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: v1.1 working paper. v1.1 is an epistemic-status revision of v1.0: no proposition was added or removed; every claim is now stated exactly as proved, every load-bearing assumption is explicit, and all numerical parameters remain placeholders. v2.0 will incorporate real data for calibration. 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: v1.1 working paper. v1.1 is an epistemic-status revision of v1.0: no proposition was added or removed; every claim is now stated exactly as proved, every load-bearing assumption is explicit, and all numerical parameters remain placeholders. v2.0 will incorporate real data for calibration. Status: v1.2 working paper. v1.2 (2026-09-25): five-point revision — (1) corrected the 'electricity is the only real cost' phrasing (electricity is the core variable cost; hardware/network/land/cooling/operations/capital costs folded into c_ops); (2) Proposition 7(iii) restated as a testable cold-start hypothesis; (3) all references re-verified against originals, two misattributed entries corrected; (4) explicit author line added; (5) full primary-energy → kWh → AI compute → knowledge → TOKEN → query payments → pool reflux chain written into the introduction. No proposition added or removed; all numerical parameters remain placeholders.