The confluent Kelvin atlas: embedding passive Bessel media into Tricomi memory laws

Classical Bessel media provide exact passive memory laws for radial diffusion and viscoelastic damping, yet their rigid structure locks high-frequency square-root responses to fixed low-frequency exponents. We demonstrate that these media represent a symmetric trajectory within a broader two-parameter ‘confluent Kelvin atlas’, derived from the exact connection between modified Bessel functions and Tricomi's confluent hypergeometric function. Off-trajectory Tricomi ratios deform the Kelvin dissipation profile, decoupling the low-frequency memory exponent while preserving the universal high-frequency square-root onset. We derive the asymptotic structure of this deformation, clarify generalized loss factor sign conventions, and provide numerical illustrations of generalized Kelvin profiles and atlas geometry. Finally, we distinguish the Bessel passivity certificate from the broader off-trajectory Stieltjes problem, outlining a route toward full two-edge Gauss-hypergeometric generalizations.