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Long-term magma ocean phases on rocky exoplanets orbiting closer to theirstar than the runaway greenhouse threshold - the inner edge of the classicalhabitable zone - may offer insights into the physical and chemical processesthat distinguish potentially habitable worlds from others. Thermalstratification of runaway planets is expected to significantly inflate theiratmospheres, potentially providing observational access to the runawaygreenhouse transition in the form of a "habitable zone inner edgediscontinuity" in radius-density space. Here, we use Bioverse, a statisticalframework combining contextual information from the overall planet populationwith a survey simulator, to assess the ability of ground- and space-basedtelescopes to test this hypothesis.  We find that the demographic imprint of the runaway greenhouse transition islikely detectable with high-precision transit photometry for sample sizes$\gtrsim 100$ planets if at least ~10 % of those orbiting closer than thehabitable zone inner edge harbor runaway climates. Our survey simulationssuggest that in the near future, ESA's PLATO mission will be the most promisingsurvey to probe the habitable zone inner edge discontinuity. We determinesurvey strategies that maximize the diagnostic power of the obtained data andidentify as key mission design drivers: 1. A follow-up campaign of planetarymass measurements and 2. The fraction of low-mass stars in the target sample.Observational constraints on the runaway greenhouse transition will providecrucial insights into the distribution of atmospheric volatiles among rockyexoplanets, which may help to identify the nearest potentially habitableworlds.

Bioverse: The Habitable Zone Inner Edge Discontinuity as an Imprint of Runaway Greenhouse Climates on Exoplanet Demographics