The question of where and how the first living system arose remains the most contested issue in contemporary astrobiology, with the debate running for decades between two schools: the submarine alkaline hydrothermal vent hypothesis and the surface “warm little pond” (hot spring) hypothesis. This article does not attempt to declare a winner. Instead, it introduces a new analytical framework — the topology of the free-energy gradient — which reframes the entire debate as a distinction between a standing vectorial gradient (the chemiosmotic proton and redox gradient across a barrier, characteristic of vents) and a cyclic temporal gradient (alternating wetting and drying, characteristic of ponds). Alongside the framework, a measurable Free-Energy Coupling Index (FECI) is proposed, scoring each environment along five dimensions: gradient persistence, vectorial coupling, spatial compartmentalization, cyclic condensation, and carbon–energy flux. A comparative synthesis of thermodynamic parameters from peer-reviewed literature (2019–2026) shows that vents achieve a high “metabolic bootstrap” score (FECI-M ≈ 0.82), whereas ponds achieve a high “replicative bootstrap” score (FECI-R ≈ 0.79). The central finding is that these two environments are not competing but thermodynamically complementary along the metabolism→replication transition: the vent provides the continuous vectorial gradient required to bootstrap carbon and energy metabolism, while the pond provides the cyclic dehydration regime required for polymerization and encapsulation. The article concludes that the origin of life is tied not to a single location but to a sequence of gradient regimes, interpreted here within a morphology of the first cause (prauzrok).