Hierarchical self-inventing operators: economic market dynamics for autonomous reasoning

AbstractWe formalize autonomous reasoning systems that construct hierarchical operator algebras through economic market dynamics. A super-task framework requires: (1) solvingprogressively complex tasks, (2) maintaining polynomial operator growth, (3) ensuring verifiable correctness. We introduce an economic model where operators earn income fromutility and pay Levin complexity rent, augmented with venture capital grace periods andparent-child subsidization. Stratified frontier exploration ensures non-vanishing learningsignals via REINFORCE gradients. We prove market equilibrium existence, polynomialgrowth bounds, and type-theoretic soundness. Experiments on ARC-AGI show 67% solverates (+29pp over baseline) with emergent 4-level hierarchies. Theorem proving demonstrates 69% success (+18pp) with invented induction operators. Five open problems guide future research.