# dissimilarity → Gram operator D ∈ ℝ^n×n, B = −½·J·D∘D·J # the obstruction lives in the spectrum spec(B) = { λ₁ ≥ … ≥ λ_n } defect = Σλ⁻ / Σ|λ| residual = 1 − Σ_i≤dλ_i⁺ / Σλ⁺ stress = med |‖xᵢ−xⱼ‖ − Dᵢⱼ| / Dᵢⱼ # certificate iff within budget, d ≤ 3 χ ⇔ defect≤τ₁ ∧ residual≤τ₂ ∧ stress≤τ₃