What percentile sound levels identify: energy bounds, background recovery, and source combination

We determine what percentile sound levels identify about equivalent energy, background recovery and source combination. Under a nonnegative additive-energy model, partial identification yields sharp bounds over compatible distributions. Finite percentile reports leave equivalent levels unbounded above; support bounds yield sharp intervals with endpoint conditions. Background and source mean-energy intervals follow from known total distributions or percentile packages, with declared activity, support and mean constraints. Recovery conditions and an error identity separate source-off selection error from background change. Without support restrictions, substituting total-record $L_{95}$ for background $L_{\mathrm{eq}}$ has no finite error bound in either direction under at least $5\%$ exact inactivity; at least $95\%$ gives a sharp, unattained overestimation supremum of approximately $0.4576$ dB, while underestimation remains unbounded. Component percentiles yield a sharp lower bound under arbitrary dependence and a sharp envelope under justified mutual independence. Additional information gives exact independent-source intervals in specified regimes, finite reductions and certified grid bounds on bounded supports. Two fixed finite marginals permit probability, rank and exact transport bounds under dependence budgets. Percentile subtraction permits unlimited overestimation; pooling identifies the closed interval between extreme window percentiles. These results inform assessment standards and measurement reporting while distinguishing identification within a measured window from representativeness beyond it.