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SOLUTION TO GIT PROBLEM: NONSTABLE LOCI
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Group: A3 RepresentationA3(5,0,0,0)
Set of maximal non-stable states:
(1) 1-PS = (1, 1/2, 0, -3/2) yields a state with 33 characters
Maximal nonstable state={(1, 2, 1, 1), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (1, 2, 2, 0), (1, 1, 2, 1), (1, 3, 0, 1), (2, 3, 0, 0), (1, 0, 4, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (3, 1, 0, 1), (2, 1, 2, 0), (5, 0, 0, 0), (2, 2, 1, 0), (3, 1, 1, 0), (0, 3, 2, 0), (3, 2, 0, 0), (3, 0, 1, 1), (0, 2, 3, 0), (2, 1, 1, 1), (3, 0, 2, 0), (2, 0, 3, 0), (0, 1, 4, 0), (1, 3, 1, 0), (1, 4, 0, 0), (0, 0, 5, 0), (4, 1, 0, 0), (0, 3, 1, 1), (4, 0, 0, 1), (2, 2, 0, 1)}
(2) 1-PS = (1, 6/7, -4/7, -9/7) yields a state with 31 characters
Maximal nonstable state={(3, 0, 1, 1), (2, 1, 0, 2), (0, 3, 0, 2), (1, 2, 1, 1), (1, 2, 0, 2), (0, 4, 0, 1), (4, 0, 1, 0), (0, 2, 3, 0), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (1, 3, 1, 0), (3, 1, 1, 0), (1, 4, 0, 0), (3, 1, 0, 1), (4, 1, 0, 0), (2, 1, 2, 0), (5, 0, 0, 0), (2, 2, 1, 0), (0, 3, 1, 1), (4, 0, 0, 1), (2, 2, 0, 1), (0, 3, 2, 0), (3, 2, 0, 0)}
(3) 1-PS = (1, 1/5, -2/5, -4/5) yields a state with 28 characters
Maximal nonstable state={(3, 0, 1, 1), (2, 1, 0, 2), (2, 0, 1, 2), (1, 2, 1, 1), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (1, 3, 1, 0), (1, 4, 0, 0), (3, 1, 0, 1), (4, 1, 0, 0), (2, 1, 2, 0), (5, 0, 0, 0), (2, 2, 1, 0), (4, 0, 0, 1), (2, 2, 0, 1), (3, 1, 1, 0), (3, 2, 0, 0)}
(4) 1-PS = (1, 0, -1/3, -2/3) yields a state with 27 characters
Maximal nonstable state={(3, 0, 1, 1), (2, 1, 0, 2), (2, 0, 1, 2), (1, 2, 1, 1), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (2, 0, 0, 3), (1, 1, 3, 0), (0, 5, 0, 0), (1, 3, 1, 0), (1, 4, 0, 0), (3, 1, 0, 1), (4, 1, 0, 0), (2, 1, 2, 0), (5, 0, 0, 0), (2, 2, 1, 0), (4, 0, 0, 1), (2, 2, 0, 1), (3, 1, 1, 0), (3, 2, 0, 0)}
(5) 1-PS = (1, 1/2, -1/4, -5/4) yields a state with 31 characters
Maximal nonstable state={(3, 0, 1, 1), (2, 1, 0, 2), (1, 2, 1, 1), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (0, 2, 3, 0), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (1, 0, 4, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (1, 3, 1, 0), (3, 1, 1, 0), (1, 4, 0, 0), (3, 1, 0, 1), (4, 1, 0, 0), (2, 1, 2, 0), (5, 0, 0, 0), (2, 2, 1, 0), (0, 3, 1, 1), (4, 0, 0, 1), (2, 2, 0, 1), (0, 3, 2, 0), (3, 2, 0, 0)}
(6) 1-PS = (1, 1/3, -2/3, -2/3) yields a state with 29 characters
Maximal nonstable state={(3, 0, 1, 1), (2, 1, 0, 2), (2, 0, 1, 2), (1, 2, 1, 1), (1, 2, 0, 2), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (2, 0, 0, 3), (0, 4, 1, 0), (0, 5, 0, 0), (1, 3, 1, 0), (1, 4, 0, 0), (3, 1, 0, 1), (4, 1, 0, 0), (2, 1, 2, 0), (5, 0, 0, 0), (2, 2, 1, 0), (4, 0, 0, 1), (2, 2, 0, 1), (3, 1, 1, 0), (3, 2, 0, 0)}
