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Theorem 3 — small noise pushes the optimum off the minimum-variance end

At an exact minimum-variance endpoint the population curve is flat (V₀′(1) = 0), so any positive marginal noise sensitivity wins locally and the optimizer moves inside by order τ²: 1 − γ*(τ) ≈ (G′(1)/V₀″(1))τ². For Family A the paper computes the coefficient exactly: with e = 2τ, 1 − γ* ≈ (1025/153)e².

Dots: minimizers of the exact F found by search, plotted as 1 − γ* against e². Line: slope 1025/153 from the theorem.
What to look for: the dots approach the line as e ↓ 0. The theorem is a small-noise statement, and the curvature away from the line at larger e is the O(e⁴) term.

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.