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The aim of the study is to evaluate the complexity matching between the HRVs of the group of Healers and the Healee during the various stages of the meditation protocol by employing a novel mathematical approach based on the H-rank algorithm. The complexity matching of heart rate variability is assessed before and during a heart-focused meditation in a close non-contact healing exercise. The experiment was conducted on a group of individuals (eight Healers and one Healee) throughout the various phases of the protocol over a ~75-minute period. The HRV signal for the cohort of individuals was recorded using high-resolution HRV recorders with internal clocks for time synchronization. The Hankel transform (H-rank) approach was employed to reconstruct the real-world complex time series in order to measure the algebraic complexity of the heart rate variability and to assess the complexity matching between the reconstructed H-rank of the Healers and Healee during the different phases of the protocol. The integration of the embedding attractor technique was used to aid in the visualization of reconstructed H-rank in state space across the various phases. The findings demonstrate the changes in the degree of reconstructed H-rank (between the Healers and the Healee) during the heart-focused meditation healing phase by employing mathematically anticipated and validated algorithms. It is natural and thought-provoking to contemplate the mechanisms causing the complexity of the reconstructed H-rank to come closer; it can be explicitly stated that the purpose of the study is to communicate a clear idea that the H-rank algorithm is capable of registering subtle changes in the healing process, and that there was no intention of delving deep to uncover the mechanisms involved in the HRV matching. Therefore, the latter might be a distinct goal of future research.