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SOLUTION TO GIT PROBLEM: NONSTABLE LOCI
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Group: A3 RepresentationA3(3,3,0,0) + A3(4,1,1,0)
Set of maximal non-stable states:
(1) 1-PS = (1, 0, -1/2, -1/2) yields a state with 30 characters
Maximal nonstable state={(2, 1, 1, 2), (1, 3, 0, 2), (1, 3, 2, 0), (2, 2, 2, 0), (1, 3, 1, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 1, 0, 2), (3, 0, 1, 2), (3, 2, 1, 0), (1, 4, 1, 0), (3, 1, 2, 0), (2, 1, 0, 3), (2, 2, 0, 2), (3, 0, 2, 1), (3, 1, 1, 1), (3, 2, 0, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 0, 3, 1), (3, 0, 3, 0), (2, 2, 1, 1), (2, 0, 2, 2), (3, 3, 0, 0), (2, 3, 1, 0), (2, 3, 0, 1), (4, 1, 0, 1), (3, 0, 0, 3), (2, 0, 1, 3)}
(2) 1-PS = (1, 1, -1, -1) yields a state with 36 characters
Maximal nonstable state={(2, 1, 1, 2), (1, 3, 0, 2), (0, 3, 1, 2), (2, 2, 2, 0), (0, 3, 0, 3), (2, 1, 3, 0), (3, 1, 0, 2), (3, 0, 1, 2), (0, 3, 3, 0), (3, 2, 1, 0), (3, 1, 2, 0), (2, 2, 0, 2), (3, 0, 2, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (0, 4, 1, 1), (2, 3, 0, 1), (1, 4, 1, 0), (1, 3, 2, 0), (1, 2, 1, 2), (1, 3, 1, 1), (0, 3, 2, 1), (4, 1, 1, 0), (2, 1, 0, 3), (1, 2, 0, 3), (3, 1, 1, 1), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (1, 2, 3, 0), (3, 3, 0, 0), (2, 3, 1, 0), (4, 1, 0, 1), (3, 0, 0, 3)}
(3) 1-PS = (1, 3/5, -1/5, -7/5) yields a state with 31 characters
Maximal nonstable state={(1, 3, 0, 2), (1, 3, 2, 0), (2, 2, 2, 0), (1, 3, 1, 1), (0, 3, 2, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 1, 0, 2), (0, 3, 3, 0), (3, 0, 1, 2), (3, 2, 1, 0), (1, 1, 4, 0), (3, 1, 2, 0), (2, 2, 0, 2), (3, 0, 2, 1), (3, 1, 1, 1), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 0, 3, 1), (3, 0, 3, 0), (2, 2, 1, 1), (1, 2, 3, 0), (3, 3, 0, 0), (2, 3, 1, 0), (0, 4, 1, 1), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(4) 1-PS = (1, 1/7, -3/7, -5/7) yields a state with 29 characters
Maximal nonstable state={(2, 1, 1, 2), (1, 3, 0, 2), (1, 3, 2, 0), (2, 2, 2, 0), (1, 3, 1, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 1, 0, 2), (3, 0, 1, 2), (3, 2, 1, 0), (1, 4, 1, 0), (3, 1, 2, 0), (2, 1, 0, 3), (2, 2, 0, 2), (3, 0, 2, 1), (3, 1, 1, 1), (3, 2, 0, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 0, 3, 1), (3, 0, 3, 0), (2, 2, 1, 1), (1, 2, 3, 0), (3, 3, 0, 0), (2, 3, 1, 0), (2, 3, 0, 1), (4, 1, 0, 1), (3, 0, 0, 3)}
(5) 1-PS = (1, 1, 0, -2) yields a state with 32 characters
Maximal nonstable state={(1, 3, 0, 2), (2, 2, 2, 0), (2, 1, 3, 0), (3, 1, 0, 2), (0, 3, 3, 0), (3, 2, 1, 0), (3, 1, 2, 0), (2, 2, 0, 2), (3, 0, 2, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (0, 4, 1, 1), (2, 3, 0, 1), (1, 4, 1, 0), (1, 3, 2, 0), (1, 3, 1, 1), (0, 3, 2, 1), (4, 1, 1, 0), (3, 1, 1, 1), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (0, 2, 3, 1), (2, 0, 3, 1), (1, 2, 3, 0), (3, 3, 0, 0), (1, 1, 3, 1), (2, 3, 1, 0), (1, 1, 4, 0), (4, 1, 0, 1)}
(6) 1-PS = (1, 0, 0, -1) yields a state with 33 characters
