Part 1: K = F_3(t), R = F_3[t], J = (t^2+1)R, sigma_12 = F_3 + J, sigma_21 = F_3 t + J, sigma_ij = J otherwise
PASS 1a pair (F_3, F_3*tbar) in SL2(F_9): closed (H cap U12 = t12(F_3), H cap U21 = t21(F_3 tbar)), |H| = 120 (= |SL(2,5)|)
PASS 1b A0 B0 A0 = F_3 tbar is not inside A0 = F_3  (so the lifted net is not completable)
PASS 1c control: pair (F_3, F_3*(1+1tbar)) is NOT closed (generates SL(2,9))
PASS 1c control: pair (F_3, F_3*(1+2tbar)) is NOT closed (generates SL(2,9))
PASS 1d BFS: |H| = 120, entries of upper unitriangular elements [0, 1, 2], of lower [0, 3, 6], element orders {1: 1, 2: 1, 3: 20, 4: 30, 5: 24, 6: 20, 10: 24} (those of SL(2,5))
PASS 1e n=3: net axioms on 480 random products (sigma_ir * sigma_rj in sigma_ij)
PASS 1e n=4: net axioms on 1920 random products (sigma_ir * sigma_rj in sigma_ij)
PASS 1f non-completability witness: 1 in sigma_12, t in sigma_21, 1*t*1 = t not in sigma_12
PASS 1g every sigma_ij is an F_3[t^2]-module (t^2 * sigma_ij <= sigma_ij); F_3[t^2] is a PID and F_3(t) is algebraic (degree 2) over F_3(t^2): the hypotheses of Kourovka 19.48 hold
Part 2: closed pairs (A0,B0) over Q = F_p[t]/(g) with A0B0A0 not in A0 or B0A0B0 not in B0
   F_3[e]/(e^2): |Q| = 9, 5 nonzero subspaces, 11 pairs tested, 4 closed, closed & violating the triple-product condition: 0 []  (0.0s)
   F_3[e]/(e^3): |Q| = 27, 27 nonzero subspaces, 187 pairs tested, 31 closed, closed & violating the triple-product condition: 0 []  (0.0s)
   F_3 x F_3 = F_3[t]/(t(t-1)): |Q| = 9, 5 nonzero subspaces, 14 pairs tested, 8 closed, closed & violating the triple-product condition: 0 []  (0.0s)
   F_9[e]/(e^2) = F_3[t]/((t^2+1)^2): |Q| = 81, 211 nonzero subspaces, 5933 pairs tested, 49 closed, closed & violating the triple-product condition: 2 [([0, 1, 2], [0, 27, 54], 120), ([0, 1, 2, 9, 10, 11], [0, 3, 6, 10, 13, 16], 87480)]  (5.1s)
   F_5[e]/(e^2): |Q| = 25, 7 nonzero subspaces, 15 pairs tested, 4 closed, closed & violating the triple-product condition: 0 []  (0.0s)
   F_5[e]/(e^3): |Q| = 125, 63 nonzero subspaces, 553 pairs tested, 55 closed, closed & violating the triple-product condition: 0 []  (2.4s)
   F_5 x F_5: |Q| = 25, 7 nonzero subspaces, 18 pairs tested, 8 closed, closed & violating the triple-product condition: 0 []  (0.0s)
   F_5^3 = F_5[t]/(t(t-1)(t-2)): |Q| = 125, 63 nonzero subspaces, 828 pairs tested, 89 closed, closed & violating the triple-product condition: 0 []  (1.9s)
   F_5[e]/(e^2) x F_5 = F_5[t]/(t^2(t-1)): |Q| = 125, 63 nonzero subspaces, 673 pairs tested, 58 closed, closed & violating the triple-product condition: 0 []  (2.2s)
   F_7[e]/(e^2): |Q| = 49, 9 nonzero subspaces, 19 pairs tested, 4 closed, closed & violating the triple-product condition: 0 []  (0.0s)
   F_7 x F_7: |Q| = 49, 9 nonzero subspaces, 22 pairs tested, 8 closed, closed & violating the triple-product condition: 0 []  (0.0s)
   F_7[e]/(e^3): |Q| = 343, 115 nonzero subspaces, 1231 pairs tested, 87 closed, closed & violating the triple-product condition: 0 []  (64.8s)
ALL PART-1 CHECKS PASSED
