Krishna's affine zero-cycle divisibility and kernel input

Assume the Axiom of Choice and the fixed universe bounds of the affine perfect comparison. Let $k$ be algebraically closed and let $X$ be a reduced, pure-dimensional affine $k$-scheme of finite type and dimension $3$. For the Levine–Weibel zero-cycle group and actual residue-class cycle map ${\mathrm{cyc}}_X:{\mathrm{CH}}_0^{LW}(X)\to K_0(X)$ imported from Krishna’s Section 2.1 and transported to perfect $K_0$ by the affine comparison, multiplication by every positive integer is bijective on ${\mathrm{CH}}_0^{LW}(X)$, and every element of $\ker ({\mathrm{cyc}}_X)$ is killed by $2$.

This is the $d=3$ instance of Krishna's Theorems 1.3 and 1.4. Section 2.1 defines the source group using closed smooth points on top-dimensional components and its cycle map by their residue-sheaf classes. For this reduced pure-dimensional affine $X$, its displayed source definition is the presentation of Levine–Weibel zero cycles. Apply Affine perfect K zero and bundle K zero to its commutative coordinate algebra: the isomorphism to the actual perfect $K_0$ sends the source residue Euler class to the same perfect residue-sheaf class, so it preserves the kernel and the stated annihilation bound. Krishna’s own §2.1, equation (2.2), supplies the quotient map for this reduced scope; no extension from the separate normal-only import is inferred. The cited theorems are imported established inputs; no local reconstruction of their proofs is asserted.