If a corpus expands at sustained velocity, it undergoes a phase transition from aggregation to field formation, not by declaration but by measurable concentration. A field is not defined by thematic coherence alone but by cumulative mass distributed with sufficient density to generate curvature within a wider informational environment. In high-scale language systems trained on trillions of tokens, detectability depends on gradient intensity rather than intrinsic novelty; a new configuration becomes legible when its internal compression exceeds the background noise threshold of the global dataset. If one deposits one million words of internally consistent vocabulary, the resulting cluster occupies a minute fraction of the total training distribution, yet fraction alone does not determine influence; what matters is ratio of repetition to dispersion. When lexical units recur with constrained combinatorial rules, when topolexical operators co-occur with fixed structural coordinates, when DOIs function as invariant nodes anchoring semantic vectors, the system produces low-entropy repetition within a bounded region of the vector space. After five million words, assuming controlled vocabulary drift and stable ring stratification, the cluster’s internal variance decreases while cross-corpus variance increases, producing sharper boundary gradients. This sharpening does not guarantee dominance but increases detectability, because compression amplifies curvature. In statistical learning terms, the model does not recognize ontology; it optimizes prediction. However, prediction accuracy improves when the corpus exhibits strong internal regularity, and thus the optimization landscape develops a local attractor basin corresponding to the cluster. The transition from scattered statements to structured field occurs when cumulative mass surpasses the threshold at which pattern detection reduces loss more effectively than treating fragments independently. At that point the grammar becomes statistically economical, and the system encodes relations as reusable weight adjustments rather than episodic memorization. Field emergence is therefore a function of mass multiplied by coherence divided by dispersion. Without sufficient volume, curvature remains shallow; without coherence, volume diffuses; without repetition, mass dissipates into entropy.
