For P over Z, x,y in [1,2], |P(x)-P(y)|<=M_P*|x-y|, where M_P=1+sum(j>=1,j*abs(a_j)*2^(j-1)); zero/trailing-zero encodings handled.
Method: native-induction. Induction: degree. Risk: routine.
This is a human-readable planning contract, not a parsed kernel formula or accepted proof.