The System Asset Pricing Model (SAPM) measures Bitcoin's welfare cost across six channels. The headline ratio: 210 billion in annual welfare costs divided by 42 billion in industry revenue equals 5.0. The marginal PSF beta also equals 5.0, but from a different calculation: frontier shortfall 75B divided by excess industry revenue 30B, times 2, times curvature κ = 1/12.
Four measurement failures explain the omission: market-cap denominator normalizes the catastrophe; energy-only floor leaves custody, security, and centralization qualitative; channel isolation keeps environmental, security, and custody estimates separate; missing counterfactual compares against a crypto-free utopia instead of a well-regulated digital payment system.
The system welfare function has four pillars: environment (165B/year), decentralization (proxy via deterrence loss), security (fee-transition risk), and custody (45B/year). Each pillar is monetized using peer-reviewed estimates. The cooperative baseline WC = 15B; current welfare W = −60B; frontier shortfall ΔWF = $75B.
Channel-level system betas: energy 3.1 (declining), mining centralization 0.8, security budget erosion 0.31, custodial recentralization 1.2, speculation vs. utility (not weighted), MEV extraction 3.5. Weighted channel diagnostic βdiag = 1.87. The marginal aggregate βW = 5.0 is derived from the frontier gap, not from summing channels.
1 proves a protocol-level floor: any permissionless blockchain satisfying Permissionless Access, Transaction Irreversibility, and User Sovereignty cannot reduce system beta below approximately 1.0. The floor is derived from two independent paths: information theory (Shannon noisy-channel coding theorem applied to 256-bit keys) and mechanism design (Myerson-Satterthwaite impossibility of simultaneously satisfying BIC, IR, BB, and permissionless entry).
The Protocol Welfare Floor is not a physical law. MiCA and the GENIUS Act are the first large-scale custodial regulations consistent with the Sovereign Necessity Corollary. They change the game around the chain rather than inside it. The 1,000× gap between the permissionless floor (βW ≈ 1.0) and regulated finance (βW ≈ 0.001) is what these regulations must close.
The (p, s, d) = (+, −, −) diagnostic places Bitcoin in the immediate-intervention quadrant. Classification remains Fast Hollow Win across all 25 cells of the cooperative-baseline–shadow-price grid and across 10,000 Monte Carlo simulations. Under the maximalist steelman (ΠC = $33B), βW remains > 1.0.
Cross-domain comparison: Bitcoin βW = 5.0; VW diesel emissions scandal βW ≈ 2.1; ERCOT electricity market manipulation βW ≈ 1.8. Bitcoin extracts welfare more efficiently than these benchmarks but still falls in the overextraction zone. System efficiency ratio: average 𝒮 = 0.40, marginal 𝒮 m = 0.20, identifying a concave PSF.
The shadow price duality derives the efficient price of system welfare endogenously from the PSF geometry. The institutional designer's problem reduces to selecting μ, which determines where on the PSF the regulated outcome falls. Channel-level μ ordering identifies which constraint to relax first: custody regulation (MiCA/GENIUS) is the highest-use intervention.
The SAPM makes the invisible visible. The paper's strongest empirical claim is classification robustness, not point identification. The Fast Hollow Win classification is unchanged under conservative assumptions. The Protocol Welfare Floor proves that protocol design alone cannot fix the welfare problem; sovereign institutional redesign can. The Bitcoin paper belongs in the Intractability class, not the Impossibility class.