A single operational continuum is assembled in which weighted testing-function topologies carry digital-twin residuals, green-logistics energy accounts, blockchain hash-chain provenance, and quantum-annealed packing decisions. A complete, metrizable locally convex testing-function space is assembled from a countable family of exponentially weighted seminorms; sequential completeness, seminorm separation, and dual growth bounds are established so that distributional FKF and FKL transforms become continuous operators on the associated dual. The same architecture encodes hash-chain provenance, swipe-controller actuation, unit-load-device packing, multi-echelon lead-time spectra, and solar-assisted hybrid-electric energy balances as constrained resilience programmes. Mapping a non-local time-fractional space-diffusive system into the Laplace domain yields closed-form distributional kernels built from two-parameter Mittag-Leffler memory, while parabolic Talbot contours supply a numerically stable inversion route. The resulting operational continuum unifies testing-function topology, residue-based resonance extraction, Industry 5.0 human-centric automation, blockchain traceability, and QUBO formulations of disruption management.

Keywords— spectral analysis; digital twins; supply-chain resilience; green logistics; blockchain provenance; multi-echelon lead time; quantum annealing/QUBO; ULD; IoT/ITS; Industry 5.0; hybrid-electric mobility; battery sizing; solar mobility; power-line communication; anti-theft;