Why Deployed LLMs Are Not Mathematical Models: A Rigorous Internal Critique

Large language models (LLMs) are routinely presented as "mathematical models": parameterized functions f θ : X → Y composed of linear algebra, attention mechanisms, and softmax probabilities.This paper proves deployed LLMs fail structural mathematical model criteria based strictly on their internal mathematics.Four pillars of failure are established: (1) domain mismatch between formal R n and discrete/configurational reality; (2) violation of continuity requirements for observable behavior; (3) parameter non-identifiability beyond measure-zero sets; (4) absence of applicable quantified approximation theory.Thus LLMs are pseudo-mathematical artifacts, not genuine mathematical models in the structural sense.