Constant-loss nuclear-error transfer without matrix ordering

The manuscript proves that the transfer holds with the universal constant
$C = 11$: for real positive semidefinite $A$ and $\widehat A$, any ordered
eigenbasis of $\widehat A$ used for both truncations, every continuous
operator monotone $f : [0, \infty) \to [0, \infty)$ and every
$\varepsilon \ge 0$, $\|A - \widehat A_k\|_* \le (1 + \varepsilon)\|A - A_k\|_*$
implies
$\|f(A) - f(\widehat A)_k\|_* \le (1 + 11\varepsilon)\|f(A) - f(A)_k\|_*$, with
no ordering or commutation between $A$ and $\widehat A$. The new ingredient is
a compression estimate for the functions $f_s(x) = x/(s + x)$, bounding the
trace of the positive part of $f_s(PAP) - f_s(A)$ for a rank-$k$ orthogonal
projection $P$. With eigenvalue comparisons and a resolvent identity it gives
the bound with constant $11$ for every $f_s$, uniformly in $s > 0$; the
positive integral representation of operator monotone functions then gives
the general case, including $f(0) > 0$ and zero optimal tail. Optimality of
the constant is not claimed.