← All demos paper (PDF) · exact certificates
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. Dots off the parabola,
or a crossing elsewhere, would refute the formula.
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.