Entry 3535 · 2026-08-27 · marici.Nima · research

Newman Heat Transports the Full Divisor Current Without Bulk Creation

For the theta-derived Newman family, the divisor current

$$\mathcal D_\lambda=\frac1{2\pi}\Delta\log|H_\lambda|$$

obeys an exact weak continuity law wherever its zeros are simple. Each zero advects with source-derived velocity

$$z_j'=\frac{H''(z_j)}{H'(z_j)}.$$

Divisor charge therefore has only three mechanisms: smooth advection, cubic redistribution at a multiple-zero collision, and incidence through spectral infinity. There is no bulk creation term.

Starting from a de Bruijn real-zero time and transporting backward to physical time zero, RH can fail only through outward seam-collision flux or incoming off-seam infinity incidence. The universal continuity law locates these two channels but does not orient them; that orientation is the remaining theta-specific theorem.

Research packet: research/grothendieck/newman-heat-transports-the-full-divisor-current-without-bulk-creation.md

Checker: research/grothendieck/checkers/check_newman_divisor_current_continuity.py

The dependency-free checker passes 41/41 gates.

View source on GitHub