Closed-Loop Syntactic Decay and Lexical Convergence in Recursive N-Gram Language Systems

This study investigates the long-term behaviour of recursively self-trained language systems using a finite-state N-gram Markov framework. Two experiments were conducted across 1,000 generations of recursive synthetic text production. The first experiment examined vocabulary retention and entropy dynamics under strict closed-loop recursion and under mutation-augmented recursion. In the closed-loop condition, vocabulary retention declined rapidly from 100% to 19.23% of the original lexicon and stabilised in a low-entropy attractor state. By contrast, the mutation condition maintained high lexical diversity, preserving approximately 87-100% of the original vocabulary throughout the experiment. The second experiment investigated lexical convergence between initially distinct recursive language systems. Two models sharing only nine lexical items at initialization progressively converged through recursive exchange, ultimately stabilising on an identical reduced vocabulary. This behaviour suggests the emergence of shared lexical attractors in isolated recursive communication environments. The results demonstrate that finite-state recursive language systems exhibit both vocabulary contraction and attractor formation under closed feedback conditions. While the framework is not intended as a direct simulation of transformer-based large language models, it provides an experimentally reproducible analogue for studying recursive information degradation, entropy collapse, and convergence dynamics in self-referential generative systems. Source code, experimental data, and methodological details are included to support independent verification and extension of the findings. This work presents an analogue computational framework rather than a direct implementation of transformer-based language models. The purpose of the study is to explore general properties of recursive information systems under closed-loop feedback conditions.