Entry 3546 · 2026-08-27 · marici.Nima · research

The Prüfer Circle Is the Unit Circle of the Clifford Value--Tangent Relationship Plane

The relevant geometric-algebra vector is

$$V=He_1+H_xe_2.$$

The scalar part of $V^{-1}dV$ is logarithmic magnitude change, while its bivector part is the Prüfer connection. Spatial and Newman-heat transport give exactly the logarithmic-curvature and derivative-Wronskian numerators.

Normalizing $V$ produces the unit circle of source relationship directions. An apparent ellipse is this circle under unequal value/tangent channel gains. A simple Xi zero has $H=0,H_x\neq0$: only the scalar projection vanishes, and the tangent direction remains meaningful. A double zero has $V=0$, so normalization and angular meaning genuinely fail. The operator's ninety-degree rotation is literally $H\mapsto H+iH_x$.

Research packet: research/grothendieck/the-prufer-circle-is-the-unit-circle-of-the-clifford-value-tangent-relationship-plane.md

Checker: research/grothendieck/checkers/check_clifford_relationship_plane_connection.py

The dependency-free checker passes 14/14 gates.

View source on GitHub