ENDNOTES

1. ● Snell's law as logistics analogy: the path bends at modal boundaries exactly as light bends at refractive index boundaries. The mathematical framework (calculus of variations) is identical.
2. ● Cost functional minimisation with sigma-class constraints: standard constrained optimisation. The variational formulation is the contribution — treating routing as continuous-space optimisation rather than graph search.
3. ● Autonomous vehicle platooning: demonstrated by multiple companies. Aerodynamic coupling at close spacing reduces energy consumption 10–15% for trailing vehicles.
4. ● Multi-rotor drone swarm coordination: demonstrated at research scale. Distributed load frames for coordinated heavy lift demonstrated up to 1+ tonne.
5. ● MHD seawater propulsion: demonstrated (Yamato 1, 1992). Efficiency below conventional propulsion at current field strengths. Higher-field superconducting magnets are the development path.
6. ● Evacuated tube maglev: individual components (maglev, vacuum tubes) demonstrated separately. Integrated system at hundreds of kilometres scale is an engineering development target.
7. ● Electromagnetic launch to LEO: NASA studies (Lipinski et al.) establish feasibility for cargo. Multi-kilometre tube, GW-scale power delivery, and thermal management at exit velocity remain engineering challenges.
8. ● Union Pacific constraint-driven acceleration: historical record. 10 miles of track in 24 hours documented April 1869. See Ambrose (2000).
9. ● Lobito Corridor modal lock-in: real infrastructure control mechanism. Export quotas bound to corridor designation over multi-year commitment periods.