External Operational Topologies and Internal Motion States in Energy-Transfer Systems: A Reproducible Baseline Study

This manuscript investigates whether energy-transfer optima should be understood as isolated performance points or as measurable state topologies. The study reconstructs energy-transfer behavior across three minimal physical domains: coupled RLC resonators, coupled damped mechanical oscillators, and coupled thermal bodies. Instead of treating maximum transfer, efficiency, speed, and dissipation as separate optimization targets, the manuscript interprets them as external operational states. It then separates those external states from internal energy-motion states associated with receiver storage, useful-load delivery, and internal loss. The central result is a two-layer picture of energy transfer. The external operational topology changes from domain to domain: electrical, mechanical, and thermal systems do not follow the same external route. Beneath those external differences, useful-load variation reveals a recurring internal storage-to-useful-delivery motif. This suggests that energy-transfer systems may share internal motion patterns even when their observable operational regimes differ. The manuscript is deliberately conservative. It does not claim a universal internal graph or a hybrid energy state. Instead, it provides a reproducible baseline: simulation code, state amplitudes, route reconstructions, validation maps, adjacency outputs, projection outputs, robustness outputs, and a claim-status structure. The paper introduces a validation grammar for deciding when a label becomes a supported physical state rather than merely an optimum, marker, or diagnostic variable.