CRR derives the scalar property from first principles: CV = 1/(4π) ≈ 7.96% for any continuous timing process, regardless of speed. This experiment tests that prediction across four tempi and two task types.
1. Breathing (2 min): Press A = inhale, D = exhale. A biological SO(2) reference.
2–5. Sweep at 250ms, 400ms, 550ms, 750ms: Side-to-side across the midline.
6–9. Circles at 250ms, 400ms, 550ms, 750ms: One revolution per beat. ~11 min total.
The CRR prediction: CV = Ω/2 = 1/(4π) ≈ 7.96% at every tempo, for every continuous emergent timing task. This value is derived from the Cramér-Rao bound on the SO(2) statistical manifold — it's geometry, not a fitted parameter. If CV is constant across a 3× range of speeds, the scalar property is derived, not assumed.
CRR predicts a flat line at 7.96%. Classical timing predicts CV varying with speed.