Raw Coxeter kernels before Y-relations: rational stability in type A and a new relative sector in type D

For the symmetric and demihyperoctahedral families we study the rawfull-reflection Coxeter cover: the Coxeter group Ŵ_raw generated by allreflections of W subject only to the pairwise product orders, with kernelK_raw = ker(Ŵ_raw → W). This is the group before the Y- and fork-relations ofRowen–Teicher–Vishne and Amram–Shwartz–Teicher are imposed. We determine the rational first homology in both classical families. For type A we prove H^1(K_raw(A_(n−1)); Q) ≅ t_n · U_(n−1) for n ≥ 5, wheret_n = C(n,2) − n + 1 is the cycle rank of the complete graph and U_(n−1) thestandard module. The module shape coincides with the abelianisationZ^(t_n(n−1)) of the Y-quotient kernel computed by Rowen–Teicher–Vishne, and weclaim no novelty for that target. What is new is the stability statement: forevery n ≥ 5 the surjection K_raw ↠ K_Y induces an isomorphism on rational H₁,and integrally its kernel is exactly the torsion subgroup, so the Y-relationskill precisely the torsion. The invariant factors are (Z/2)^(t_n−1) forn = 5, 6, 7 by exact Smith reduction. For type D we prove H^1(K_raw(D_n); Q) ≅ t_n · U_(n−1) ⊕ n(n−2) · V_n for n ≥ 5,with V_n the reflection module. Both multiplicities are graph-theoretic ranks:t_n is the cycle rank of K_n, and n(n−2) is the rank of the flow space of thedoubled signed complete graph, which is unbalanced, so that|E| − |V| + b = n(n−1) − n + 0 = n(n−2). The summand n(n−2) V_n, with thismultiplicity, is specific to the raw cover, and we identify it canonically withthe relative residual of the sign-forgetting map K_raw(D_n) → K_raw(A_(n−1)). All statements are theorems with complete proofs; the base case n = 5 and theintegral torsion computations are computer-assisted, by exact integer Smithreduction with unit pivots, and are reproducible from the supplementary scripts.