(1) random subgroups of Aut(T_n), n=3..6, 100 trials: layered != sympy Schreier-Sims in 0 cases; broken variant (no closure) != sympy in 98 cases (must be > 0)
(2) neg_flip_one_label: log2|G_n| n=4..8 = [5, 9, 15, 27, 49] (Bellaterra: [7, 10, 13, 16, 19])
(2) neg_swap_sections: log2|G_n| n=4..8 = [5, 6, 7, 8, 9] (Bellaterra: [7, 10, 13, 16, 19])
(2) coding kappa_10 o s = S_t o kappa_10 against automaton bartholdi_right: {'a': True, 'b': True, 'c': True}
(2) coding kappa_10 o s = S_t o kappa_10 against automaton neg_flip_one_label: {'a': False, 'b': False, 'c': False}
(2) coding kappa_10 o s = S_t o kappa_10 against automaton neg_swap_sections: {'a': False, 'b': False, 'c': False}
(2) coding kappa_10 o s = S_t o kappa_10 against automaton automgrp_bellaterra: {'a': False, 'b': False, 'c': False}
(3) k=4: C'=C_t*diag(3,1) in Q: False; log2|<A,B,C'>_k| = 8 vs log2|Q_k| = 8; all gens of <A,B,C'> in Q-group: False
(3) k=6: C'=C_t*diag(3,1) in Q: False; log2|<A,B,C'>_k| = 14 vs log2|Q_k| = 14; all gens of <A,B,C'> in Q-group: False
(3) k=8: C'=C_t*diag(3,1) in Q: False; log2|<A,B,C'>_k| = 20 vs log2|Q_k| = 20; all gens of <A,B,C'> in Q-group: False
