# Steady-cloak calibration

The steady-flow sweep used rear counter-rotation \(\alpha_U=-A\), \(\alpha_L=A\), \(A=0,\ldots,6\), with the front cylinder stationary. The maximum legacy DTW similarity occurred at \(A=5\), with similarity 0.9872. The current Kármán joint law produced similarity 0.9665 when deployed without an upstream disturbance.

In the steady deployment, the rear lift feedback nearly cancels between the reflected upper/lower states. The rear action therefore equals the fitted constant to numerical precision: the last-cycle mean is \((-3.4306,3.4318)\), compared with the analytical constant magnitude 3.4312. This is 68.6% of the sweep optimum (5.0) in action magnitude, yet it recovers most of the achievable downstream sensor similarity.

This supports a limited but quantitative interpretation: the Kármán law contains a persistent rear-counter-rotation component of the same order as the steady open-loop rotation required to restore the downstream sensor signature. It does not establish a one-to-one conversion between velocity deficit and cylinder surface speed; that conversion is nonlinear and geometry-dependent. The correct claim is therefore an order-of-magnitude and closed-loop correspondence, not a direct momentum-balance equality.

The prior expectation of approximately 4 U0 lies between the fitted constant 3.43 U0 and the discrete sweep optimum 5 U0. A finer sweep around 4–5 U0 would be needed to locate the continuous optimum, but is not required for the present mechanism conclusion.
