E1 SOFTWARE VERIFICATION · NUMPY-ONLY

Executable reconstruction of the spin-2 tensor-cube Casimir, the 47-dimensional invariant kernel, the spectral projector, and the minimax contraction to the projector.

Canonical object

• Ambient carrier: V = V₂^{⊗3}, dim V = 125
• Kernel selector: K = (C - 6I)(C - 30I)
• Invariant subspace: E₄₇ = ker K, dim E₄₇ = 47
• Contraction: Γ = I - K² / 99144
• Off-kernel spectral radius: ρ = 15/17
• Finite execution: Γ^252 compared directly with the eigenspace projector P

Verified execution

• Casimir spectrum: {0, 2, 6, 12, 20, 30, 42}
• Multiplicities: {1, 9, 25, 28, 27, 22, 13}
• rank(K) = 78
• nullity(K) = 47
• tr(P) ≈ 47
• K² spectrum: {0, 11664, 12544, 19600, 32400, 186624}
• ||Γ^252 - P||₂ ≈ 2.367153995007914e-14
• maximum entry error ≈ 2.0038679292982884e-14
• random-state residual ratio ≈ 1.3173480345660011e-14
• theoretical worst-case bound (15/17)^252 ≈ 2.0038679292982893e-14