We introduce obligation density (OD) as a general diagnostic for systemic fragility. Modern risk analysis focuses on the level of obligations — debt, liabilities, guarantees — but ignores their concentration relative to the survivable capacity of the system carrying them. We define Ω(t) as the ratio of total claims M(t) to effective capacity C(t)·S(t), where S(t) synthesises interest efficiency, fiscal alignment, and maturity structure into a survivability index. The fragility gradient F(t) = d/dt ln Ω(t) decomposes into claim-growth and capacity-growth rates; instability emerges when claim-growth exceeds capacity-growth in sustained form and Ω approaches a system-specific threshold. A key theorem establishes that modern accounting systematically underestimates OD because true claims exceed recorded claims: contingent, derivative, and legal obligations accumulate off balance sheets. The under-measurement is not an accounting failure correctable by improved instruments; it is the macro-financial manifestation of a deeper constitutional structure formalised in the companion Foundation Paper. We apply the framework to the United States sovereign (2010–2025), constructing a proxy index from public data, and find structural deterioration over the period.