Resolve the vanishing-boost singularity in the holonomy-only closure expression

Determine how to treat configurations with vanishing boost parameter Re ω_vf in the holonomy-only expression for geometric closure, and establish whether the resulting singularity is a defect or a harmless feature restricted to nondegenerate geometric configurations.

Background

The paper extracts the face normal N_ef from a wedge holonomy through the polar decomposition of g_vf, using division by Re ω_vf. Consequently, the holonomy-only closure expression becomes ill defined at critical points where Re ω_vf=0.

The main theorem is restricted to a nondegenerate Lorentzian geometric region in which these configurations do not occur. Nevertheless, the authors leave unresolved whether the singularity reflects a genuine defect in the proposed amplitude-level implementation or is harmless because the affected configurations lie outside the sector relevant to their theorem. A complete quantum definition must specify how such sectors are handled.

References

This form also makes clear that the holonomy-only expression is ill defined at critical points with $Re\omega_{vf}=0$. We do not know whether this is a defect or a useful feature: such configurations lie outside the nondegenerate geometric region used in the theorem of Section~\ref{sec:closure-spinors}.

— Closing the Loop: from EPRL-FK spinfoams to Regge dynamics  (2609.37179 - Bruno et al., 29 Sep 2026) in Section 5, “A candidate implementation of geometric closure in the EPRL-FK amplitude”; Discussion