A.19:5.2.1.2 - Embedding and lossy mapping

An embedding iota : CS_1 -> CS_2 is point-injective and preserves every structure named by its declaration. It gives an injective slot correspondence and an injective value map for each corresponding slot. Identity maps and exact, reversible unit conversions can support an embedding when they preserve the declared Scale meaning. The declaration states its domain, image, preserved structures, and any A.19.UNM instances used.

A coarse-graining, binning, many-to-one normalization, or dropped-coordinate operation is not an embedding. Declare it as a lossy mapping or projection, state the preserved and lost distinctions, and let each consumer decide whether that loss is admissible for its comparison, prediction, gate, or assurance use. When the use relates two exact F.17 local senses and the F.9 predicate obtains, cite that Bridge and a separate bounded-use claim. A ReferencePlane change instead cites its applicable plane relation. The coordinate mapping, semantic relation, plane relation, and C.16 calibration or measurement backing remain separate.