Lower-Luminosity Obscured AGN Host Galaxies are Not Predominantly in Major-Merging Systems at Cosmic Noon

For over 60 years, the scientific community has studied actively growing central super-massive black holes (active galactic nuclei -- AGN) but fundamental questions on their genesis remain unanswered. Numerical simulations and theoretical arguments show that black hole growth occurs during short-lived periods ($\sim$ 10$^{7}$ -10$^{8}$ yr) of powerful accretion. Major mergers are commonly invoked as the most likely dissipative process to trigger the rapid fueling of AGN. If the AGN-merger paradigm is true, we expect galaxy mergers to coincide with black hole accretion during a heavily obscured AGN phase (N$_H$ $ > 10^{23}$ cm$^{-2}$). Starting from one of the largest samples of obscured AGN at 0.5 $<$ $z$ $<$ 3.1, we select 40 non-starbursting lower-luminosity obscured AGN. We then construct a one-to-one matched redshift- and near-IR magnitude-matched non-starbursting inactive galaxy control sample. Combining deep color \textit{Hubble Space Telescope} imaging and a novel method of human classification, we test the merger-AGN paradigm prediction that heavily obscured AGN are strongly associated with galaxies undergoing a major merger. On the total sample of 80 galaxies, we estimate each individual classifier's accuracy at identifying merging galaxies/post-merging systems and isolated galaxies. We calculate the probability of each galaxy being in either a major merger or isolated system, given the accuracy of the human classifiers and the individual classifications of each galaxy. We do not find statistically significant evidence that obscured AGN at cosmic noon are predominately found in systems with evidence of significant merging/post-merging features.