This preprint addresses inverse problems in the two-point fiber-collision theory of holomorphic maps. By fixing a base point and analyzing anchored slices, the work determines maps up to additive, affine, and Mobius postcompositions using connection, curvature, and projective slices. It provides explicit reconstruction formulas, characterizes determining sets, relates diagonal jets to inverse data and the Schwarzian derivative, and establishes local Lipschitz stability. The results organize partial two-point data into an additive-affine-projective hierarchy.
Mohammad Abu-Ghuwaleh (Tue,) studied this question.