Do Relic Neutrinos Survive? Survival Fractions, Lifetime Scales, and Why the Temperature Budget Already Constrains Decay

If relic neutrinos decay invisibly with a rest-frame lifetime equal to the age of the universe, only 0.368 of them survive to be detected today; at ten times the age the surviving fraction is 0.905, at half the age it falls to 0.135, and at a hundred times the age it is 0.9900. This paper computes the survival bookkeeping, states the time-dilation caveat that makes the simple exponential conservative, and argues that the observed consistency of the energy-density budget already disfavours lifetimes near the cosmic age, so that a future capture experiment should plan on a substantially intact background while treating a deficit as a possible decay signal. The frame under study supplies no lifetime prediction of its own, which is recorded as an explicit gap rather than filled by assumption. Computed, not measured.