Zero-partition (Fejer-Riesz factor split) route, the surviving route to existence: partitioning the N circle-roots of the degree-N extremal as q = q_m q_n and normalizing, the deficit D(N) = M_N - max_partition[<v_m^2>+<v_n^2>] is NEGATIVE up to N~16 (best split carries more energy than M_N: D(6)=-0.59, D(12)=-0.20, D(16)=-0.06), crosses zero at N~18, then D(24)=+0.19, D(32)=+0.90 (balanced splits; interleaved/arc/random seeds + swap hill-climb). If some explicit partition rule achieves D(N)=O(log N), then M_{m+n} <= M_m+M_n+O(log) and existence of Lambda = lim M_n/n follows from the de Bruijn-Erdos approximate-Fekete lemma. The observed growth (increments +0.25 for 16->24, +0.72 for 24->32) cannot yet separate O(log N) from Theta(N): the partition search is a heuristic whose quality degrades with N (measured D is only an upper estimate of the true deficit), and N=32 sits at the float-validity edge. Unresolved; the sharpest computational question this round leaves.