A critical question in astrobiology is whether exoEarth candidates (EECs) are Earth-like, in that they originate life that progressively oxygenates their atmospheres similarly to Earth. We propose answering this question statistically by searching for O2 and O3 on EECs with missions such as HabEx or LUVOIR. We explore the ability of these missions to constrain the fraction, fE, of EECs that are Earth-like in the event of a null detection of O2 or O3 on all observed EECs. We use the Planetary Spectrum Generator to simulate observations of EECs with O2 and O3 levels based on Earths history. We consider four instrument designs: LUVOIR-A (15m), LUVOIR-B (8m), HabEx with a starshade (4m, HabEx/SS), HabEx without a starshade (4m, HabEx/no-SS); as well as three estimates of the occurrence rate of EECs (eta_earth): 24%, 5%, and 0.5%. In the case of a null-detection, we find that for eta_earth = 24%, LUVOIR-A, LUVOIR-B, and HabEx/SS would constrain fE to <= 0.094, <= 0.18, and <= 0.56, respectively. This also indicates that if fE is greater than these upper limits, we are likely to detect O3 on at least 1 EEC. Conversely, we find that HabEx/no-SS cannot constrain fE, due to the lack of an coronagraph ultraviolet channel. For eta_earth = 5%, only LUVOIR-A and LUVOIR-B would be able to constrain fE, to <= 0.45 and <= 0.85, respectively. For eta_earth = 0.5%, none of the missions would allow us to constrain fE, due to the low number of detectable EECs. We conclude that the ability to constrain fE is more robust to uncertainties in eta_earth for missions with larger aperture mirrors. However all missions are susceptible to an inconclusive null detection if eta_earth is sufficiently low.
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