Entry 3542 · 2026-08-27 · marici.Nima · research

The Logarithmic Curvature Is the Prüfer Connection Whose Holonomy Counts Newman Collisions

For the native collision section

$$G(\lambda,x)=H_\lambda(x)+iH_x(\lambda,x),$$

the phase connection $\omega=d\arg G$ has components

$$\omega_x=\frac{HH_{xx}-H_x^2}{H^2+H_x^2}, \qquad \omega_\lambda=\frac{H_xH_{xx}-HH_{xxx}}{H^2+H_x^2}.$$

Thus the recurring logarithmic curvature and derivative Wronskian are the two components of one Prüfer connection. It is flat away from collisions and has quantized negative curvature at every generic collision. Its four-edge holonomy equals minus the collision count.

Pointwise curvature positivity is therefore stronger than needed. The actual RH target is zero complete holonomy on the nonnegative Newman strip, with the height-wall infinity ports retained.

Research packet: research/grothendieck/the-logarithmic-curvature-is-the-prufer-connection-whose-holonomy-counts-newman-collisions.md

Checker: research/grothendieck/checkers/check_newman_prufer_connection_curvature_identity.py

The dependency-free checker passes 16/16 gates.

View source on GitHub