pi_+ : ['0', '0', '1/10', '1/5', '1/10', '3/10', '1/5', '1/10']
pi_- : ['2/11', '2/11', '3/22', '1/11', '3/22', '1/22', '1/11', '3/22']
level one (-1/4,-1/8,-1/8): classes {1},{2,3}; supp pi_+ misses: [(1, 1, 1), (1, 1, -1)]
h' = h raised by 1 at ++-: 8h' = -2 - y1 - 2y3 - y1y2 - y1y3 - 2y2y3 + y1y2y3  [exact]
rho_+ : {'++--': '1/10', '+-+-': '1/10', '+---': '1/5', '-++-': '1/10', '-+-+': '1/10', '-+--': '1/10', '--++': '1/10', '--+-': '1/10', '---+': '1/10'}
rho_- : {'++++': '1/11', '+++-': '1/11', '++-+': '1/11', '++--': '1/22', '+-++': '1/11', '+-+-': '1/22', '+--+': '1/11', '-+++': '1/11', '-++-': '1/22', '-+-+': '1/22', '-+--': '1/22', '--++': '1/22', '--+-': '1/22', '---+': '1/22', '----': '1/11'}
rho_b >= 0; (x,z,v) ~ (w2,w3,w1), (x,z') ~ (z,z') ~ (w2,w3), (z',v) ~ (w3,w1) under pi_b; w2 ~ w3  [exact]
8R = -2 - x - z' - v - xv - xz' - zz' - z'v + xzv = -(nonnegative products), so R <= 0 on [-1,1]^4; R vanishes at 10 vertices including all atoms of rho_+  [exact]
flipping the class [1] gives (-1, 1, 0, -1, -2, -2, -1, 0), in the orbit of rep9, classes kept  [exact]
flipping the class [2, 3] gives (0, -1, -2, -2, -1, 0, 1, -1), in the orbit of rep9, classes kept  [exact]
1360 random exact tests (k <= 3, every nu): Gamma <= Gamma'[pi] = E_rho[R] <= 0 in every case; largest Gamma' = 0 (k=1, nu=(1,))
rep1 (and rep9) trivial: Gamma_nu(F) <= 0 for every k, nu and class-wise decoder  [proof in MAIN_RESULT.tex]
