2.1 Coherent certificate
Under the common non-collapsing carrier, asset-specific synchronous slack, coherent joint-law, marginal, and integrability premises, every normalized long-only portfolio satisfies
\[ V_{\mathrm{sys}}(q) \leq \sum _i q_i v_i-\mathcal C(q). \]
The result is a conditional upper bound on systematic variance, not a covariance point estimate or an empirical coverage statement.
Proof
The carrier-and-slack restriction supplies pairwise W2 floors. Applying each floor to the coordinate pairs of one coherent joint law and summing with the portfolio weights deducts \(\mathcal C(q)\) from the weighted marginal term.