PASS class list derived twice: nondegenerate GL(m,2)-orbit sizes of t-dim subspaces of Alt(m), m+t<=6: [((2, 1), [1]), ((3, 1), []), ((3, 2), [7]), ((3, 3), [1]), ((4, 1), [28]), ((4, 2), [56, 210, 280]), ((5, 1), [])] = hand classification
PASS n=5: the 3 class representatives hit the 3 nondegenerate orbits (m+t<=5) bijectively
PASS n=6: the 7 class representatives hit the 7 nondegenerate orbits (m+t<=6) bijectively
PASS Pauli predicates calibrated (route-2 literal test and concrete test): among all 12288 monomial operators on 2 qubits with phase 0 at |00>, each accepts exactly the 16 Paulis X^b Z^a
PASS n=5 TOF (m=2, t=1, idle=2): A_pi derived twice (route 1 psi-formula/Moebius, route 2 literal C_3 definition), Lemma-C certified, mutually contained, log2|A_pi| = 38 = 38 (expected 38)
PASS n=5 TOF (m=2, t=1, idle=2): A_pi = Cliff + Cliff.pi + H_pi (all 45 generators in A_pi, generated subgroup log2 size 38 = 38 by elementary divisors)
PASS n=5 TOF (m=2, t=1, idle=2): pi.D_h fixes every Z_c (c non-target) and X_tau (tau target), all 14 generators h of H_pi
PASS n=5 TOF (m=2, t=1, idle=2): all 21 kernel generators literally in C_3, Lagrangian <Z_c, X_tau Z^M_tau> with unique symmetric M
PASS n=5 B (m=4, t=1, idle=0): A_pi derived twice (route 1 psi-formula/Moebius, route 2 literal C_3 definition), Lemma-C certified, mutually contained, log2|A_pi| = 38 = 38 (expected 38)
PASS n=5 B (m=4, t=1, idle=0): A_pi = Cliff + Cliff.pi + H_pi (all 45 generators in A_pi, generated subgroup log2 size 38 = 38 by elementary divisors)
PASS n=5 B (m=4, t=1, idle=0): pi.D_h fixes every Z_c (c non-target) and X_tau (tau target), all 14 generators h of H_pi
PASS n=5 B (m=4, t=1, idle=0): all 21 kernel generators literally in C_3, Lagrangian <Z_c, X_tau Z^M_tau> with unique symmetric M
PASS n=5 C (m=3, t=2, idle=0): A_pi derived twice (route 1 psi-formula/Moebius, route 2 literal C_3 definition), Lemma-C certified, mutually contained, log2|A_pi| = 33 = 33 (expected 33)
PASS n=5 C (m=3, t=2, idle=0): A_pi = Cliff + Cliff.pi + H_pi (all 38 generators in A_pi, generated subgroup log2 size 33 = 33 by elementary divisors)
PASS n=5 C (m=3, t=2, idle=0): pi.D_h fixes every Z_c (c non-target) and X_tau (tau target), all 7 generators h of H_pi
PASS n=5 C (m=3, t=2, idle=0): all 20 kernel generators literally in C_3, Lagrangian <Z_c, X_tau Z^M_tau> with unique symmetric M
PASS n=6 TOF (m=2, t=1, idle=3): A_pi derived twice (route 1 psi-formula/Moebius, route 2 literal C_3 definition), Lemma-C certified, mutually contained, log2|A_pi| = 56 = 56 (expected 56)
PASS n=6 TOF (m=2, t=1, idle=3): A_pi = Cliff + Cliff.pi + H_pi (all 68 generators in A_pi, generated subgroup log2 size 56 = 56 by elementary divisors)
PASS n=6 TOF (m=2, t=1, idle=3): pi.D_h fixes every Z_c (c non-target) and X_tau (tau target), all 25 generators h of H_pi
PASS n=6 TOF (m=2, t=1, idle=3): all 33 kernel generators literally in C_3, Lagrangian <Z_c, X_tau Z^M_tau> with unique symmetric M
PASS n=6 B (m=4, t=1, idle=1): A_pi derived twice (route 1 psi-formula/Moebius, route 2 literal C_3 definition), Lemma-C certified, mutually contained, log2|A_pi| = 56 = 56 (expected 56)
PASS n=6 B (m=4, t=1, idle=1): A_pi = Cliff + Cliff.pi + H_pi (all 68 generators in A_pi, generated subgroup log2 size 56 = 56 by elementary divisors)
PASS n=6 B (m=4, t=1, idle=1): pi.D_h fixes every Z_c (c non-target) and X_tau (tau target), all 25 generators h of H_pi
PASS n=6 B (m=4, t=1, idle=1): all 33 kernel generators literally in C_3, Lagrangian <Z_c, X_tau Z^M_tau> with unique symmetric M
PASS n=6 C (m=3, t=2, idle=1): A_pi derived twice (route 1 psi-formula/Moebius, route 2 literal C_3 definition), Lemma-C certified, mutually contained, log2|A_pi| = 47 = 47 (expected 47)
PASS n=6 C (m=3, t=2, idle=1): A_pi = Cliff + Cliff.pi + H_pi (all 57 generators in A_pi, generated subgroup log2 size 47 = 47 by elementary divisors)
PASS n=6 C (m=3, t=2, idle=1): pi.D_h fixes every Z_c (c non-target) and X_tau (tau target), all 14 generators h of H_pi
PASS n=6 C (m=3, t=2, idle=1): all 29 kernel generators literally in C_3, Lagrangian <Z_c, X_tau Z^M_tau> with unique symmetric M
