Part A: pairs (A,B), 1 in A, closedness decided by orbit-stabiliser
   F_9 (modulus [1, 0, 1]): 5 nonzero subspaces, 2 contain 1; 10 pairs (1 in A); 4 with ABA not in A; 2 complementable; 3 closed; closed with ABA not in A: 1 [(3, 3, 120)]; closed with BAB not in B: 1 [(3, 3, 120)]  (0.0s)
PASS A F_9: every closed pair violating ABA<=A or BAB<=B has |A| = |B| = 3 and |H| = 120 (SL(2,5)); counts 1, 1
   F_25 (modulus [1, 1, 1]): 7 nonzero subspaces, 2 contain 1; 14 pairs (1 in A); 6 with ABA not in A; 2 complementable; 2 closed; closed with ABA not in A: 0 []; closed with BAB not in B: 0 []  (0.0s)
PASS A F_25: every closed pair is complementable
   F_27 (modulus [1, 0, 2, 1]): 27 nonzero subspaces, 6 contain 1; 162 pairs (1 in A); 134 with ABA not in A; 2 complementable; 2 closed; closed with ABA not in A: 0 []; closed with BAB not in B: 0 []  (0.1s)
PASS A F_27: every closed pair is complementable
   F_49 (modulus [1, 0, 1]): 9 nonzero subspaces, 2 contain 1; 18 pairs (1 in A); 8 with ABA not in A; 2 complementable; 2 closed; closed with ABA not in A: 0 []; closed with BAB not in B: 0 []  (0.0s)
PASS A F_49: every closed pair is complementable
   F_81 (modulus [1, 0, 1, 1, 1]): 211 nonzero subspaces, 28 contain 1; 5908 pairs (1 in A); 5691 with ABA not in A; 3 complementable; 4 closed; closed with ABA not in A: 1 [(3, 3, 120)]; closed with BAB not in B: 1 [(3, 3, 120)]  (5.2s)
PASS A F_81: every closed pair violating ABA<=A or BAB<=B has |A| = |B| = 3 and |H| = 120 (SL(2,5)); counts 1, 1
   F_121 (modulus [1, 0, 1]): 13 nonzero subspaces, 2 contain 1; 26 pairs (1 in A); 12 with ABA not in A; 2 complementable; 2 closed; closed with ABA not in A: 0 []; closed with BAB not in B: 0 []  (0.4s)
PASS A F_121: every closed pair is complementable
   F_125 (modulus [1, 0, 1, 1]): 63 nonzero subspaces, 8 contain 1; 504 pairs (1 in A); 440 with ABA not in A; 2 complementable; 2 closed; closed with ABA not in A: 0 []; closed with BAB not in B: 0 []  (2.8s)
PASS A F_125: every closed pair is complementable
   contrast, characteristic 2 (not covered by Theorem 2 of RESULT.md):
   F_4 (modulus [1, 1, 1]): 4 nonzero subspaces, 2 contain 1; 8 pairs (1 in A); 3 with ABA not in A; 2 complementable; 4 closed; closed with ABA not in A: 2 [(2, 2, 10), (2, 2, 10)]; closed with BAB not in B: 2 [(2, 2, 10), (2, 2, 10)]  (0.0s)
   F_8 (modulus [1, 0, 1, 1]): 15 nonzero subspaces, 5 contain 1; 75 pairs (1 in A); 59 with ABA not in A; 2 complementable; 8 closed; closed with ABA not in A: 6 [(2, 2, 14), (2, 2, 18), (2, 2, 14), (2, 2, 18), (2, 2, 18), (2, 2, 14)]; closed with BAB not in B: 6 [(2, 2, 14), (2, 2, 18), (2, 2, 14), (2, 2, 18), (2, 2, 18), (2, 2, 14)]  (0.0s)
   F_16 (modulus [1, 0, 0, 1, 1]): 66 nonzero subspaces, 16 contain 1; 1056 pairs (1 in A); 985 with ABA not in A; 3 complementable; 17 closed; closed with ABA not in A: 14 [(2, 2, 30), (2, 2, 34), (2, 2, 30), (2, 2, 34), (2, 2, 34), (2, 2, 34), (2, 2, 34), (2, 2, 30)]; closed with BAB not in B: 14 [(2, 2, 30), (2, 2, 34), (2, 2, 30), (2, 2, 34), (2, 2, 34), (2, 2, 34), (2, 2, 34), (2, 2, 30)]  (0.1s)
   F_32 (modulus [1, 0, 0, 1, 0, 1]): 373 nonzero subspaces, 67 contain 1; 24991 pairs (1 in A); 24617 with ABA not in A; 2 complementable; 32 closed; closed with ABA not in A: 30 [(2, 2, 62), (2, 2, 62), (2, 2, 62), (2, 2, 62), (2, 2, 62), (2, 2, 22), (2, 2, 66), (2, 2, 66)]; closed with BAB not in B: 30 [(2, 2, 62), (2, 2, 62), (2, 2, 62), (2, 2, 62), (2, 2, 62), (2, 2, 22), (2, 2, 66), (2, 2, 66)]  (2.9s)
   F_9 modulus [1, 0, 1] (element u = a0 + a1*t  <->  integer a0 + 3*a1; t = 3)
   exceptional pairs over F_9 (A = F_3, B listed by elements): [[0, 3, 6]]
Part B: all irreducible elementary nets of order 3 and 4 over small fields (no closedness assumed)
PASS B n=3 F_4: 2 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (0.0s)
PASS B n=3 F_8: 2 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (0.0s)
PASS B n=3 F_9: 2 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (0.0s)
PASS B n=3 F_16: 3 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (0.3s)
PASS B n=3 F_25: 2 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (0.0s)
PASS B n=3 F_27: 2 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (0.0s)
PASS B n=3 F_49: 2 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (0.0s)
PASS B n=3 F_32: 2 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (147.9s)
PASS B n=3 F_81: 3 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (9.1s)
PASS B n=4 F_4: 2 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (0.0s)
PASS B n=4 F_9: 2 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (0.0s)
PASS B n=4 F_8: 2 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (0.0s)
PASS B n=4 F_25: 2 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (0.0s)
PASS B n=4 F_27: 2 irreducible elementary nets (normalised: 1 in sigma_1j for all j) found; non-completable: 0; explicit completion failures: 0 (0.1s)
Part C: no normalisation, n = 3
PASS B n=3 F_4: 10 irreducible elementary nets (ALL nets, no normalisation) found; non-completable: 0; explicit completion failures: 0 (0.0s)
PASS B n=3 F_8: 50 irreducible elementary nets (ALL nets, no normalisation) found; non-completable: 0; explicit completion failures: 0 (0.0s)
PASS B n=3 F_9: 17 irreducible elementary nets (ALL nets, no normalisation) found; non-completable: 0; explicit completion failures: 0 (0.0s)
ALL AUDIT CHECKS FOR THEOREM 2 PASSED
