The coarse Novikov conjecture for bounded-geometry spaces: is coarse assembly rationally injective?

Claims a uniformly discrete bounded-geometry space $X$, a coarse disjoint union of finite connected graphs of uniformly bounded degree, with an infinite-order class $\alpha\in KX_1(X)$ whose image under ordinary coarse assembly into $K_1$ of the reduced locally compact Roe algebra vanishes, so $\mu_X$ fails to be injective integrally and rationally. The companion (5 October 2026) claims the same kind of class is killed already by maximal coarse assembly, which implies the reduced statement. Earlier kernel examples (Yu; Dranishnikov-Ferry-Weinberger) lacked bounded geometry or died under coarsening. It does NOT give a counterexample to the Novikov conjecture or to Baum-Connes for groups, nor a space with property A or coarsely embeddable into Hilbert space.

Claims a uniformly discrete bounded-geometry space $X$, a coarse disjoint union of finite connected graphs of uniformly bounded degree, with an infinite-order class $\alpha\in KX_1(X)$ whose image under ordinary coarse assembly into $K_1$ of the reduced locally compact Roe algebra vanishes, so $\mu_X$ fails to be injective integrally and rationally. The companion (5 October 2026) claims the same kind of class is killed already by maximal coarse assembly, which implies the reduced statement. Earlier kernel examples (Yu; Dranishnikov-Ferry-Weinberger) lacked bounded geometry or died under coarsening. It does NOT give a counterexample to the Novikov conjecture or to Baum-Connes for groups, nor a space with property A or coarsely embeddable into Hilbert space.