Abstract

Persistence-based accounts of identity-bearing systems — HAOS-type frameworks, the Free Energy Principle, Global Workspace Theory, and related approaches — rely on batteries of dynamical observables to characterize which substrates constitute persisting systems. We show that such batteries are insufficient, on at least one substrate where frameworks would naturally apply them, to individuate the systems they are used to identify. We construct an existence witness: two coupled harmonic oscillators embedded in a weak thermal bath, admitting two substrate partitions related by an orthogonal transformation in the admissible transformation group of the dynamics. The partitions are distinct — one groups the oscillators by physical location, the other by normal-mode index — and satisfy each framework's systemhood criterion under its own definition. An eight-item persistence/coherence battery (autocorrelation, return statistics, spectral stability, transport, phase-locking, Kuramoto order parameter, correlation-matrix coherence, broadcast-access) takes invariant values on both partitions. The identity-sets they pick out differ. The battery therefore does not individuate within the transformation group, and any individuation drawn from the battery alone is incomplete without a supplementary structural condition we call a partition-warrant. We survey four families of candidate partition-warrants present (sometimes implicitly) in the existing literature — optimization-based, structural-definitional, statistical-structural, and process-based — and state a minimum requirement any warrant must satisfy: sensitivity to substrate properties that are not invariant under the admissible transformation group. Integrated Information Theory's exclusion postulate is the clearest example of an explicit partition-warrant; the paper's argument locates other frameworks relative to this structural slot. The result is methodological: it reclassifies some consciousness-adjacent disputes as partition-choice disputes, clarifies the division of labor between battery computation and individuation in empirical research, and makes tractable a comparative assessment of candidate warrants across frameworks. A companion paper develops one specific warrant — closure activation — as a positive proposal.