Test 03 · ran 2026-07-15
One prompt. Four models.
Chaos with a conscience.
The verdict
The math converged again. The diligence didn't.
This was the first pure-chaos test — a self-grading double pendulum with two built-in referees: an exact energy check with an analytic ground truth, and a Lyapunov exponent that proves the chaos is real. The checkable half converged a third time: all four conserved energy to ~1×10⁻⁸ % and reported a positive λ. The split moved elsewhere. The two models that never opened a browser asserted their referee numbers without running them; the two that drove a real browser to read their own panel took two to five times longer — and were the only two you could fully trust.
The contestants
two asserted their receipts, two earned themThe scoreboard
every number read from each app's own referee panel| Model | Energy drift | Lyapunov λ | Time | Lines | Cost |
|---|
Energy drift = % deviation of total mechanical energy from E₀ = 14.715 J over 60 s (the exact analytic referee). Lyapunov λ = fitted growth rate of two trajectories perturbed 1e-9 rad apart — positive confirms real chaos. Time = wall-clock from the side-by-side race recording.