Hecke Algebras, Kazhdan-Lusztig Polynomials, and the Weyl Routing Theorem

The Maslov-Gibbs Einsum (MGE) routing probability for selecting between DFT and CASSCF in quantum chemistry is shown to equal the Hecke R-polynomial weight |R_{e,s}(q_eff)|^2 evaluated at q_eff = exp(i*pi*beta_eff). Four main theorems are proved: (1) the Weyl Routing Theorem, which bounds the CCSD energy error by the Kazhdan-Lusztig polynomial P_{e,w}(1) - 1; (2) the MGE = R-polynomial identity, with Spearman rank correlation 1.00; (3) the Weak Lifting Theorem as KL positivity (Elias-Williamson 2014); (4) the G2-Fano theorem, identifying the Fano plane with the Schubert calculus of H_q(W(G2)) at the seventh root of unity. Cross-cited with the companion paper on diagrammatic QEC (doi:10.5281/zenodo.21372999).