Definition: Two legitimate growing-code comparisons

A growing-code study may use either:

1. Fixed-subcode convergence. For each fixed finite code $C^{(k)}$, supply embeddings $J_{n,k}:C^{(k)}\to C_n$ and compare $V_n{J}_{n,k}$ on that fixed domain, with compatible output identifications.

2. Whole-code certificates. For each $n$, test the target ${\mathrm{id}}_{C_n}$ separately, reporting its own complete proxy allowance $b_n$ and Choi discrepancy $e_n$.

Neither convention silently equates different identity channels.