(7) 1-PS = (1, 1/2, 1/2, -2) yields a state with 36 characters
Maximal nonstable state={(1, 2, 1, 1), (0, 2, 2, 1), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (1, 2, 2, 0), (1, 1, 2, 1), (1, 3, 0, 1), (0, 1, 3, 1), (2, 3, 0, 0), (1, 0, 4, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (3, 1, 0, 1), (2, 1, 2, 0), (5, 0, 0, 0), (2, 2, 1, 0), (3, 1, 1, 0), (0, 3, 2, 0), (3, 2, 0, 0), (3, 0, 1, 1), (0, 2, 3, 0), (2, 1, 1, 1), (3, 0, 2, 0), (0, 0, 4, 1), (2, 0, 3, 0), (1, 0, 3, 1), (0, 1, 4, 0), (1, 3, 1, 0), (1, 4, 0, 0), (0, 0, 5, 0), (4, 1, 0, 0), (0, 3, 1, 1), (4, 0, 0, 1), (2, 2, 0, 1)}
(8) 1-PS = (1, -1/9, -2/9, -2/3) yields a state with 26 characters
Maximal nonstable state={(3, 0, 1, 1), (2, 1, 0, 2), (2, 0, 1, 2), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (2, 0, 0, 3), (1, 0, 4, 0), (1, 1, 3, 0), (1, 3, 1, 0), (1, 4, 0, 0), (3, 1, 0, 1), (4, 1, 0, 0), (2, 1, 2, 0), (5, 0, 0, 0), (2, 2, 1, 0), (4, 0, 0, 1), (2, 2, 0, 1), (3, 1, 1, 0), (3, 2, 0, 0)}
(9) 1-PS = (1, 1/2, -1/2, -1) yields a state with 30 characters
Maximal nonstable state={(3, 0, 1, 1), (2, 1, 0, 2), (1, 2, 1, 1), (1, 2, 0, 2), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (1, 3, 1, 0), (3, 1, 1, 0), (1, 4, 0, 0), (3, 1, 0, 1), (4, 1, 0, 0), (2, 1, 2, 0), (5, 0, 0, 0), (2, 2, 1, 0), (0, 3, 1, 1), (4, 0, 0, 1), (2, 2, 0, 1), (0, 3, 2, 0), (3, 2, 0, 0)}
(10) 1-PS = (1, 0, 0, -1) yields a state with 34 characters
Maximal nonstable state={(2, 1, 0, 2), (2, 0, 1, 2), (1, 2, 1, 1), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (1, 2, 2, 0), (1, 1, 2, 1), (1, 3, 0, 1), (2, 3, 0, 0), (1, 0, 4, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (3, 1, 0, 1), (2, 1, 2, 0), (5, 0, 0, 0), (2, 2, 1, 0), (3, 1, 1, 0), (0, 3, 2, 0), (3, 2, 0, 0), (3, 0, 1, 1), (0, 2, 3, 0), (2, 1, 1, 1), (3, 0, 2, 0), (2, 0, 3, 0), (1, 0, 3, 1), (0, 1, 4, 0), (1, 3, 1, 0), (1, 4, 0, 0), (0, 0, 5, 0), (4, 1, 0, 0), (4, 0, 0, 1), (2, 2, 0, 1)}


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SOLUTION TO GIT PROBLEM: UNSTABLE LOCI
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Group: A3 RepresentationA3(5,0,0,0)
Set of maximal unstable states:
(1) 1-PS = (1, 1, -3/5, -7/5) yields a state with 31 characters
Maximal unstable state={(3, 0, 1, 1), (2, 1, 0, 2), (0, 3, 0, 2), (1, 2, 1, 1), (1, 2, 0, 2), (0, 4, 0, 1), (4, 0, 1, 0), (0, 2, 3, 0), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (1, 3, 1, 0), (3, 1, 1, 0), (3, 1, 0, 1), (1, 4, 0, 0), (4, 1, 0, 0), (2, 1, 2, 0), (2, 2, 1, 0), (5, 0, 0, 0), (0, 3, 1, 1), (4, 0, 0, 1), (2, 2, 0, 1), (0, 3, 2, 0), (3, 2, 0, 0)}
(2) 1-PS = (1, 5/13, 1/13, -19/13) yields a state with 32 characters
