arXiv 2606.15078 models cognitive debt via two state variables and multiplicative production function

The model tracks per-agent cognitive capital and cognitive debt under a production technology where capital serves as collateral for AI returns. Six propositions establish that rational agents accept positive debt because costs are deferred and masked by short-term output gains. Tranquil conditions reduce perceived risk, increase substitution intensity, and compound aggregate leverage until a cognitive Minsky moment occurs.

Expected losses are convex in leverage. Post-shock output pressure triggers a false-correction loop in which agents apply more AI to AI failures. Decentralized equilibrium over-adopts substitutive AI relative to social optimum due to unpriced systemic risk and cognitive public-good externalities. High-capital agents erode their unaided capabilities fastest, inverting initial skill rankings.

Related empirical patterns appear in longitudinal studies of automation and skill retention. Autor et al. (2015) documented task displacement without complementary skill formation; recent LLM usage logs show substitution rates above 60 percent on analytical workflows within twelve months of deployment. These observations align with the paper's prediction that subjective risk assessments decline while true fragility rises.

Operational implication is that monitoring aggregate cognitive debt requires direct measurement of unaided reasoning performance rather than output metrics alone. Regulators and firms lack instruments to observe the state variable in real time.