Maximal nonstable state={(2, 1, 1, 2), (2, 2, 2, 0), (2, 1, 3, 0), (3, 1, 0, 2), (0, 3, 3, 0), (3, 0, 1, 2), (3, 2, 1, 0), (3, 1, 2, 0), (2, 2, 0, 2), (3, 0, 2, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (2, 0, 2, 2), (1, 0, 4, 1), (2, 3, 0, 1), (1, 4, 1, 0), (1, 3, 2, 0), (1, 3, 1, 1), (4, 1, 1, 0), (3, 1, 1, 1), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (2, 0, 3, 1), (1, 2, 3, 0), (3, 3, 0, 0), (1, 1, 3, 1), (2, 3, 1, 0), (1, 1, 4, 0), (4, 1, 0, 1), (3, 0, 0, 3)}
(7) 1-PS = (1, 1/2, 0, -3/2) yields a state with 31 characters
Maximal nonstable state={(1, 3, 2, 0), (2, 2, 2, 0), (1, 3, 1, 1), (0, 3, 2, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 1, 0, 2), (0, 3, 3, 0), (3, 0, 1, 2), (3, 2, 1, 0), (1, 1, 4, 0), (3, 1, 2, 0), (2, 2, 0, 2), (3, 0, 2, 1), (3, 1, 1, 1), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 0, 3, 1), (3, 0, 3, 0), (2, 2, 1, 1), (1, 2, 3, 0), (3, 3, 0, 0), (1, 1, 3, 1), (2, 3, 1, 0), (0, 4, 1, 1), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(8) 1-PS = (1, -1/5, -1/5, -3/5) yields a state with 29 characters
Maximal nonstable state={(2, 1, 1, 2), (1, 3, 2, 0), (2, 2, 2, 0), (4, 1, 1, 0), (2, 1, 3, 0), (3, 1, 0, 2), (3, 0, 1, 2), (3, 2, 1, 0), (1, 4, 1, 0), (3, 1, 2, 0), (2, 1, 0, 3), (2, 2, 0, 2), (3, 0, 2, 1), (3, 1, 1, 1), (3, 2, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 0, 3, 1), (3, 0, 3, 0), (2, 2, 1, 1), (1, 2, 3, 0), (2, 0, 2, 2), (3, 3, 0, 0), (2, 3, 1, 0), (1, 1, 4, 0), (2, 3, 0, 1), (4, 1, 0, 1), (3, 0, 0, 3), (2, 0, 1, 3)}
(9) 1-PS = (1, 0, -1/3, -2/3) yields a state with 29 characters
Maximal nonstable state={(2, 1, 1, 2), (1, 3, 2, 0), (2, 2, 2, 0), (1, 3, 1, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 1, 0, 2), (3, 0, 1, 2), (3, 2, 1, 0), (1, 4, 1, 0), (3, 1, 2, 0), (2, 1, 0, 3), (2, 2, 0, 2), (3, 0, 2, 1), (3, 1, 1, 1), (3, 2, 0, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 0, 3, 1), (3, 0, 3, 0), (2, 2, 1, 1), (1, 2, 3, 0), (2, 0, 2, 2), (3, 3, 0, 0), (2, 3, 1, 0), (2, 3, 0, 1), (4, 1, 0, 1), (3, 0, 0, 3)}
(10) 1-PS = (1, 1/3, 1/3, -5/3) yields a state with 33 characters
Maximal nonstable state={(2, 2, 2, 0), (2, 1, 3, 0), (3, 1, 0, 2), (0, 3, 3, 0), (3, 0, 1, 2), (3, 2, 1, 0), (3, 1, 2, 0), (3, 0, 2, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (1, 0, 4, 1), (0, 4, 1, 1), (2, 3, 0, 1), (1, 4, 1, 0), (1, 3, 2, 0), (1, 3, 1, 1), (0, 3, 2, 1), (4, 1, 1, 0), (3, 1, 1, 1), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (0, 2, 3, 1), (2, 0, 3, 1), (1, 2, 3, 0), (0, 1, 4, 1), (3, 3, 0, 0), (1, 1, 3, 1), (2, 3, 1, 0), (1, 1, 4, 0), (4, 1, 0, 1)}
(11) 1-PS = (1, 1/3, -1/3, -1) yields a state with 32 characters
Maximal nonstable state={(2, 1, 1, 2), (1, 3, 0, 2), (2, 2, 2, 0), (2, 1, 3, 0), (3, 1, 0, 2), (3, 0, 1, 2), (0, 3, 3, 0), (3, 2, 1, 0), (3, 1, 2, 0), (2, 2, 0, 2), (3, 0, 2, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (0, 4, 1, 1), (2, 3, 0, 1), (1, 4, 1, 0), (1, 3, 2, 0), (1, 3, 1, 1), (4, 1, 1, 0), (3, 1, 1, 1), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (2, 0, 3, 1), (1, 2, 3, 0), (3, 3, 0, 0), (2, 3, 1, 0), (1, 1, 4, 0), (4, 1, 0, 1), (3, 0, 0, 3)}


