The CSI_F conjecture on canonical forms of CSI spacetimes

Let a spacetime have a Riemann tensor $R$ and all of its covariant derivatives. A null frame is a frame adapted to the Lorentzian structure, and the boost order and boost weight refer to the associated boost-weight decomposition. A spacetime is CSI when all scalar polynomial curvature invariants are constant. CSI_F conjecture. A spacetime is CSI if and only if there exists a null frame in which the Riemann tensor and its derivatives can be brought into one of the following forms: either the Riemann tensor and its derivatives are constant, in which case the spacetime is locally homogeneous, or the Riemann tensor and its derivatives have boost order zero with constant boost-weight-zero components at each order. The latter implies that the Riemann tensor is of type II or less. The if direction is stated to be trivial, whereas the only-if direction would require considering second-order curvature invariants; the corresponding statement for $CSI_1$ requires including all 1-curvature-homogeneous spacetimes.