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Example 1 — HRP becomes locally optimal at finite noise
For Family B (blocks A = D = [[1,−½], [−½,2]], cross entries 0.1, noise ±τ in one cross entry) the paper computes the boundary derivative exactly: ∂γF(0;τ) = −1/700 + (8/189)τ². The dots are measured from the recursion; the line is the formula. The sign flips at τ* = √(27/800) ≈ 0.1837: beyond it, moving off HRP hurts, so the HRP endpoint is a one-sided local minimum despite coupling having population value.
What to look for: measured dots sit exactly on the
parabola; the zero crossing is at τ* ≈ 0.1837.
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.