C_u^*(X) can be a hereditary corner of C_u^*(Y) with no coarse embedding X→Y; sparse compact-ghost targets restore injective coarse embeddability.
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On the embedding rigidity problem for uniformly locally finite coarse spaces
C_u^*(X) can be a hereditary corner of C_u^*(Y) with no coarse embedding X→Y; sparse compact-ghost targets restore injective coarse embeddability.