A diamond allowance is not a Holevo value

This is an actual conversion from a specified channel allowance to a one-use information allowance. Merely quoting a diamond budget would not perform that conversion. The general entropy-continuity framework is due to Fannes-type inequalities and their sharp refinements Audenaert.

The proposition does not by itself yield a uniform all-block-length capacity comparison. A telescoping estimate for $n$ uses has allowance at most $n\delta$, capped at one. It cannot silently be treated as the same fixed allowance for every block length.