Complete-channel evolution limits are a separate interface

If a later construction also claims a continuous-time channel evolution, it must first construct:

1. a refinement family and its scale or tick prescription;

2. complete channels ${\mathcal{C}}_n(t)$;

3. encoders ${\mathcal{E}}_n$ and decoders ${\mathcal{D}}_n$ on common identified interfaces;

4. a limiting family ${\mathcal{T}}_t$, with its asserted composition law and continuity;

5. the claimed convergence theorem.

For example, one possible complete-channel criterion is

Retained quantum systems, classical histories, and untouched references must be included in the actual comparison interfaces CheungXIXC (def:limit).

The parameter $t$, the channels, and their composition are not present in the frozen datum merely because its experiments have integer identifiers.

XIX-C gives two distinct refinement families sharing a coarse complete channel and a one-site support ceiling but converging to different semigroups CheungXIXC (prop:two-limits). Those families choose different missing refinement data; they do not satisfy an unstated consistency condition with the coarse tick. The result is a failure of inference from the coarse data, not a universal prohibition of unique limits with additional data.

Finite sampling can likewise leave interpolation ambiguity CheungXIXC (prop:interpolation). A uniqueness claim needs a specific theorem under specific extra conditions. Naming “projective consistency” or “interpolation” does not prove uniqueness.