A complete finite-shot certificate

Hoeffding's inequality is a statistical input, not a physical acquisition theorem Hoeffding. The test bank has $d^4-1$ settings. Its size and the dimension factor in (eq:confidence) are generally exponential in $n$. This is a finite certificate, not a polynomial-in-$n$ verification algorithm.

No target inverse $U^{†}$ is needed as a physical gate for this Pauli-tomography procedure. However, the target matrix or certified target expectations must actually be available. A target-dependent oracle's bare existence does not provide them efficiently.