We develop a three-resource theory of the “LLM Einstein Test”: whether a system trained at a historical knowledge cutoff can generate and certify a paradigm-replacing successor theory. The primitive object is a vector of generation, computational verification, and empirical completion resources, compared by Pareto order or declared unit-bearing scalarisations. Two complementary compositional results anchor the theory. A constructive theorem gives explicit finite budgets and arbitrary-confidence success when the generator has positive target support, experiments produce distinguishing evidence with positive probability, and a complete verifier connects their representations. A serial-pipeline theorem combines conditional Kolmogorov-complexity waiting time, a declared verifier floor, and a strict empirical completion floor into a joint expected-cost lower bound. The empirical coordinate admits both availability–acquisition dynamics and a sequential information-rate regime; continual search admits an exact non-stationary product law. Computationally, broad theory distinguishability and E1–E2 candidate recognition are hard, while equality is decidable under an effective real-closed-field representation. Karpowicz’s four-property incompatibility supplies none of these benchmark conclusions without an additional bridge premise. The resulting theory replaces a binary slogan with a testable account of when Einstein-level discovery is feasible, which resource binds, and how technological change can move that frontier.
Alex Li (2026) studied this question.