Point cloud registration aligns observations of objects and scenes, yet repeated structures leave a correspondence-selection problem unresolved: semantic grouping can reduce matching ambiguity while removing spatial support needed to constrain rigid motion, making label accuracy an incomplete guide to registration quality. A semantic–spatial framework, SSAR, addresses this problem by linking multiscale contextual descriptors, semantic candidate groups, and soft-correspondence-based rigid estimation, with analytical conditions that relate preferential retention of true matches and the geometry of retained points to pose sensitivity. The empirical analysis draws on recorded baseline experiments using Bunny for neighborhood description, ShapeNet Part for object decomposition and alignment, and Stanford Large-Scale 3D Indoor Spaces (S3DIS) for indoor-scene structure, together with positional-encoding comparisons, feature-learning histories, and runtime measurements under controlled experimental settings. The multiscale pathway yields higher descriptor recall and decomposition scores within the reported comparisons, while the analysis shows that increasing the inlier fraction and maintaining noncollinear support are complementary requirements, linking the composition of the candidate set to the conditioning of rotation estimation. These findings provide a basis for assessing semantic decomposition through the correspondence information it preserves and for designing local registration procedures that jointly consider matching ambiguity, geometric support, and the consistency of retained structures with a common rigid transformation.