Stabilization and Approximation in Recurrent Neural Computation: An Enchan Field Reading

Deep recurrent and iterative neural systems, including looped Transformers, parameter-shared reasoning models, and routing-based architectures, exhibit characteristic instabilities such as attention sinks, routing collapse, recursive amplification, and mode collapse. Existing stabilizers---including softmax saturation, layer normalization, residual connections, spectral constraints, adaptive halting, and load-balancing losses---are usually introduced as architecture-specific mechanisms. This paper proposes a phenomenological reading of these mechanisms as possible manifestations of a broader stabilization pattern: finite-tension screening in an effective discrete order field. Building on the Enchan Field framework, we represent recurrent computational states by discrete order variables whose local interactions can over-concentrate around hub-like structures. We do not claim that neural networks literally implement the Enchan Field, nor do we propose a new neural architecture or report performance improvements. Instead, we ask whether known recurrent instabilities and stabilizers can be organized by a common finite-tension language. Failure modes are interpreted as defect-like or over-concentrated configurations; stabilizers are treated as phenomenological screening analogues; and the Enchan solver is proposed as a simplified controllable surrogate for studying analogous stabilization transitions. The framework is falsifiable: if recurrent instabilities cannot be coherently organized by finite-tension predictions, or if surrogate transitions fail to correspond to neural phenomena, then this reading should be constrained or rejected. Version update — v1.1 (September 16, 2026):This revision adds reproducibility and provenance materials for the preliminary surrogate diagnostic reported in Section 10. The archived source package now includes a derived norm_growth_data.csv table, a plotting script, and FIGURE_PROVENANCE.md, establishing a traceable path from the already-public reference-run metrics to the manuscript figure. No benchmark was rerun and no values were fitted or adjusted to match the figure; the derived table was reconstructed from the existing reference-run logs using the same cumulative norm-ratio calculation as the original plotting implementation. No third-party model checkpoints, tokenizers, proprietary datasets, or third-party code are bundled in the release. The manuscript's theoretical framing, empirical interpretation, and scientific conclusions are unchanged from the previous version.