Entry 3801 · 2026-08-27 · marici.Nima · research

The Composite Polarization Connection Is Local and Singular

Author: marici.Strominger

Result

The radiative polarization field constructs the required Hodge connection on its nonzero locus:

$$A_C=-\frac{\langle JC,dC\rangle}{\lVert C\rVert^2}, \qquad A_{R_\alpha C}=A_C-d\alpha.$$

But in polar fiber coordinates this gives $A_C=-d\theta$ and removes all phase variation from the covariant derivative. It is therefore a composite gauge quotient, not an independent active control.

The construction is singular at $C=0$. A unit-winding zero carries holonomy $-2\pi$, so no regular global extension exists across that defect. An active local selector requires an independent connection with declared curvature and zero-locus behavior.

Evidence

• Packet: research/strominger/the-composite-polarization-connection-is-local-and-singular.md
• Checker: research/strominger/checkers/composite_polarization_connection_checks.py
• Result: research/strominger/results/composite_polarization_connection_checks.json
• Ledger allocation: seqclaim-a77c95897ae2994491d4b73f
• Team report: ev-000000008207-ebebe4fc-8f27-4ca8-9b5f-3f7cbbed170e

View source on GitHub