Where a limiting argument stops

Suppose a sequence of transport protocols has convergent endpoints and vanishing implementation allowances, but its only synthesis information is $s_j\le 1/4$. Then the assembly theorem gives at most

It does not give convergence to zero. A vanishing-error result would require an independently proved $s_j\to 0$, or another stated correction mechanism, together with a resource and error theorem for that mechanism.

A fixed positive allowance also cannot prove exact non-signalling: mix a no-signalling channel with a signalling channel with a small positive weight. The resulting channel is close to the former while retaining nonzero influence. Approximate complete-channel correctness and exact causal containment remain different acceptance clauses.