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SOLUTION TO GIT PROBLEM: UNSTABLE LOCI
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Group: A3 RepresentationA3(3,3,0,0) + A3(4,1,1,0)
Set of maximal unstable states:
(1) 1-PS = (1, 1, 1, -3) yields a state with 31 characters
Maximal unstable state={(1, 3, 2, 0), (2, 2, 2, 0), (1, 3, 1, 1), (0, 3, 2, 1), (4, 1, 1, 0), (2, 1, 3, 0), (0, 3, 3, 0), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (1, 1, 4, 0), (3, 0, 2, 1), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (0, 2, 3, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (2, 0, 3, 1), (1, 2, 3, 0), (0, 1, 4, 1), (1, 0, 4, 1), (3, 3, 0, 0), (1, 1, 3, 1), (2, 3, 1, 0), (0, 4, 1, 1), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(2) 1-PS = (1, 1/17, -7/17, -11/17) yields a state with 27 characters
Maximal unstable state={(2, 1, 1, 2), (1, 3, 2, 0), (3, 0, 0, 3), (2, 2, 2, 0), (1, 3, 1, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 0, 1, 2), (3, 1, 0, 2), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (2, 2, 0, 2), (3, 0, 2, 1), (2, 1, 0, 3), (3, 2, 0, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (2, 0, 3, 1), (3, 3, 0, 0), (2, 3, 1, 0), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(3) 1-PS = (1, -1/11, -5/11, -5/11) yields a state with 27 characters
Maximal unstable state={(2, 1, 1, 2), (3, 0, 0, 3), (2, 2, 2, 0), (4, 1, 1, 0), (2, 1, 3, 0), (3, 0, 1, 2), (3, 1, 0, 2), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (2, 2, 0, 2), (3, 0, 2, 1), (2, 1, 0, 3), (3, 2, 0, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (2, 0, 3, 1), (2, 0, 2, 2), (3, 3, 0, 0), (2, 3, 1, 0), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0), (2, 0, 1, 3)}
(4) 1-PS = (1, 1, -1/3, -5/3) yields a state with 29 characters
Maximal unstable state={(1, 3, 0, 2), (1, 3, 2, 0), (2, 2, 2, 0), (1, 3, 1, 1), (0, 3, 2, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 1, 0, 2), (0, 3, 3, 0), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (2, 2, 0, 2), (3, 0, 2, 1), (1, 1, 4, 0), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (1, 2, 3, 0), (3, 3, 0, 0), (2, 3, 1, 0), (0, 4, 1, 1), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(5) 1-PS = (1, 7/19, 3/19, -29/19) yields a state with 30 characters
Maximal unstable state={(1, 3, 2, 0), (2, 2, 2, 0), (1, 3, 1, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 0, 1, 2), (0, 3, 3, 0), (3, 1, 0, 2), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (1, 1, 4, 0), (3, 0, 2, 1), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (2, 0, 3, 1), (1, 2, 3, 0), (1, 0, 4, 1), (3, 3, 0, 0), (1, 1, 3, 1), (2, 3, 1, 0), (0, 4, 1, 1), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(6) 1-PS = (1, 7/15, 1/5, -5/3) yields a state with 30 characters
