Surface Fixed-Point Labels and Hidden-State Continuity in Recurrent Systems

A nearly stationary readout need not specify the state required to continue a recurrent trajectory. We examine this distinction in small, untrained recurrent systems from the Demian research codebase. In a deterministic reconstruction, four dual-GRU variants receive the same operational fixed-point surface label across eight initial conditions per variant, while their message-state norms and threshold-defined interior labels differ. Separate checkpoint experiments compare full-state replay with reconstruction from the readout while preserving the model parameters and runtime clock. Full-state replay has zero measured continuation error in all tested conditions; surface reconstruction leaves a positive error in each of twelve conditions across two native substrates. Matched perturbation runs in six recurrent architectures provide recovery context, without establishing a performance ranking or a distinct mechanism. We also audit the provenance and limitations of earlier mechanism claims. The contribution is a reproducible diagnostic case study: report the readout classifier, internal-state measurements, and controlled reconstruction tests separately. These experiments establish neither exact full-state fixed points nor useful computation within them, but show what is lost when a surface label is used as a complete description of recurrent state.