$F(t)=e^{-tK^2}$ acts as the identity on $E_{47}$ and damps $E_{47}^{\perp}$.
$PF(t)=F(t)P=P,\qquad \lim_{t\to\infty}F(t)=P.$
Machine results: kernel preservation error $1.04\times10^{-15}$; complement ratio $0.0623811$ at the executed filter time.
This citizen links the spectral contraction certificate to the quantum filter route without promoting hardware or arbitrary-channel claims.