A Pre-Registered QEC Prediction: The Turning Rate of the Vorticity Direction in Turbulence

Quaternionic Eulerian Calculus (QEC) holds that the direction of vorticity cannot turn faster than the unit rotator ε morphs. Combined with the QEC square-root rule (the tensor takes the ordinary root, the angle is halved), this gives a definite, dimensionally homogeneous bound on how sharply the vorticity direction may bend in strong-vorticity regions of a Navier–Stokes flow: |∇ε| ≤ 0.5 · sqrt(|ω| / ν). The factor 1/2 (0.5) is fixed by the theory, with no adjustable constant. The bound held in five direct numerical simulations. This note records the prediction, its derivation, the evidence so far, and the exact test against high-Reynolds-number turbulence data, before that test is run.