Completed-Observation Statistics in Metastable de Sitter Space: Beyond Expected Boltzmann-Brain Abundances

Boltzmann-brain arguments are commonly expressed through expected observer abundances. A companion causal-relational analysis showed that a completed-observation contract requires preservation of the full count distribution whenever the corresponding audit belongs to the physical contract. The present paper applies that requirement to a metastable de Sitter vacuum with spatial Poisson bubble nucleation, null bubble walls, and a supplied constant rate of completed fluctuation-origin observations per surviving physical four-volume. Bubble correlations are retained exactly. The geometry maps to a scale-invariant Poisson ball model whose critical covering theorem yields a sharp three-regime classification. Below the Page threshold, a fixed finite comoving region has a positive-probability sector with infinite surviving exposure. Above threshold, the expected total exposure is finite. At the critical equality, however, every fixed finite comoving region is completely converted after a finite random time almost surely, so the completed Boltzmann-brain count is finite almost surely, while its expectation is infinite. After ordinary observers are included on the same bubble histories through any integrable comoving production profile, the probability of Boltzmann-brain dominance conditioned on at least one ordinary observation can approach zero as the completed fluctuation rate approaches zero, despite the divergent Boltzmann-brain mean at every fixed positive rate. A realistic matter–cosmological-constant background leaves the asymptotic threshold unchanged. The remaining ambiguity is dynamical rather than statistical: semiclassical vacuum decay and conditional de Sitter detector thermality do not determine whether autonomous observer-producing transitions occur.