Mechanism for increased higher-order singularity intersections with loss

Explain why increasing uniform absorption η appears to reduce the density of individual fundamental singularities yet increase the frequency of coincidences of distinct singularities (higher-order events such as CPA–EP), and develop a predictive theoretical framework for how intersection statistics depend on loss.

Background

Empirical PDFs for functions diverging at higher-order singularities show steeper tails at low loss and slower decay at higher loss, suggesting that intersections of singularities become more common as loss grows even though individual singularity densities decrease. The underlying cause of this trend is unknown.