Did the Gran Sasso Experiment Rule Out the Diósi-Penrose Theory? Musing on the 2021 Result and the Present Experimental Status

In 2021, a low-background experiment at the Gran Sasso National Laboratory searched for spontaneous radiation predicted by the standard Markovian Diósi-Penrose (DP) dynamics and obtained the new bound R₀ > 5.4 × 10⁻¹¹\,m at $95%$ probability for the short-length cutoff parameter. For germanium at the experimental temperature, the parameter-free prescription identifying R₀ with the spatial quantum spread of a nucleus gives R₀ 5 × 10⁻¹²\,m. That particular combination, Diósi's stochastic dynamics and the Penrose-motivated mass-density resolution, was therefore excluded. Subsequent searches strengthened the cutoff bound. The Majorana Demonstrator improved it in 2022, and XENONnT has now obtained the world-leading limits R₀ > 4.9 × 10⁻¹⁰\,m at $90%$ confidence level and R₀ > 4.5 × 10⁻¹⁰\,m at $95%$ confidence level. These advances reinforce the 2021 exclusion but do not alter its logical scope: they parametrically constrain the Markovian, effectively white-noise DP dynamics, not Penrose's (and Diósi's) lifetime criterion independently of a dynamics, and not all colored-noise, dissipative, or otherwise modified gravity-related spontaneous collapse theories. We reconstruct what Gran Sasso did and did not rule out and place that conclusion in the present experimental context.