Proof of `Local analytic realization of generating series` (2nd statement)
What this proof establishes
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Use normalized, centered polynomial residuals as coordinates on the residual-kernel annihilator. Both the output and the letter residuals of the coordinates satisfy (C), so their coordinate expressions converge.