We prove a multilevel non-shadow refinement of the Alon--Babai--Suzuki (ABS) nonuniform restricted-intersection theorem. Let $K=\{ k_1,\dots,k_r\}$ and let $L$ be a set with $|L|=s$. If $\mathcal{ F}\subseteq \bigcup_{ k\in K}\binom{ [n]}{ k}$ is $L$-intersecting and $k_i>s-r$ for every $i$, then $|\mathcal{ F}| + \sum_{ j=s-r+1}^{ s} |\mathcal{ N}_j(\mathcal{ F})| \le N(n,s,r),$ equivalently $|\mathcal{ F}| \le \sum_{ j=s-r+1}^{ s} |\partial_j\mathcal{ F}|.$ Thus the ABS bound is sharpened by the total non-shadow deficit on the top $r$ levels. In the modular setting, we take a coefficient-sensitive viewpoint: the polynomial method depends not just on the degree of the annihilator polynomial $P_L(t)=\prod_{ \ell\in L}(t-\ell)\in\mathbb{ F}_p[t]$, but on which binomial terms actually appear in it. This yields a gap-free modular bound depending only on the active support levels of $P_L$. For almost-initial residue patterns $L=\{ 0,1,\dots,s-m-1\}\cup R \pmod p$ we obtain the collapse $|\mathcal{ F}|\le \sum_{ i=0}^{ m}\binom{ n}{ s-i}.$ In particular, for consecutive residues $L=\{ 0,1,\dots,s-1\}\pmod p$ we get the sharp bound $|\mathcal{ F}|\le \binom{ n}{ s}$, giving a partial negative answer to a question of Alon--Babai--Suzuki: the modular ABS bound $N(n,s,r)$ is not attainable in the consecutive-residue regime whenever $r\ge 2$.
Categories: math.CO