Civic statement

$\Pi_E P_{\rm adm}\Pi_E=P_{\rm adm}$ implies

$\operatorname{ran}(P_{\rm adm})\subseteq E_{47},\qquad P_{\rm adm}\preceq\Pi_E,\qquad \Pi_Ev=v\ \forall v\in\operatorname{ran}(P_{\rm adm}).$

Joint-kernel credential

$\ker(K^\dagger K+I-\Pi_E)=\ker K\cap E_{47}.$

$\mathcal E_{\rm joint}(v)=\|Kv\|^2+\|(I-\Pi_E)v\|^2.$

Machine certificate

• Carrier dimension: 125
• E47 rank: 47
• Admissibility rank: 2
• Exact lock defect: $1.0245800793612824\times10^{-15}$
• Controlled lock defect: $1.0004437600801488\times10^{-12}$
• Commutator defect: $1.0000008934068597\times10^{-12}$
• Quantum measurement completeness residual: $2.171718689467803\times10^{-15}$
• Exact postselection fidelity: 1
• Controlled state leakage: $4.557195731227404\times10^{-13}$

Constraint correction

For a general constraint operator, use $P_{\rm adm}=P_{\ker K}$. The identity $P_{\rm adm}=I-K^\dagger K$ requires $K^\dagger K=I-P_{\rm adm}$. The validation uses $K_c=I-P_{\rm adm}$.

Archive anchors

Google Drive validation proof