PASS n=6 SEC (m=4, t=2, idle=0): A_pi derived twice (route 1 psi-formula/Moebius, route 2 literal C_3 definition), Lemma-C certified, mutually contained, log2|A_pi| = 47 = 47 (expected 47)
PASS n=6 SEC (m=4, t=2, idle=0): A_pi = Cliff + Cliff.pi + H_pi (all 57 generators in A_pi, generated subgroup log2 size 47 = 47 by elementary divisors)
PASS n=6 SEC (m=4, t=2, idle=0): pi.D_h fixes every Z_c (c non-target) and X_tau (tau target), all 14 generators h of H_pi
PASS n=6 SEC (m=4, t=2, idle=0): all 29 kernel generators literally in C_3, Lagrangian <Z_c, X_tau Z^M_tau> with unique symmetric M
PASS n=6 TAN (m=4, t=2, idle=0): A_pi derived twice (route 1 psi-formula/Moebius, route 2 literal C_3 definition), Lemma-C certified, mutually contained, log2|A_pi| = 47 = 47 (expected 47)
PASS n=6 TAN (m=4, t=2, idle=0): A_pi = Cliff + Cliff.pi + H_pi (all 57 generators in A_pi, generated subgroup log2 size 47 = 47 by elementary divisors)
PASS n=6 TAN (m=4, t=2, idle=0): pi.D_h fixes every Z_c (c non-target) and X_tau (tau target), all 14 generators h of H_pi
PASS n=6 TAN (m=4, t=2, idle=0): all 29 kernel generators literally in C_3, Lagrangian <Z_c, X_tau Z^M_tau> with unique symmetric M
PASS n=6 EXT (m=4, t=2, idle=0): A_pi derived twice (route 1 psi-formula/Moebius, route 2 literal C_3 definition), Lemma-C certified, mutually contained, log2|A_pi| = 47 = 47 (expected 47)
PASS n=6 EXT (m=4, t=2, idle=0): A_pi = Cliff + Cliff.pi + H_pi (all 57 generators in A_pi, generated subgroup log2 size 47 = 47 by elementary divisors)
PASS n=6 EXT (m=4, t=2, idle=0): pi.D_h fixes every Z_c (c non-target) and X_tau (tau target), all 14 generators h of H_pi
PASS n=6 EXT (m=4, t=2, idle=0): all 29 kernel generators literally in C_3, Lagrangian <Z_c, X_tau Z^M_tau> with unique symmetric M
PASS n=6 TRI (m=3, t=3, idle=0): A_pi derived twice (route 1 psi-formula/Moebius, route 2 literal C_3 definition), Lemma-C certified, mutually contained, log2|A_pi| = 43 = 43 (expected 43)
PASS n=6 TRI (m=3, t=3, idle=0): A_pi = Cliff + Cliff.pi + H_pi (all 50 generators in A_pi, generated subgroup log2 size 43 = 43 by elementary divisors)
PASS n=6 TRI (m=3, t=3, idle=0): pi.D_h fixes every Z_c (c non-target) and X_tau (tau target), all 7 generators h of H_pi
PASS n=6 TRI (m=3, t=3, idle=0): all 29 kernel generators literally in C_3, Lagrangian <Z_c, X_tau Z^M_tau> with unique symmetric M
PASS diagonal classification n=1 (pi = id): A_id derived twice, certified, mutually contained; A_id = Cliff + H_id (T, CS, CCZ): all 3 generators in A_id, log2 sizes 6 = 6 = 3+3n+2C(n,2)+C(n,3) = 6 (expected 6)
PASS diagonal classification n=2 (pi = id): A_id derived twice, certified, mutually contained; A_id = Cliff + H_id (T, CS, CCZ): all 7 generators in A_id, log2 sizes 11 = 11 = 3+3n+2C(n,2)+C(n,3) = 11 (expected 11)
PASS diagonal classification n=3 (pi = id): A_id derived twice, certified, mutually contained; A_id = Cliff + H_id (T, CS, CCZ): all 14 generators in A_id, log2 sizes 19 = 19 = 3+3n+2C(n,2)+C(n,3) = 19 (expected 19)
PASS diagonal classification n=4 (pi = id): A_id derived twice, certified, mutually contained; A_id = Cliff + H_id (T, CS, CCZ): all 25 generators in A_id, log2 sizes 31 = 31 = 3+3n+2C(n,2)+C(n,3) = 31 (expected 31)
PASS diagonal classification n=5 (pi = id): A_id derived twice, certified, mutually contained; A_id = Cliff + H_id (T, CS, CCZ): all 41 generators in A_id, log2 sizes 48 = 48 = 3+3n+2C(n,2)+C(n,3) = 48 (expected 48)
PASS diagonal classification n=6 (pi = id): A_id derived twice, certified, mutually contained; A_id = Cliff + H_id (T, CS, CCZ): all 63 generators in A_id, log2 sizes 71 = 71 = 3+3n+2C(n,2)+C(n,3) = 71 (expected 71)
PASS M9 control TOF*T(idle 3): in C_3 and A_pi, dim S_U = 8 (TOF alone: 9), coisotropic
PASS negative control TOF*T(target): not in C_3, not in A_pi, S_U not coisotropic, Step-6 check rejects it
PASS control n=7 cubic permutation (nonzero triple product): a bijection, in C_3 (literal generator check), (dim S_U, dim rad S_U) = (4, 4), sum 8 < 14 so NOT semi-Clifford (Lemma A)
VERDICT PASS: C_3(5) and C_3(6) consist of semi-Clifford gates (given the reductions); n_min = 7