Maximal unstable state={(1, 3, 2, 0), (2, 2, 2, 0), (1, 3, 1, 1), (0, 3, 2, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 1, 0, 2), (0, 3, 3, 0), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (1, 1, 4, 0), (3, 0, 2, 1), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (2, 0, 3, 1), (1, 2, 3, 0), (1, 0, 4, 1), (3, 3, 0, 0), (1, 1, 3, 1), (2, 3, 1, 0), (0, 4, 1, 1), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(7) 1-PS = (1, 3/7, -5/7, -5/7) yields a state with 28 characters
Maximal unstable state={(2, 1, 1, 2), (1, 3, 0, 2), (1, 3, 2, 0), (3, 0, 0, 3), (2, 2, 2, 0), (1, 3, 1, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 1, 0, 2), (3, 0, 1, 2), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (2, 2, 0, 2), (3, 0, 2, 1), (2, 1, 0, 3), (3, 2, 0, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (3, 3, 0, 0), (2, 3, 1, 0), (0, 4, 1, 1), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(8) 1-PS = (1, 5/9, -1/3, -11/9) yields a state with 29 characters
Maximal unstable state={(1, 3, 0, 2), (1, 3, 2, 0), (2, 2, 2, 0), (1, 3, 1, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 0, 1, 2), (3, 1, 0, 2), (0, 3, 3, 0), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (2, 2, 0, 2), (3, 0, 2, 1), (1, 1, 4, 0), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (1, 2, 3, 0), (3, 3, 0, 0), (2, 3, 1, 0), (0, 4, 1, 1), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(9) 1-PS = (1, 1/13, -3/13, -11/13) yields a state with 28 characters
Maximal unstable state={(2, 1, 1, 2), (1, 3, 2, 0), (3, 0, 0, 3), (2, 2, 2, 0), (1, 3, 1, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 0, 1, 2), (3, 1, 0, 2), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (2, 2, 0, 2), (3, 0, 2, 1), (3, 2, 0, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (2, 0, 3, 1), (1, 2, 3, 0), (3, 3, 0, 0), (2, 3, 1, 0), (1, 1, 4, 0), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(10) 1-PS = (1, 7/11, -1/11, -17/11) yields a state with 29 characters
Maximal unstable state={(1, 3, 2, 0), (2, 2, 2, 0), (1, 3, 1, 1), (0, 3, 2, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 1, 0, 2), (0, 3, 3, 0), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (2, 2, 0, 2), (3, 0, 2, 1), (1, 1, 4, 0), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (2, 0, 3, 1), (1, 2, 3, 0), (3, 3, 0, 0), (2, 3, 1, 0), (0, 4, 1, 1), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(11) 1-PS = (1, 7/19, -9/19, -17/19) yields a state with 28 characters
Maximal unstable state={(2, 1, 1, 2), (1, 3, 0, 2), (1, 3, 2, 0), (3, 0, 0, 3), (2, 2, 2, 0), (1, 3, 1, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 1, 0, 2), (3, 0, 1, 2), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (2, 2, 0, 2), (3, 0, 2, 1), (3, 2, 0, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (1, 2, 3, 0), (3, 3, 0, 0), (2, 3, 1, 0), (0, 4, 1, 1), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(12) 1-PS = (1, 3/7, -1/7, -9/7) yields a state with 29 characters