Maximal unstable state={(1, 2, 1, 1), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (1, 2, 2, 0), (1, 1, 2, 1), (1, 3, 0, 1), (2, 3, 0, 0), (1, 0, 4, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (3, 1, 0, 1), (2, 1, 2, 0), (2, 2, 1, 0), (5, 0, 0, 0), (3, 1, 1, 0), (0, 3, 2, 0), (3, 2, 0, 0), (3, 0, 1, 1), (0, 2, 3, 0), (2, 1, 1, 1), (3, 0, 2, 0), (2, 0, 3, 0), (0, 1, 4, 0), (1, 3, 1, 0), (1, 4, 0, 0), (0, 0, 5, 0), (4, 1, 0, 0), (4, 0, 0, 1), (2, 2, 0, 1)}
(3) 1-PS = (1, 1/5, 1/5, -7/5) yields a state with 32 characters
Maximal unstable state={(1, 2, 1, 1), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (1, 2, 2, 0), (1, 1, 2, 1), (1, 3, 0, 1), (2, 3, 0, 0), (1, 0, 4, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (3, 1, 0, 1), (2, 1, 2, 0), (2, 2, 1, 0), (5, 0, 0, 0), (3, 1, 1, 0), (0, 3, 2, 0), (3, 2, 0, 0), (3, 0, 1, 1), (0, 2, 3, 0), (2, 1, 1, 1), (3, 0, 2, 0), (2, 0, 3, 0), (1, 0, 3, 1), (0, 1, 4, 0), (1, 3, 1, 0), (1, 4, 0, 0), (0, 0, 5, 0), (4, 1, 0, 0), (4, 0, 0, 1), (2, 2, 0, 1)}
(4) 1-PS = (1, 5/17, -3/17, -19/17) yields a state with 30 characters
Maximal unstable state={(3, 0, 1, 1), (2, 1, 0, 2), (1, 2, 1, 1), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (0, 2, 3, 0), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (1, 0, 4, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (1, 3, 1, 0), (3, 1, 1, 0), (3, 1, 0, 1), (1, 4, 0, 0), (4, 1, 0, 0), (2, 1, 2, 0), (2, 2, 1, 0), (5, 0, 0, 0), (4, 0, 0, 1), (2, 2, 0, 1), (0, 3, 2, 0), (3, 2, 0, 0)}
(5) 1-PS = (1, 1/5, -3/5, -3/5) yields a state with 29 characters
Maximal unstable state={(3, 0, 1, 1), (2, 1, 0, 2), (2, 0, 1, 2), (1, 2, 1, 1), (1, 2, 0, 2), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (2, 0, 0, 3), (0, 4, 1, 0), (0, 5, 0, 0), (1, 3, 1, 0), (3, 1, 0, 1), (1, 4, 0, 0), (4, 1, 0, 0), (2, 1, 2, 0), (2, 2, 1, 0), (5, 0, 0, 0), (4, 0, 0, 1), (2, 2, 0, 1), (3, 1, 1, 0), (3, 2, 0, 0)}
(6) 1-PS = (1, 1, 1, -3) yields a state with 36 characters
Maximal unstable state={(1, 2, 1, 1), (0, 2, 2, 1), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (1, 2, 2, 0), (1, 1, 2, 1), (0, 1, 3, 1), (1, 3, 0, 1), (2, 3, 0, 0), (1, 0, 4, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (3, 1, 0, 1), (2, 1, 2, 0), (2, 2, 1, 0), (5, 0, 0, 0), (3, 1, 1, 0), (0, 3, 2, 0), (3, 2, 0, 0), (3, 0, 1, 1), (0, 2, 3, 0), (2, 1, 1, 1), (3, 0, 2, 0), (0, 0, 4, 1), (2, 0, 3, 0), (1, 0, 3, 1), (0, 1, 4, 0), (1, 3, 1, 0), (1, 4, 0, 0), (0, 0, 5, 0), (4, 1, 0, 0), (0, 3, 1, 1), (4, 0, 0, 1), (2, 2, 0, 1)}
(7) 1-PS = (1, -3/29, -7/29, -19/29) yields a state with 26 characters
Maximal unstable state={(3, 0, 1, 1), (2, 1, 0, 2), (2, 0, 1, 2), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (2, 0, 0, 3), (1, 0, 4, 0), (1, 1, 3, 0), (1, 3, 1, 0), (3, 1, 0, 1), (1, 4, 0, 0), (4, 1, 0, 0), (2, 1, 2, 0), (2, 2, 1, 0), (5, 0, 0, 0), (4, 0, 0, 1), (2, 2, 0, 1), (3, 1, 1, 0), (3, 2, 0, 0)}
