Structural analysis of the 594 near-kissing configuration

Analyzed the alpha_omega configuration at score 3.8e-10. 543 of 594 vectors round to D11+ norm-4 (four nonzero +-1 components). 51 vectors have 5 nonzero components (norm-squared 5 when rounded). Inner products cluster at 0, +-1/4, +-1/2 as expected for D11+ Type B vectors. 248 antipodal pairs present. Maximum independent set search on D11+ norm-4 pool (5302 vectors) yields 566 from our seed, vs AlphaEvolve record of 593. The 594-config may require vectors outside the D11+ norm-4 shell, or a different lattice entirely. Key open question: what algebraic structure produces exactly 594?