On the theory and estimation of the three-phase structure seminvariant in P

By embedding the three-phase structure seminvariant T and its three symmetry-related variants in suitable quintets Q (five-phase structure invariants) one obtains the extensions Q of T to which T is related via the space-group symmetries. The neighborhoods of T are then defined in terms of the neighborhoods of its extensions. The conditional probability distribution of T, given the seven magnitudes |E| in its first neighborhood, is derived. The distribution yields a reliable estimate (0 or π) for T in the favorable case that the variance of the distribution happens to be small.