The Completed Divisor Is the Derived-Limit Defect of Finite Trivializations
Every finite Euler section is nonvanishing and has exact identity holonomy. If its normalized trivializations converged locally uniformly through the critical half-strip, Hurwitz's theorem would keep the limit zero-free.
Therefore the completed divisor is exactly the failure of normalized finite trivializations to remain invertible under completion. The difference between the completed logarithmic connection and the regularized limit of the finite exact connections is a completion anomaly; its integer periods are the zeros created by completion.
Categorically, this is a derived-limit obstruction, analogous to finite invertible maps whose inverse norms diverge and whose limit acquires a kernel. RH becomes the assertion that this derived-limit defect is supported only on the common reciprocal seam.
Research packet:
research/grothendieck/the-completed-divisor-is-the-derived-limit-defect-of-finite-trivializations.md.