Abstract

The same resistant outgrowth can reflect pre-existing state, selective survival, within-cell switching or altered daughter production. We ask which observations separate these mechanisms in a finite-state continuous-time branching model with correlated sister states. An independently randomized exponential deadline, competing with the founder’s first division or death, turns the observation law into a resolvent: calibrated initial and endpoint markers together with joint daughter records recover the switching generator, the demographic rates and the daughter kernel at every finite rate and for any finite number of states, without matrix logarithms and without a diagonalizability assumption. A monitored delayed daughter readout preserves identification through an explicit channel with interruption flags. For two states we give a rational formula for the switching rate that cancels every marker determinant before it is evaluated, and we replace Hoeffding radii by Chernoff–Kullback–Leibler feature sets, of which the Hoeffding radii are exactly the Pinsker relaxation. On a synthetic two-arm dataset with uncertain calibration these two changes narrow the conservative 95%95\% induction interval from [0.362,1.498][0.362,1.498] to [0.578,1.092][0.578,1.092] per hour, around a true contrast of 0.80.8 per hour, using the same observations and the same coverage event; and they lower the certified budget of a separated-class prospective decision from 2×1062\times10^{6} to 3×1053\times10^{5} founders. Known calibration mixtures replace pure-state calibration exactly, and a six-category coarsening suffices when only within-cell switching is targeted. Finally, increasing sister concordance at fixed daughter marginals increases finite-time extinction weakly, and strictly in a stated case, while leaving every mean trajectory unchanged. These are model-conditional observation and prediction theorems, not a calibrated assay. The probabilistic arguments are conventional proofs; a declared finite-algebra subset is verified in Lean.