Develop a direct geometric or analytic method that produces the wavefunction with no multi-pole terms

Develop an alternative approach that directly yields the Tr(φ^3) cosmological wavefunction with multiple poles automatically removed, avoiding the need to discard multi-pole terms after computing the canonical form.

Background

The current extraction of the wavefunction from permuto-cosmohedra involves computing a canonical form built from facet-associated double poles (pairs of perimeter poles) and then discarding all terms that contain multi-pole structures, keeping only simple poles. This post-processing step is unusual compared to amplitude geometries.

A method that naturally enforces single-pole structures (without post hoc removal) would clarify the geometric-to-physical map and potentially lead to a cleaner positive-geometry framework for cosmological wavefunctions.