A Gated FKF–FKL Spectral Digital Twin for Constrained, Green, and Quantum-Enabled Logistics

Resilient logistics increasingly operate as cyber-physical systems in which sensor observations, mobility constraints, energy availability, authorization, provenance, and optimization must agree before an operational decision is committed. This reconstruction develops a gated digital-twin architecture that places an FKF–FKL spectral layer upstream of an integrity-aware dispatch layer. The spectral component separates translation, exponential intensity modulation, slow-scale FKL behavior, and residue-associated resonance; the operational component admits only observations and actions that satisfy freshness, human authorization, physical-integrity, and energy-reserve conditions. The framework therefore treats constrained resilience as a feasible-set problem rather than as a post hoc score. Digital-twin state is linked to green-logistics mode selection and blockchain-style hash-chain provenance, while quantum annealing and QUBO formulations are restricted to admissible unit-load-device configurations. IoT and intelligent transportation telemetry provide the observation stream, Industry 5.0 supplies the human-authority principle, and hybrid-electric or solar-assisted mobility supplies an energy envelope. The resulting formulation is deliberately interpretive: it unifies published instruments without claiming field validation, and it provides a reproducible mathematical structure for subsequent calibration and industrial trials. Keywords— constrained resilience; digital twins; green logistics; blockchain traceability; FKF/FKL transforms; sequential convergence; multi-echelon lead time; quantum logistics; quantum annealing; QUBO; ULD; IoT; intelligent transportation; Industry 5.0; human-centric automation; sustainable mobility; battery sizing; solar-assisted mobility; power-line communication; anti-theft; anomaly diagnosis.