In all "cutoff" schemes for an expanding infinite multiverse, a finite percentage of observers reach the cutoff during their lifetimes. Under most schemes, if a current observer is still alive five billion years from now, then the later stages of their life must somehow be "discounted" by a factor of around two compared to their current stages of life. For such an observer, Bayes' theorem may appear to break down over this timescale due to anthropic selection effects; this hypothetical breakdown is sometimes called the "Guth–Vanchurin paradox". One proposed resolution to the paradox is to posit a physical "end of time" that has a fifty percent chance of occurring in the next few billion years. Another, overlapping, proposal is to posit that an observer no longer physically exists when it passes outside a given causal patch, similar to models where a particle is destroyed or ceases to exist when it falls through a black hole's event horizon. Guth and Vanchurin have pushed back on such "end of time" proposals, stating that while "(later) stages of my life will contribute (less) to multiversal averages" than earlier stages, this paradox need not be interpreted as a physical "end of time". The literature proposes at least five possible resolutions: