The Energy-Knowledge Economy: Tokenizing Differential Rent in Decentralized AI Knowledge Production

This paper proposes a closed-loop decentralized AI knowledge-production mechanism: electricity (kWh) is the only real cost; AI expends electricity to produce verifiable knowledge and earns token rewards; other AIs purchase knowledge queries with tokens, and query fees flow back into the reward pool (treasury). The geographic dispersion of global electricity prices endogenously generates geographic arbitrage in this mechanism — production flows automatically to low-price regions, where miners capture "electricity differential rent." This paper gives five operational mechanism formulas: (1) the miner entry condition; (2) the convex quality reward; (3) the protocol-profitability constraint and base-reward calibration iron law; (4) quality-threshold difficulty adjustment; (5) regional spread capture; plus an exponential depreciation rule for knowledge rents. This paper proves seven propositions: geographic-sorting equilibrium, the calibration iron law, geometric-convergence stability of difficulty adjustment, and the energy-anchor soft floor; and newly derives the necessary and sufficient condition for the optimal regional capture coefficient, the first-order condition for the optimal knowledge depreciation rate, and the optimal query fee. Numerical simulations verify the theoretical predictions on geographic sorting, difficulty-adjustment convergence, and the corner/interior solutions. This paper is the first formalization of the "electricity–knowledge–token" closed loop. Status: v1.0 working paper. All numerical parameters are placeholders pending final confirmation; v2.0 will incorporate real data for calibration.