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 $R_0 > 5.4 \times 10^{-11}\,\mathrm{m}$ at $95\%$ probability for the short-length cutoff parameter. For germanium at the experimental temperature, the parameter-free prescription identifying $R_0$ with the spatial quantum spread of a nucleus gives $R_0 \simeq 5 \times 10^{-12}\,\mathrm{m}$. 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 $R_0 > 4.9 \times 10^{-10}\,\mathrm{m}$ at $90\%$ confidence level and $R_0 > 4.5 \times 10^{-10}\,\mathrm{m}$ at $95\%$ confidence level. These advances reinforce the 2021 exclusion but do not alter its logical scope: they \emph{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.