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The large public interest in Advanced Air Mobility (AAM) will soon lead to congested skies overhead cities, analogously to what happened with other transportation means, including commercial aviation. In the latter case, the combination of large distances and demanded number flights is such that a system with centralized control, with most of the decisions made by human operators, is safe. However, for AAM, it is expected a much higher demand, because it will be used for people's daily commutes. Thus, higher automation levels will become a requirement for coordinating this traffic, which might not be effectively managed by humans. The establishment of fixed air routes can abate complexity, however at the cost of limiting capacity and decreasing efficiency. Another alternative is the use of a powerful central system based on Artificial Intelligence (AI), which would allow flexible trajectories and higher efficiency. However, such system would require concentrated investment, could contain Single-Points-of-Failure (SPoFs), would be a highly sought target of malicious attacks, and would be subject to periods of unavailability. This work proposes a new technology that solves the problem of managing the high complexity of the AAM traffic with a secure distributed approach, without the need for a proprietary centralized automation system. This technology enables distributed airspace allocation management and conflict resolution by means of trusted shared data structures and associated smart contracts running on a blockchain ecosystem. This way, it greatly reduces the risk of system outages due to SPoFs, by allowing peer-to-peer conflict resolution, and being more resilient to failures in the ground communication infrastructure. Furthermore, it provides priority-based balancing mechanisms that help to regulate fairness among participants in the utilization of the airspace.