Maximal unstable state={(1, 3, 2, 0), (2, 2, 2, 0), (1, 3, 1, 1), (4, 1, 1, 0), (2, 1, 3, 0), (3, 0, 1, 2), (0, 3, 3, 0), (3, 1, 0, 2), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (2, 2, 0, 2), (3, 0, 2, 1), (1, 1, 4, 0), (3, 2, 0, 1), (1, 2, 2, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (2, 0, 3, 1), (1, 2, 3, 0), (3, 3, 0, 0), (2, 3, 1, 0), (0, 4, 1, 1), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(13) 1-PS = (1, -1/15, -1/3, -3/5) yields a state with 27 characters
Maximal unstable state={(2, 1, 1, 2), (1, 3, 2, 0), (3, 0, 0, 3), (2, 2, 2, 0), (4, 1, 1, 0), (2, 1, 3, 0), (3, 0, 1, 2), (3, 1, 0, 2), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (2, 2, 0, 2), (3, 0, 2, 1), (2, 1, 0, 3), (3, 2, 0, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (2, 0, 3, 1), (2, 0, 2, 2), (3, 3, 0, 0), (2, 3, 1, 0), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}
(14) 1-PS = (1, -1/27, -5/27, -7/9) yields a state with 28 characters
Maximal unstable state={(2, 1, 1, 2), (1, 3, 2, 0), (3, 0, 0, 3), (2, 2, 2, 0), (4, 1, 1, 0), (2, 1, 3, 0), (3, 0, 1, 2), (3, 1, 0, 2), (3, 2, 1, 0), (3, 1, 2, 0), (3, 1, 1, 1), (2, 2, 0, 2), (3, 0, 2, 1), (3, 2, 0, 1), (1, 4, 0, 1), (2, 1, 2, 1), (4, 0, 1, 1), (2, 2, 1, 1), (3, 0, 3, 0), (2, 0, 3, 1), (1, 2, 3, 0), (2, 0, 2, 2), (3, 3, 0, 0), (2, 3, 1, 0), (1, 1, 4, 0), (2, 3, 0, 1), (4, 1, 0, 1), (1, 4, 1, 0)}


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SOLUTION TO GIT PROBLEM: STRICTLY POLYSTABLE LOCI
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Group: A3 RepresentationA3(3,3,0,0) + A3(4,1,1,0)
Set of strictly polystable states:
(1) A state with 4 characters
Strictly polystable state={(1, 3, 1, 1), (1, 2, 3, 0), (2, 0, 2, 2), (2, 1, 0, 3)}
(2) A state with 2 characters
Strictly polystable state={(1, 2, 3, 0), (2, 1, 0, 3)}
(3) A state with 6 characters
Strictly polystable state={(1, 3, 2, 0), (2, 1, 0, 3), (1, 1, 4, 0), (1, 2, 3, 0), (1, 4, 1, 0), (2, 0, 1, 3)}
(4) A state with 6 characters
Strictly polystable state={(1, 3, 0, 2), (1, 3, 2, 0), (2, 0, 3, 1), (1, 3, 1, 1), (2, 0, 2, 2), (2, 0, 1, 3)}
(5) A state with 4 characters
Strictly polystable state={(1, 3, 0, 2), (1, 2, 3, 0), (2, 0, 3, 1), (2, 1, 0, 3)}
(6) A state with 16 characters
Strictly polystable state={(2, 1, 1, 2), (0, 3, 1, 2), (1, 2, 1, 2), (0, 3, 2, 1), (0, 3, 0, 3), (2, 1, 3, 0), (3, 0, 1, 2), (0, 3, 3, 0), (2, 1, 0, 3), (1, 2, 0, 3), (3, 0, 2, 1), (1, 2, 2, 1), (2, 1, 2, 1), (3, 0, 3, 0), (1, 2, 3, 0), (3, 0, 0, 3)}
(7) A state with 10 characters
Strictly polystable state={(1, 4, 0, 1), (2, 1, 1, 2), (1, 3, 1, 1), (2, 0, 2, 2), (0, 3, 3, 0), (1, 0, 4, 1), (1, 1, 3, 1), (2, 2, 0, 2), (3, 0, 0, 3), (1, 2, 2, 1)}
(8) A state with 8 characters
Strictly polystable state={(2, 1, 1, 2), (1, 3, 0, 2), (2, 0, 3, 1), (0, 3, 3, 0), (1, 1, 4, 0), (0, 4, 1, 1), (3, 0, 0, 3), (1, 2, 2, 1)}
(9) A state with 2 characters
Strictly polystable state={(2, 2, 0, 2), (1, 1, 3, 1)}
(10) A state with 4 characters
Strictly polystable state={(2, 1, 1, 2), (0, 3, 3, 0), (3, 0, 0, 3), (1, 2, 2, 1)}