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Demonstrates a thermodynamic basis for risk premium in natural-capital valuation, indicating new financial insights.
Paper supported by machine-verified Lean 4. The Symbiotic Risk-Premium Theorem (SRPT) gives the first thermodynamic derivation of a risk premium, where classical finance imports the price of risk as an exogenous constant. Its results: (i) a thermodynamic-uncertainty-relation floor on the premium (no riskless natural-capital asset at finite dissipation); (ii) mutualistic-in-risk if and only if covariance is negative; (iii) the Diversification Wall — a strictly positive, undiversifiable residual risk set by shared entropy production, with no classical-finance precedent; (iv) a contagion/mutualism sign transition at zero covariance; and (v) hedging efficiency equal to cos²Θ. SRPT closes the risk / second-moment layer of the D-Capital valuation stack. This version (1.0.0) deposits the clean analytic core (9 machine-verified theorems). Part of the S1 D-Capital Valuation series; derived from the Viridis Intelligence-Bound canon, concept DOI 10.5281/zenodo.19317982.
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Hart et al. (2026) studied this question.
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