UCM 48 — The Correct Gullstrand-Painlevé Form of the Kerr Metric and the Ricci Tensor for Rotating Substrate Flows

Paper 12 (Part K) of the UCM preprint series derived the Kerr metric from the Doran substrate flow using a Gullstrand-Painlevé line element with flat spatial slices (gᵣr = 1, gᵣₚhi = 0). We show by explicit coordinate transformation from Boyer-Lindquist that the correct Doran metric has gᵣr = Sigma / (r² + a²) and a non-vanishing cross-term gᵣₚhi. The corrected metric satisfies Rₘuₙu = 0 exactly by coordinate invariance, closing Open Problem 3 of Part K. Theorem 6. 1 of Part K (consistency with the Einstein field equations) is promoted from conditional to unconditional. All other Part K results — frame-dragging, Lense-Thirring precession, Carter-Robinson uniqueness, Klainerman-Szeftel stability — remain valid.