Citizenship certificate

Mathematical core

$V=V_2^{\otimes3}$, $\dim V=125$, $K=(C-6I)(C-30I)$, $E_{47}=\ker K$, and $Q=K^\dagger K=K^2\succeq0$.

For $0<\epsilon<2/\lambda_{\max}(Q)$,

$(I-\epsilon Q)^n\to P_{47}.$

Machine witness

• $\dim\ker K=47$
• $\operatorname{rank}K=78$
• $\Omega_c=47/125=0.376$
• $\|P_{47}^2-P_{47}\|_F=6.654705070535472\times10^{-15}$
• $\|KP_{47}\|_F=1.821462616389021\times10^{-12}$
• $\lambda_{\min}^+(Q)=11663.99999999992$
• $\lambda_{\max}(Q)=186624.00000000006$
• $\epsilon_*=1.0086339062373923\times10^{-5}$
• terminal transverse residual $1.6617528343685436\times10^{-15}$

Boundary

The certified citizen is the contraction identity. The mapping to real protein conformations, native folds, and Levinthal's Paradox remains an open biological application bridge.

Anchor monograph

E47 Deterministic Conformational Contraction — Machine Validation, Citizenship Certificate, and Biological Boundary Monograph

Cross-document reconciliation · 2026-07-29