Canonical identity

$V_1^{\otimes3}\cong V_0\oplus3V_1\oplus2V_2\oplus V_3$

$K_{10}=C-6I,\qquad E_{10}=\ker(C-6I)=2V_2$

$\dim E_{10}=10,\qquad \Omega_{10/27}=\dfrac{10}{27}$

Evidence class

E0 exact Clebsch–Gordan and kernel identity; E1 QuTiP finite-dimensional simulation record.

Civic role

A distinct lower-dimensional sibling of $E_{47}$, demonstrating that the kernel-selection architecture is a family rather than a singleton.

Transit credential

Representation District → Casimir Junction → Blue Verification Line → Quantum Borough.

Boundary

The supplied code establishes finite-dimensional projection behavior. Hardware realization remains open.