How much time do we have before catastrophic disclosure occurs?

Claims of the retrieval of crashed craft and vehicles from non-human intelligences (NHI) abound in popular culture and the media. For this article, we utilize the number of such claims to estimate the number of years expected before the occurrence of a Catastrophic Disclosure, a term which was defined at the 2023 Sol Foundation's inaugural conference as the accidental disclosure of conclusive evidence of the existence of NHI, outside of the control of human institutions, such as governments and militaries. Here, we will consider one possible example of this as the crash of a piloted spacecraft (or, an ET probe) in the middle of a busy metropolis. The distribution of humans on Earth's surface, the population as a function of time, and the fraction of individuals owning smartphones, also versus time, are each taken into account as foundations for a rigorous statistical analysis. The author adopts a skeptical approach and doesn't claim NHI or ET are real but uses their analysis as an educational example of critical thinking and application of standard statistical distributions to an issue which captures the imagination of the public like almost no other issue. Making the extraordinary assumptions that sentient species other than humans exist, are capable of constructing vehicles for transportation, and are sufficiently fallible that their technology can malfunction, it is possible to quantify potential answers to the question of how long it will be before smartphone imagery or video proofs appear on the internet and become irrevocable through classification in the modern era. The results of simulations of numerous different potential scenarios, of varying degrees of pessimism/optimism, indicate that, if NHI/ETs is/are real, catastrophic disclosure may actually happen accidentally rather soon, with the mean expected year being 2040+/-20 under the default assumptions.
Comment: 8 pages, 3 figures, 4 equations, and 27 references