Certified Spectral Multiplets of an SU(3) Lattice Gauge Hamiltonian on a Single Cube

We give a computer-assisted proof that the first twelve excitations of the neutral SU(3) lattice gauge Hamiltonian on a single cube form two isolated six-dimensional spectral subspaces. Their representations under spatial symmetry and charge conjugation are A+ ⊕ E+ ⊕ T + and A− ⊕ E− ⊕ T − . Complete electric- 1g g 1u 1u u 1g energy windows, rational Ritz bounds, and full Wilson-output Gram matrices yield certified eigenvalue counts for the untruncated operator. The main theorems use interior thresholds with larger comparison-form margins and give separations of at least 0.78482728 between the clusters and 0.72784037 above the second cluster. A separate refinement improves these values to 0.89782728 and 0.85184037. The neutral gap lies in [4.415605103, 4.978456040]. All multiplicities are retained, and selected matrix entries are audited with an independent Haar-integration algorithm. No ordering of the irreducible components within either cluster, volume-uniform gap, or continuum limit is asserted.