A Kontorovich–Lebedev (KL) operator is reconstructed as a spectral calculus for traces that arise in sustainable logistics, electric-vehicle packs, intelligent transportation telemetry, and digital-twin supply chains. The kernel is the modified Bessel function of imaginary order, realized as a Fourier integral that is real and even in the spectral index. Analytic continuation into a vertical strip supplies a uniform majorant that absorbs quantization, contact-resistance spikes, and demand shocks. Asymptotics at the origin and at infinity fix the natural domain as a scale of weighted Lebesgue spaces containing the usual  and weighted  classes used for current, voltage, irradiance, and order-flow signals. An adjoint identity converts forward KL analysis into a reconstruction formula suitable for residue extraction of multi-scale logistics modes and for preconditioning combinatorial assignments that later meet a quantum annealing layer. The development is theoretical and operator-theoretic; numerical illustrations are schematic envelopes rather than field trials.

Keywords: Kontorovich–Lebedev transform; modified Bessel kernel; adjoint operator; uniform estimates; spectral residues; battery telemetry; smart mobility; supply-chain resilience; digital twins; quantum logistics