Inconsistent outputs and hallucinations from large language models (LLMs) are major obstacles to reliable AI systems. When different proprietary reasoning models (RMs), such as those by OpenAI, Google, Anthropic, DeepSeek, and xAI, are given the same complex request, they often produce divergent results due to variations in training and inference. This paper proposes a novel consensus mechanism, inspired by distributed ledger technology, to validate and converge these outputs, treating each RM as a black-box peer. Building on the Hashgraph consensus algorithm, our approach employs gossip-about-gossip communication and virtual voting to achieve agreement among an ensemble of RMs. We present an architectural design for a prototype system in which RMs iteratively exchange and update their answers, using information from each round to improve accuracy and confidence in subsequent rounds. This approach goes beyond simple majority voting by incorporating the knowledge and cross-verification content of every model. We justify the feasibility of this Hashgraph-inspired consensus for AI ensembles and outline its advantages over traditional ensembling techniques in reducing nonfactual outputs. Preliminary considerations for implementation, evaluation criteria for convergence and accuracy, and potential challenges are discussed. The proposed mechanism demonstrates a promising direction for multi-agent AI systems to self-validate and deliver high-fidelity responses in complex tasks.