Flouri et al.'s MSci identifiability conjecture, for clock-JC data with long loci

For every fixed finite admitted MSci model and its unchanged labelled sample panel, a finite site cutoff works uniformly over parameter pairs: complete sequence laws agree exactly when route-marginal timed-genealogy laws agree. All identifiable functionals and all genuine ambiguities transfer. Multiple introgressions, expansions, equal rates, rank-deficient routing and source-allowed inheritance endpoints are covered. The A–D compiler preserves tied ages and current-lineage routing. Trees end at the sample MRCA; route flags are marginalized. The channel is complete contemporaneous haploid data under homogeneous stationary clock-JC in mutation units. No arbitrary short-locus claim, universal cutoff over unbounded complexity, or general demographic uniqueness is made. Unknown locus-rate mixtures, unphased genotypes and other mutation/clock channels remain separate. No calendar calibration, finite-data accuracy or reliable numerical inference is supplied.

For every fixed finite admitted MSci model and its unchanged labelled sample panel, a finite site cutoff works uniformly over parameter pairs: complete sequence laws agree exactly when route-marginal timed-genealogy laws agree. All identifiable functionals and all genuine ambiguities transfer. Multiple introgressions, expansions, equal rates, rank-deficient routing and source-allowed inheritance endpoints are covered. The A–D compiler preserves tied ages and current-lineage routing. Trees end at the sample MRCA; route flags are marginalized. The channel is complete contemporaneous haploid data under homogeneous stationary clock-JC in mutation units. No arbitrary short-locus claim, universal cutoff over unbounded complexity, or general demographic uniqueness is made. Unknown locus-rate mixtures, unphased genotypes and other mutation/clock channels remain separate. No calendar calibration, finite-data accuracy or reliable numerical inference is supplied.