinction yields a central conceptual result: physical history can track a previously specified token without canonically selecting the initial token from a symmetric snapshot. We then analyze the repair space available to an exclusive subject theory. Relative to explicit desiderata—totality, determinism, uniqueness, top-tier fidelity, physical equivariance, and snapshot supervenience—a non-fixed symmetric top tier forces at least one commitment to be relaxed. Set-valued, randomized, descent, symmetry-breaking, history-dependent, and unresolved responses occupy different points in this design space. As a concrete case study, we directly recompute a three-unit stochastic system using an unmodified official PyPhi checkout under IIT 4.0 (2026). Across sampled points spanning a reflection-symmetric parameter crossing, including \(|\lambda|=10^{-6}\), the maximal complex returned by the official search is \(BC\) on the negative side, \(AC\) at the exact symmetry point, and \(AB\) on the positive side; the corresponding accepted families are \(\{BC,A\}\), \(\{AC,B\}\), and \(\{AB,C\}\). At the symmetry point, \(AB\) and \(BC\) tie in both system integrated information and structure \(\Phi\), fail exclusion, and the cascade descends to \(AC\). The abstract theory identifies the conditions under which such a fixed-point descent becomes a genuine discontinuity; the numerical study is reported as a high-precision realization rather than an interval-arithmetic proof. Finally, we contrast exclusive extraction with a nonexclusive process-landscape representation and prove local Hausdorff continuity of a finite enriched landscape whenever its underlying candidate branches vary continuously. The results motivate treating subject selection and subject tracking as distinct formal problems in mathematical theories of consciousness. **Keywords:** consciousness; subject individuation; integrated information theory; exclusion; symmetry; monodromy; equivariance; choice correspondence; PyPhi; phenomenal unity TA-TR-2026-19, version 1.0. Human author of record and responsible depositor: Hongju Liu. Substantial ChatGPT assistance under human direction. Not peer reviewed; no institutional endorsement is claimed. Adjacent first-party non-amending scholarship. The paper does not claim new group theory, topology, continuous-choice theory, the first discovery of IIT complex switching, empirical consciousness measurement, or proof of the broader UCT program. Its narrower proposed contribution is the combined local/global selection-tracking framework and official current-IIT realization.