Extend HCM–GGC structure beyond the half-space point-target model

Determine whether comparable hyperbolically completely monotone and generalized gamma convolution structures persist for more general geometries or optical models beyond the homogeneous half-space model with a single fluorescent point target and a Robin boundary condition.

Background

The paper establishes strict unimodality of the exact time-domain diffuse-light response by representing the Robin boundary factor through a Stieltjes transform, proving hyperbolic complete monotonicity, and placing the propagation factors and their convolution in the generalized gamma convolution class. These arguments are developed specifically for a homogeneous half-space, a single fluorescent point target, and the stated Robin boundary condition.

The authors explicitly identify persistence of comparable HCM–GGC structures for more general geometries or optical models as a next question. Resolving it would indicate whether the probabilistic mechanism underlying exact strict unimodality extends beyond the setting treated in the paper.