Semantic Grounding and the Preservation of Information in Recursive Systems

This article presents a revised information-theoretic framework for semantic grounding and recursive training. The central claim is now a rate condition rather than a fixed collapse sequence: recursive or under-corrected training introduces diagnostic degradation pressure, \(E(t)\), while independent data, verification, or other grounding channels supply effective corrective capacity, \(C_{\mathrm{eff}}(t)\). Long-term semantic viability requires that corrective capacity remain at least comparable to degradation pressure over the relevant horizon and diagnostic target. This version formally retracts the earlier prediction that out-of-distribution or grounded accuracy should generally degrade before validation perplexity rises. Instead, the temporal lag between grounded-task degradation and perplexity degradation is treated as an empirical discriminator whose sign may vary by correction regime, model scale, benchmark sensitivity, floor effects, and grading method. The paper publishes a preregistered evaluation design for testing this revised claim across five recursive-training regimes, three seeds, and two Qwen2.5 model scales. The expected signal is comparative: low-correction regimes should show stronger diagnostic separation or instability than regimes with fresher or higher-quality correction. The preregistered empirical evaluation itself is reserved for a later version.