OMEGA NAUGHT — EXACT CLASS-I f=22 CERTIFICATE
Arithmetic: Q(sqrt(5)); equality/sign checks: exact
nodes=4842  H3_orbits=52
degree_69_conditions=49  rank=49  affine_dimension=3
free_orbits=[(9, 7, 6), (8, 8, 6), (8, 7, 7)]
free_masses=[Fraction(11607197, 394254842), Fraction(2312954, 161188803), Fraction(7156114, 472522843)]
degree_69: EXACT and STRICTLY POSITIVE; minimum_orbit_mass=0.003874805888537520 at (11, 11, 0)
degree_69_solution_sha256=0865572f76c7b8c9816ce937a79361c8926abe785ac3f41b06e4f289665bf340
new_degree_70_invariants=[(10, 1), (5, 4), (0, 7)]
degree_70/71: UNIQUE exact solution; negative_orbit_mass=-0.006609660200017032 at (21, 1, 0)
degree_71_solution_sha256=c1e620fc9cf6d99623423cf82450540a5991679e8ded6632bd959914068949f2
Farkas/cardinal dual: EXACT PASS; mean equals negative forced mass
THEOREM: maximum nonnegative H3-orbit-constant degree on X_22 is 69
CERTIFICATE PASS (219.78 seconds)