We prove lower bounds for $k$-OV, $k$-XOR, and $k$-SUM in nonuniform AC$^0$, tracking how the circuit-size exponent scales with $k$ and using no running-time hypothesis. Our framework gives depth-zero projections from colored subgraph isomorphism to the three targets at dimension, row count, or bit width $O(k\log n)$, without increasing depth or size, and preserving gate orientation. For every fixed depth and every sufficiently large fixed $k$, we obtain unconditional bounds $n^{\Omega(k)}$ for $k$-OV and $(n/k)^{\Omega(k)}$ for $k$-XOR and $k$-SUM, with an absolute exponent-rate constant independent of both $k$ and the depth, while the onset threshold may depend on $(d,k)$. For growing $k = n^{o(1)}$, we obtain, for every fixed depth $d$, the unconditional floor $n^{\Omega_d(\min\{\sqrt{k},\log n\})}$. This strengthens to $n^{\Omega(k)}$ at depth two for both top-gate orientations, i.e., top conjunction and top disjunction. Assuming a pattern-uniform strengthening of the Li--Razborov--Rossman source lower bound, the same projections complete the subpolynomial frontier with $n^{\Omega_d(k)}$ at depth three for both orientations and for every fixed depth $d \geq 4$. All direct $k$-XOR bounds stated above concern odd $k$; a black-box odd-to-even lift transfers any such lower bound through a supplied admissible parameter decomposition. The $k$-SUM projection works for both parities. At the bit width $m = \Theta(k\log(en/k))$ used by our projection, a block-carry $\Sigma_3$ upper bound of size $(n/k)^{O(k)}$ matches the fixed-$k$ specialization of the top-disjunction depth-three lower bound $(n/k)^{\Omega(k)}$ up to constants in the exponent. The remaining upper-versus-lower-bound gaps concern depth two, top-conjunction depth three, and other width regimes.