= Formal monodromy correction to an entire-system Stokes product
{title2=$S_N\cdots S_1=M_f^{-1}$}
When Stokes factors act on solution coefficient vectors, a full positive turn gives their ordered product equal to the inverse of <formal monodromy> for a <polynomial> system with no finite singularities. The true <fundamental matrix> is entire, so its actual <monodromy> is trivial, but its normalized formal branch changes by $M_f$. Indeed, write $Y_{j+1}=Y_jS_j^{-1}$; then $Y_{N+1}=Y_1(S_N\cdots S_1)^{-1}$, whereas normalized continuation after the positive turn gives $Y_{N+1}=Y_1M_f$. Cancelling the invertible <fundamental matrix> proves the identity. The uncorrected product is identity only when $M_f=I$. For a cubic-exponential two-by-two system with $U=1,V=-1,P=1,R=2,d=3/2$, the formal exponent is $\theta=1/2$, so $M_f=-I$ and the Stokes product is $-I$.
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