EXACT COMPUTATIONAL RESULTS - dimension-two 1/3-2/3 study
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Engine: exact integer DP over ideals; anchored pair-count identity;
validated vs brute force on all 4231 labeled posets n=5 (0 mismatches);
generator matches OEIS A001035 labeled-poset counts for n=2..6.

[A] ALL permutation posets exhaustive, min delta:
n=7: 1/3 ; n=8: 1/3 (36 extremal perms) ; n=9: 1/3 (62 extremal perms).
Never below 1/3 anywhere through n=9.
Extremal perms n=8:
01234567->see file permsweep_n8.json examples:
[012345786],[012345867],[012346758],[012347568],[012356478],[012364578],[012453678] ...

[B] Sum-indecomposable non-chain optima (exhaustive):
n=4 count=13   min=2/5    witnesses: 1302,2031
n=5 count=71   min=4/11   witnesses: 14203,30241
n=6 count=461  min=5/14   witnesses: 135024,304152
n=7 count=3447 min=14/39  witnesses: 1520463,3026415
n=8 count=29093 min=16/45 witnesses: 14507236,30561274
n=9 count=273343 min=30/85 witnesses: 156702384,405681237
Deficit delta-1/3 at n=6..9: 0.02381, 0.02564, 0.02222, 0.01961 (~c/n, c~0.17-0.18).

[C] Half-balance census (sum-indecomposable non-chain), exhaustive:
n=4: nonHalf=2, halfWithTwin=8, halfNoTwin=3 (ex: 1230,2301,3012)
n=5: 28 / 38 / 5 (ex: 24031,31402,34201,34120)
n=6: 146 / 265 / 50 (ex: 123450,124503,134250,134520)
n=7: 1286 / 1983 / 178 (ex: 1245630,1246053,1256340,1263450)

[D] Family checks (exact):
C_m || z family pi=(1,2,...,m,0): delta=floor((m+1)/2)/(m+1); m=3 -> 1/2 (pi=1230); m=4 -> 2/5 (pi=12340)
Dip families F_k/G_k oscillate; true argmins approach 1/3.

[E] Validation anchors:
antichain3 delta=1/2; V-poset delta=1/2; N-poset(1302-style) fast==brute;
labeled counts n=2..6 == 3,19,219,4231,130023.