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SOLUTION TO GIT PROBLEM: NONSTABLE LOCI
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Group: A4 Representation A4(4,0,0,0,0)
Set of maximal non-stable states:
(1) 1-PS = (1, 1, 0, -1, -1) yields a state with 42 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (0, 3, 0, 0, 1), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (1, 1, 0, 0, 2), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (0, 1, 2, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 3, 0, 0, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (0, 2, 0, 0, 2), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (0, 2, 0, 1, 1)}
(2) 1-PS = (1, 1, 0, 0, -2) yields a state with 45 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (0, 3, 0, 0, 1), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (0, 1, 1, 2, 0), (1, 1, 1, 0, 1), (0, 0, 0, 4, 0), (2, 1, 1, 0, 0), (0, 0, 1, 3, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 3, 0, 0, 0), (0, 1, 0, 3, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (0, 2, 0, 1, 1)}
(3) 1-PS = (1, 1/3, 1/3, -2/3, -1) yields a state with 40 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (0, 3, 0, 0, 1), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (0, 0, 3, 0, 1), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (0, 1, 2, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(4) 1-PS = (1, 3/5, 2/5, -1/5, -9/5) yields a state with 41 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (0, 3, 0, 0, 1), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (0, 1, 1, 2, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 1, 0, 3, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(5) 1-PS = (1, 2/3, 1/3, -1/3, -5/3) yields a state with 41 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (0, 3, 0, 0, 1), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (0, 1, 1, 2, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(6) 1-PS = (1, 1/3, 0, -1/3, -1) yields a state with 39 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (0, 3, 0, 0, 1), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(7) 1-PS = (1, 1/2, 1/2, -1/2, -3/2) yields a state with 42 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (0, 3, 0, 0, 1), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (0, 0, 3, 0, 1), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (0, 1, 1, 2, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (0, 1, 2, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(8) 1-PS = (1, 2/3, -1/3, -1/3, -1) yields a state with 37 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 3, 0, 0, 1), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (0, 2, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(9) 1-PS = (1, 1/3, -1/3, -1/3, -2/3) yields a state with 36 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 3, 0, 0, 1), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (1, 1, 0, 0, 2), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(10) 1-PS = (1, 0, -1/3, -1/3, -1/3) yields a state with 36 characters
Maximal nonstable state={(1, 0, 2, 1, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (1, 1, 2, 0, 0), (1, 0, 1, 1, 1), (1, 1, 0, 0, 2), (1, 0, 1, 0, 2), (1, 0, 0, 1, 2), (2, 0, 0, 1, 1), (0, 4, 0, 0, 0), (3, 0, 0, 1, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (1, 0, 0, 2, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (1, 0, 0, 0, 3), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(11) 1-PS = (1, 0, 0, 0, -1) yields a state with 46 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (1, 0, 1, 1, 1), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 1, 1, 2, 0), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (0, 0, 0, 4, 0), (2, 1, 1, 0, 0), (0, 0, 1, 3, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 