This study writes one dual-space operator chain that takes irregular freight, energy, and authorization traces into a single spectral state. Weighted test functions control growth and derivative order together, so pulses, currents, and token jumps remain comparable without a smoothness assumption. A countable family of seminorms induces a Fréchet metric; sequential telemetry is then a Cauchy problem rather than a visual trend on a dashboard. The two-sided Fourier–Kontorovich–Lebedev pairing splits clock oscillation from positive scale, and the shift and modulation identities keep origin changes distinct from structural change. Residue markers extract recurrent echelon cycles. Hereditary recovery is expressed by a Caputo generator whose Laplace image inverts through Mittag-Leffler kernels or a Talbot contour when a closed form is missing. Only after that state is declared admissible do emission costs, hash-chain provenance, human authorization, pack energy, and a QUBO annealer act. The analytic identities are retained; the contribution is to read them as operational constraints on a cyber-physical freight network rather than as isolated transform facts.

A. A Gupta,"Distributional Mixed-Kernel Analysis for Adaptive Freight Networks with Memory Dynamics, Provenance Constraints, and Annealed Assignment" International Journal of Advanced Multidisciplinary Research and Educational Development, V2(5): Page(342-345) September - October 2026. ISSN: 3107-6513. www.ijamred.com. Published by Scientific and Academic Research Publishing.