Certified Lehmann–Maehly Lower Bounds for the One-Cube SU(3) Lattice Gauge Hamiltonian

We sharpen the certified vacuum and neutral-gap bounds for the open one-cube SU(3) lattice gauge Hamiltonian at β = 1/2. The resulting enclosures are E0 ∈ [17.38264, 17.384394897] and E1 − E0 ∈ [4.725705103, 4.91069531]. They follow from the classical Lehmann–Maehly method applied to the complete electric window T < 18, using the exact full Wilson-output Gram matrix already available in G1D. The vacuum interval is approximately 39.61 times narrower than the previous enclosure. A separate verifier reconstructs the sector moment matrices in rational arithmetic and certifies inertia by rational congruences and 256-bit interval diagonal-dominance tests. All eight lower-bound claims, including a refinement using the pole 24.124, pass. The required spectral counts and inherited Ritz upper witnesses are also checked again. The order of the irreducible components inside the first cluster, a volume-uniform gap, and a continuum limit remain outside the conclusions.