A single regularized transform is constructed that carries lithium-ion pack observers, thermally constrained power split, delayed multi-echelon inventory maps, and unit-load-device reallocation. Energy-throughput identities first written for formula-hybrid packs furnish the admissible current set. Incomplete telemetry from power-line carriers and swipe-access events is placed in the same dual as impulsive demand shocks. Equivalent-circuit and fractional-diffusion operators taken from automotive-cell and materials-management reviews become the kernels inverted on the Bromwich contour. Smart-mobility and solar-assisted architecture studies substitute grid, regenerative, and cruise profiles without changing the transform. Spectral residue extraction isolates thermal poles that reappear as inventory restoration modes. Green-logistics and blockchain-AI functionals attach carbon and provenance coordinates to the inverted image. Digital-twin and resilience reviews convert recovery time, lost sales, and peak inventory into contour integrals. Quantum logistics surveys and annealing studies for unit-load configuration receive a reduced coefficient vector after Gaussian regularization. Expanded time-shift and sequential-convergence identities for product kernels keep calendar lags exact. Pack estimation, control-tower twins, and combinatorial recovery are therefore instances of one operator rather than three toolchains.

 

Keywords: operational calculus, lithium-ion observers, supply-chain resilience, digital twins, quantum annealing, FKF time-shift, green logistics.