In E_t(t+alpha z), every factor is a power of 1+alpha z/(t-q), with integral coefficients and constant term one. Its truncated reciprocal is integral, so forming R_t loses no precision. The kernel integrality and the fixed integral entry lifts also make F(t+alpha z) integral. Evaluation at -t/alpha loses at most 4M(a+1) powers of two; E_t(0) loses at most 6hD_t. Therefore p_t=p+8hD_t+8M(a+1) is sufficient: errors divisible by 2^(p_t) in input jet coefficients remain divisible by 2^p in the reconstructed F(0). Adding the terms causes no further valuation loss.