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Example 2 — one-entry noise: interior without symmetry
The solved family perturbs all four cross entries in common. This example perturbs a single covariance entry, (1,3), by ±τ, so the common-noise symmetry is gone, and the interior optimum survives. The paper's certificate point is τ = 0.15 with γ̂ = 9/10: F(9/10) < F(0) and F(9/10) < F(1) as exact rational inequalities. Here the whole curve is drawn live at any τ.
What to look for: at τ = 0.15 the minimizer sits near
γ = 0.9, matching the certificate. F(0) never moves as τ changes
(Lemma 1 again: the noised entry is in the cross-block), while the right end
rises with the noise.
The widget runs the recursion of the paper's equation (4) with the naive fitness (5), ported directly from the reference implementations, live in your browser. Nothing is pre-baked.