1, 0, 3, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (1, 0, 0, 2, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(12) 1-PS = (1, 1/5, -1/5, -2/5, -3/5) yields a state with 34 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 3, 0, 0, 1), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (1, 1, 0, 0, 2), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(13) 1-PS = (1, 1, 1, 0, -3) yields a state with 45 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (0, 3, 0, 0, 1), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (0, 0, 3, 0, 1), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (0, 1, 1, 2, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (0, 1, 2, 0, 1), (0, 0, 0, 4, 0), (0, 0, 1, 3, 0), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 1, 0, 3, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(14) 1-PS = (1, 1/9, -2/9, -1/3, -5/9) yields a state with 33 characters
Maximal nonstable state={(1, 0, 2, 1, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (1, 1, 0, 0, 2), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(15) 1-PS = (1, 1/2, 0, -1/2, -1) yields a state with 39 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (0, 3, 0, 0, 1), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(16) 1-PS = (1, 0, 0, -1/2, -1/2) yields a state with 36 characters
Maximal nonstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (1, 0, 1, 1, 1), (0, 1, 3, 0, 0), (1, 1, 0, 0, 2), (1, 0, 1, 0, 2), (2, 0, 0, 1, 1), (0, 4, 0, 0, 0), (3, 0, 0, 1, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}


**************************************
SOLUTION TO GIT PROBLEM: UNSTABLE LOCI
**************************************
Group: A4 Representation A4(4,0,0,0,0)
Set of maximal unstable states:
(1) 1-PS = (1, -1/4, -1/4, -1/4, -1/4) yields a state with 35 characters
Maximal unstable state={(1, 0, 2, 1, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (1, 1, 2, 0, 0), (1, 0, 1, 1, 1), (1, 1, 0, 0, 2), (1, 0, 1, 0, 2), (3, 0, 0, 1, 0), (1, 0, 0, 1, 2), (3, 0, 1, 0, 0), (2, 0, 0, 1, 1), (1, 2, 1, 0, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (1, 0, 0, 2, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (1, 0, 0, 0, 3), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(2) 1-PS = (1, 1, -1/4, -7/8, -7/8) yields a state with 37 characters
Maximal unstable state={(0, 2, 2, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 3, 0, 0), (1, 1, 0, 0, 2), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 3, 0, 0, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (0, 2, 0, 0, 2), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (0, 2, 0, 1, 1)}
(3) 1-PS = (1, 9/14, 2/7, -3/7, -3/2) yields a state with 39 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 1, 1, 2, 0), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(4) 1-PS = (1, 13/23, 8/23, -7/23, -37/23) yields a state with 40 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 1, 1, 2, 0), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(5) 1-PS = (1, 13/33, 8/33, -2/3, -32/33) yields a state with 37 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(6) 1-PS = (1, 3/23, 3/23, -7/23, -22/23) yields a state with 37 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(7) 1-PS = (1, 3/8, 3/8, -7/8, -7/8) yields a state with 38 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (0, 0, 3, 0, 1), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (0, 1, 2, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 2, 1, 0, 1), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(8) 1-PS = (1, 7/12, 1/6, -1/24, -41/24) yields a state with 41 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 1, 1, 2, 0), (0, 2, 0, 2, 0), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (0, 0, 1, 3, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 1, 0, 3, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(9) 1-PS = (1, 4/19, 4/19, -1/19, -26/19) yields a state with 41 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 1, 1, 2, 0), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (0, 0, 1, 3, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 1, 0, 3, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(10) 1-PS = (1, 4/19, -1/19, -6/19, -16/19) yields a state with 35 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(11) 1-PS = (1, 4/9, -1/9, -2/3, -2/3) yields a state with 36 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 3, 0, 0), (1, 1, 0, 0, 2), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(12) 1-PS = (1, 4/19, -6/19, -6/19, -11/19) yields a state with 33 characters
Maximal unstable state={(1, 0, 2, 1, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (1, 1, 0, 0, 2), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(13) 1-PS = (1, 1, -1/4, -1/4, -3/2) yields a state with 40 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 1, 1, 2, 0), (0, 2, 0, 2, 0), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 3, 0, 0, 0), (0, 1, 0, 3, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (0, 2, 0, 1, 1)}
(14) 1-PS = (1, 4/29, -6/29, -11/29, -16/29) yields a state with 32 characters
Maximal unstable state={(1, 0, 2, 1, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (1, 1, 0, 0, 2), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(15) 1-PS = (1, 4/9, 4/9, -2/3, -11/9) yields a state with 39 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (0, 0, 3, 0, 1), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (0, 1, 2, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(16) 1-PS = (1, 13/38, 4/19, -11/19, -37/38) yields a state with 37 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(17) 1-PS = (1, 13/18, -1/9, -2/3, -17/18) yields a state with 35 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(18) 1-PS = (1, 11/16, 1/16, 1/16, -29/16) yields a state with 41 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 1, 1, 2, 0), (0, 2, 0, 2, 0), (0, 0, 0, 4, 0), (2, 1, 1, 0, 0), (0, 0, 1, 3, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 1, 0, 3, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(19) 1-PS = (1, 2/7, -1/14, -3/7, -11/14) yields a state with 35 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(20) 1-PS = (1, 23/28, 3/28, -1/4, -47/28) yields a state with 40 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 1, 1, 2, 0), (0, 2, 0, 2, 0), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 1, 0, 3, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(21) 1-PS = (1, 4/49, -11/49, -16/49, -26/49) yields a state with 32 characters
Maximal unstable state={(1, 0, 2, 1, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (2, 0, 2, 0, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (1, 1, 0, 0, 2), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(22) 1-PS = (1, 8/23, -2/23, -7/23, -22/23) yields a state with 36 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 3, 0, 0), (2, 0, 0, 1, 1), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 2, 0, 2, 0), (1, 1, 1, 0, 1), (2, 1, 1, 0, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 0, 0, 0, 2), (1, 1, 0, 1, 1), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}
(23) 1-PS = (1, 1, 1, -1/4, -11/4) yields a state with 44 characters
