The Structural Determinacy of LLM Generation: Active Structure, Convergence Frontiers, and the Misreading of Randomness

Abstract

The Structural Determinacy of LLM Generation: Active Structure, Convergence Frontiers, and the Misreading of Randomness Civilization Physics - Series: Model Series This article argues that stochastic decoding does not imply structurally stochastic generation. Large language models may vary in wording, examples, style, and local realization while repeatedly producing the same strategy, causal organization, argument architecture, relational mechanism, or functional solution. The central distinction is between surface variation and load-bearing structural variation. The central claim is that randomness in LLM generation is scale-sensitive. Sampling remains real, but it operates inside a possibility space already organized by active structure. The article separates structural entropy from residual realization entropy, introduces the structural convergence frontier, and asks at what task-relevant resolution generation has already become stable. The article develops this argument through several linked mechanisms: Structural equivalence groups outputs by task, consequence horizon, and analytic resolution rather than by wording, paraphrase, or embedding similarity. Load-bearing structure is defined by counterfactual consequence: a distinction matters when changing it changes the relevant causal, legal, logical, relational, or operational result. Structural entropy measures uncertainty over structural classes, while realization entropy measures remaining linguistic or implementation freedom within a class. The structural convergence frontier identifies the finest task-relevant resolution at which generation has become stably concentrated while finer distinctions remain open. Creativity requires divergence across valid non-equivalent structures followed by convergence within each structure, rather than merely raising token-level randomness. Convergence provenance distinguishes whether narrowing comes from reality, task selection, learned priors, policy constraints, or generated history. This article reframes LLM randomness as a problem of structural resolution. The practical question is no longer simply whether a model is random or creative, but which structures are active, which distinctions are load-bearing, where convergence has occurred, what realization freedom remains, and which alternatives are still recoverable. Precision and creativity therefore require the same deeper discipline: knowing when to converge inside one valid structure and when to reopen the space of non-equivalent structures. Keywords: large language models, structural determinacy, structural entropy, active structure, latent structure, load-bearing structure, structural equivalence, convergence frontier, stochastic decoding, creativity, output diversity, realization entropy, convergence provenance, evaluation closure, synthetic data