The Optimal Regulation of Machine-Capital: Spectral Externalities and the Limits of Certification

When firms and investors rely on the same artificial reasoning tools, they think alike, and markets increasingly move together. That coupling is a systemic risk no adopter pays for, so the market over-adopts near a fragility edge where the social cost explodes. The fix is a tax tied to a well-measured index of that coupling, its spectral radius, because the risky basket cannot be measured reliably enough to regulate. The twist: the check that licenses intervention is most permissive when danger is greatest, so passing it is necessary but not sufficient. Near the edge a precautionary cap beats a price, and an externally enforced rule beats discretion. The paper pins down the direction and shape, not the level, and its data section illustrates rather than tests the mechanism.