Maximal unstable state={(0, 2, 2, 0, 0), (1, 0, 2, 1, 0), (0, 0, 4, 0, 0), (2, 2, 0, 0, 0), (2, 0, 1, 1, 0), (0, 3, 0, 0, 1), (2, 0, 2, 0, 0), (0, 2, 1, 1, 0), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0), (1, 0, 0, 3, 0), (1, 0, 1, 2, 0), (0, 3, 1, 0, 0), (1, 1, 2, 0, 0), (0, 1, 2, 1, 0), (0, 1, 3, 0, 0), (3, 0, 0, 1, 0), (0, 4, 0, 0, 0), (3, 0, 1, 0, 0), (0, 0, 3, 0, 1), (1, 2, 1, 0, 0), (0, 3, 0, 1, 0), (3, 1, 0, 0, 0), (2, 0, 0, 2, 0), (1, 1, 1, 1, 0), (0, 1, 1, 2, 0), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1), (1, 1, 1, 0, 1), (0, 1, 2, 0, 1), (2, 1, 1, 0, 0), (0, 0, 1, 3, 0), (4, 0, 0, 0, 0), (1, 2, 0, 1, 0), (0, 1, 0, 3, 0), (0, 2, 1, 0, 1), (1, 1, 0, 2, 0), (1, 0, 3, 0, 0), (2, 1, 0, 0, 1), (2, 1, 0, 1, 0), (3, 0, 0, 0, 1), (1, 3, 0, 0, 0)}


*************************************************************
SOLUTION TO GIT PROBLEM: STRICTLY POLYSTABLE LOCI
*************************************************************
Group: A4 Representation A4(4,0,0,0,0)
Set of strictly polystable states:
(1) A state with 7 characters
Strictly polystable state={(0, 3, 1, 0, 0), (0, 2, 2, 0, 0), (0, 0, 4, 0, 0), (1, 0, 1, 1, 1), (1, 1, 0, 1, 1), (0, 1, 3, 0, 0), (0, 4, 0, 0, 0)}
(2) A state with 4 characters
Strictly polystable state={(1, 1, 0, 1, 1), (1, 1, 0, 0, 2), (0, 0, 4, 0, 0), (1, 1, 0, 2, 0)}
(3) A state with 11 characters
Strictly polystable state={(1, 1, 1, 0, 1), (0, 1, 2, 0, 1), (0, 0, 0, 4, 0), (2, 1, 0, 0, 1), (0, 0, 3, 0, 1), (0, 3, 0, 0, 1), (0, 2, 1, 0, 1), (3, 0, 0, 0, 1), (2, 0, 1, 0, 1), (1, 2, 0, 0, 1), (1, 0, 2, 0, 1)}
(4) A state with 14 characters
Strictly polystable state={(0, 1, 2, 0, 1), (2, 0, 0, 0, 2), (0, 1, 2, 1, 0), (1, 1, 0, 1, 1), (1, 0, 2, 1, 0), (1, 1, 0, 0, 2), (2, 0, 0, 1, 1), (0, 0, 4, 0, 0), (0, 2, 0, 0, 2), (1, 1, 0, 2, 0), (0, 2, 0, 1, 1), (2, 0, 0, 2, 0), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1)}
(5) A state with 6 characters
Strictly polystable state={(2, 0, 0, 0, 2), (0, 1, 2, 1, 0), (0, 0, 4, 0, 0), (1, 1, 0, 1, 1), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1)}
(6) A state with 8 characters
Strictly polystable state={(1, 0, 1, 2, 0), (2, 0, 0, 0, 2), (0, 1, 2, 1, 0), (1, 1, 0, 1, 1), (0, 0, 4, 0, 0), (0, 2, 1, 0, 1), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1)}
(7) A state with 22 characters
Strictly polystable state={(0, 2, 2, 0, 0), (1, 1, 1, 0, 1), (0, 0, 0, 4, 0), (0, 0, 1, 3, 0), (0, 0, 4, 0, 0), (0, 1, 0, 3, 0), (0, 2, 1, 1, 0), (1, 2, 0, 0, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0), (0, 3, 1, 0, 0), (2, 0, 0, 0, 2), (1, 0, 1, 1, 1), (0, 1, 2, 1, 0), (1, 1, 0, 1, 1), (0, 1, 3, 0, 0), (1, 0, 0, 2, 1), (0, 4, 0, 0, 0), (0, 3, 0, 1, 0), (0, 1, 1, 2, 0), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1)}
(8) A state with 4 characters
Strictly polystable state={(1, 0, 2, 0, 1), (1, 1, 0, 0, 2), (0, 3, 0, 1, 0), (1, 0, 0, 3, 0)}
(9) A state with 3 characters
Strictly polystable state={(2, 0, 0, 1, 1), (0, 1, 2, 0, 1), (0, 2, 0, 2, 0)}
(10) A state with 7 characters
Strictly polystable state={(1, 0, 1, 2, 0), (1, 0, 3, 0, 0), (0, 2, 1, 0, 1), (2, 0, 0, 0, 2), (0, 2, 0, 1, 1), (1, 0, 2, 1, 0), (1, 0, 0, 3, 0)}
(11) A state with 8 characters
Strictly polystable state={(0, 2, 2, 0, 0), (1, 0, 1, 2, 0), (1, 0, 3, 0, 0), (1, 0, 2, 1, 0), (1, 1, 0, 0, 2), (0, 2, 1, 1, 0), (0, 2, 0, 2, 0), (1, 0, 0, 3, 0)}
(12) A state with 5 characters
Strictly polystable state={(0, 2, 1, 0, 1), (1, 0, 0, 3, 0), (2, 0, 0, 1, 1), (0, 0, 2, 2, 0), (1, 0, 2, 0, 1)}
(13) A state with 8 characters
Strictly polystable state={(1, 0, 0, 3, 0), (2, 0, 0, 0, 2), (0, 1, 2, 1, 0), (1, 1, 0, 1, 1), (0, 0, 4, 0, 0), (0, 3, 0, 0, 1), (0, 2, 0, 2, 0), (1, 0, 2, 0, 1)}
(14) A state with 2 characters
Strictly polystable state={(1, 1, 1, 0, 1), (0, 0, 0, 4, 0)}
(15) A state with 11 characters
Strictly polystable state={(1, 1, 1, 0, 1), (0, 0, 0, 4, 0), (0, 0, 1, 3, 0), (1, 1, 0, 1, 1), (0, 0, 4, 0, 0), (2, 0, 0, 1, 1), (0, 2, 1, 0, 1), (2, 0, 1, 0, 1), (0, 2, 0, 1, 1), (0, 0, 3, 1, 0), (0, 0, 2, 2, 0)}

['Ex 22 Threefolds in P4 of deg 4', A4(4,0,0,0,0), 101.999, 814.157, 4222.452, 70, 39, 56, 16, 23, 15]