Fundamental Limits Are Not Practical Frontiers: A Layered Theory of Limits for Modern Transformer and Agentic AI Systems

Abstract—Classical results from set theory, computability,complexity, information theory, and algorithmic informationtheory establish genuine constraints on digital artificial intelligencesystems. Cantor’s diagonal arguments distinguish countabledescriptions from uncountable function spaces; Turing-style undecidability rules out universal decision procedures for importantclasses of problems; computational complexity separates merecomputability from resource-bounded feasibility; Shannon entropybounds lossless source coding and, under probabilistic log-lossformulations, predictive uncertainty; and Solomonoff inductionand AIXI provide universal ideals whose exact forms are notcomputable. These facts are sometimes used to infer practicalceilings for contemporary large language models (LLMs) oragentic systems. This paper argues that such an inference isinvalid without an additional bridge from the universal result toa specified architecture, resource model, task distribution, andloss. We introduce a seven-layer taxonomy separating cardinality,computability, computational complexity, information, learnability,architectural expressivity, and resource-bounded system capability.We then give three non-implication results showing why universalimpossibility theorems do not, by themselves, yield non-trivialupper bounds on finite-distribution performance, useful selfanalysis, or finite-domain distance to an incomputable ideal.Modern Transformer theory reinforces this distinction: chainof-thought can increase effective computational expressivity andsample efficiency; decoder-only and constant-bit-size Transformermodels can be Turing complete under explicit assumptions;and fixed-precision analyses establish different, model-specificlimitations. The central claim is not that fundamental limits areobsolete, but that they define formal constraints while practicalcapability frontiers can continue to move substantially insidethem.Index Terms artificial intelligence, large language models,Transformers, computability, undecidability, chain-of-thought,AIXI, Solomonoff induction, information theory, agentic AI