<aside>
▶️
ENGAGE THE LAB
Open SPECTRA — Algebraic Visualization Lab
</aside>
Purpose
SPECTRA is the City’s interactive spectral-algebra interface. It exposes the operator chain from generators to spectrum, invariant kernel, projector, and contraction.
$$
V_2^{\otimes 3}\rightarrow C=J_{\rm tot}^2\rightarrow K=(C-6I)(C-30I)\rightarrow E_{47}=\ker K\rightarrow P_{47}
$$
Machine-validated E47 route
- Carrier dimension: 125.
- Derived kernel: $\dim E_{47}=47$; complement/rank $K=78$.
- $\Omega_c=47/125=0.376$.
- $\Delta_{K^2}=11664$, $\Lambda_{\max}=186624$, $\kappa=16$.
- Optimal discrete contraction: $\epsilon_=1/99144$, $\rho_=15/17$.
- Operator limit: $\Gamma^n\to P_{47}$ with $\Gamma=I-\epsilon_*K^2$.
Evidence bundle
City connections