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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. Dots approaching a different slope as e ↓ 0 would refute the coefficient.

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 precomputed.