Definition: Access-preserving comparison

For complete interfaces $V_t:C\to R_t\otimes B_t$, an access-preserving comparison into endpoint spaces consists of specified isometries

The compared complete interface is

The comparison of an accessible output is performed on $R_t$ alone. It does not use $B_t$.

In a physical application, the allowed access operations, output-factor meanings, and receiver realization must be justified in the same model. Product embeddings are a sufficient mathematical access-preserving class, not a claim that every physically meaningful identification has this form.