(8) 1-PS = (1, 5/9, -1/3, -11/9) yields a state with 30 characters
Maximal unstable state={(3, 0, 1, 1), (2, 1, 0, 2), (1, 2, 1, 1), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (0, 2, 3, 0), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (1, 3, 1, 0), (3, 1, 1, 0), (3, 1, 0, 1), (1, 4, 0, 0), (4, 1, 0, 0), (2, 1, 2, 0), (2, 2, 1, 0), (5, 0, 0, 0), (0, 3, 1, 1), (4, 0, 0, 1), (2, 2, 0, 1), (0, 3, 2, 0), (3, 2, 0, 0)}
(9) 1-PS = (1, 1/13, -3/13, -11/13) yields a state with 28 characters
Maximal unstable state={(3, 0, 1, 1), (2, 1, 0, 2), (2, 0, 1, 2), (1, 2, 1, 1), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (1, 0, 4, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (1, 3, 1, 0), (3, 1, 0, 1), (1, 4, 0, 0), (4, 1, 0, 0), (2, 1, 2, 0), (2, 2, 1, 0), (5, 0, 0, 0), (4, 0, 0, 1), (2, 2, 0, 1), (3, 1, 1, 0), (3, 2, 0, 0)}
(10) 1-PS = (1, 5/9, -1/9, -13/9) yields a state with 31 characters
Maximal unstable state={(3, 0, 1, 1), (1, 2, 1, 1), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (0, 2, 3, 0), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (0, 1, 4, 0), (1, 0, 4, 0), (0, 4, 1, 0), (1, 1, 3, 0), (0, 5, 0, 0), (1, 3, 1, 0), (3, 1, 1, 0), (3, 1, 0, 1), (1, 4, 0, 0), (4, 1, 0, 0), (2, 1, 2, 0), (2, 2, 1, 0), (5, 0, 0, 0), (0, 3, 1, 1), (4, 0, 0, 1), (2, 2, 0, 1), (0, 3, 2, 0), (3, 2, 0, 0)}
(11) 1-PS = (1, 5/13, -7/13, -11/13) yields a state with 28 characters
Maximal unstable state={(3, 0, 1, 1), (2, 1, 0, 2), (1, 2, 1, 1), (1, 2, 0, 2), (0, 4, 0, 1), (4, 0, 1, 0), (2, 0, 2, 1), (3, 0, 0, 2), (2, 1, 1, 1), (1, 2, 2, 0), (3, 0, 2, 0), (2, 0, 3, 0), (1, 3, 0, 1), (2, 3, 0, 0), (0, 4, 1, 0), (0, 5, 0, 0), (1, 3, 1, 0), (3, 1, 1, 0), (3, 1, 0, 1), (1, 4, 0, 0), (4, 1, 0, 0), (2, 1, 2, 0), (2, 2, 1, 0), (5, 0, 0, 0), (4, 0, 0, 1), (2, 2, 0, 1), (0, 3, 2, 0), (3, 2, 0, 0)}


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SOLUTION TO GIT PROBLEM: STRICTLY POLYSTABLE LOCI
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Group: A3 RepresentationA3(5,0,0,0)
Set of strictly polystable states:
(1) A state with 4 characters
Strictly polystable state={(1, 1, 3, 0), (2, 0, 2, 1), (1, 2, 0, 2), (0, 3, 1, 1)}
(2) A state with 12 characters
Strictly polystable state={(2, 1, 0, 2), (2, 0, 1, 2), (0, 1, 4, 0), (1, 2, 1, 1), (0, 4, 1, 0), (0, 5, 0, 0), (0, 2, 3, 0), (0, 0, 5, 0), (1, 3, 0, 1), (1, 1, 2, 1), (0, 3, 2, 0), (1, 0, 3, 1)}
(3) A state with 3 characters
Strictly polystable state={(0, 4, 0, 1), (2, 0, 1, 2), (1, 1, 3, 0)}
(4) A state with 4 characters
Strictly polystable state={(1, 1, 3, 0), (0, 5, 0, 0), (2, 0, 0, 3), (1, 2, 1, 1)}