Voevodsky's motives and zeroth slice of motivic sphere

Let S be a noetherian scheme of finite Krull dimension and let R be a commutative ring in which every positive residue characteristic of S is invertible. We prove that Voevodsky's stable Nisnevich category of motives with R-coefficients is canonically equivalent to modules over the zeroth slice of the motivic sphere with derived R-coefficients. The comparison identifies the corresponding commutative coefficient algebras and is compatible with arbitrary pullback. The theorem applies to singular and nonreduced schemes, including mixed-characteristic bases, and requires no excellence or finite-type hypothesis. Its special cases include rational coefficients over arbitrary bases, arbitrary coefficients over Q-schemes, and Z[1/p]-algebra coefficients over Z₍ₚ₎-schemes. The proof establishes base change for finite-cycle spectra using permutation quotients, families of cycles, and arithmetic power homotopies, then passes to general bases by universal homeomorphism invariance and continuity.