We introduce per-species identifiability diagnostics for template-based particle identification (PID) under Poisson counting statistics, based on the Fisher information geometry of the mixture model. The central diagnostic is the multiuser efficiency η k ∈ ( 0 , 1 ] —a quantity originating in telecommunications signal separation theory—which measures the fraction of single-species estimation precision that species k retains in the presence of all other species, capturing template overlap, abundance, and detector resolution effects invisible to pairwise separation power n σ . We show that under verified pointwise posterior dominance, deterministic maximum a posteriori (MAP) classification with natural priors can yield exactly zero recall for dominated species, and we quantify the robustness of this collapse via a dominance-margin stability lemma. We show that eigenvalue collapse of the Fisher information matrix gives a geometric diagnostic of near-nonidentifiability, and we connect Fisher geometry to classification difficulty through a Poisson-specific Kullback–Leibler (KL)–Fisher expansion with explicit remainder bounds and information-theoretic inequalities. These results are illustrated on τ -decay (7 channels) and ALICE-like π / K / p identification (3 species), and are tested with robustness and stress tests, seeded Pythia 8+ Tauola ++ generator-level τ validation ( r = 0.946 between η k and per-channel recall in both generators), and a structural comparison to published ALICE PID separation-power performance. The software implementation is described in Ablai et al (2026 Comput. Phys. Commun. 10 29).

In order to describe the heavy ion collision dynamics in hot and very dense nuclear matter formed in the overlapping region of the two colliding nuclei, we used simulated numerical calculations for FAIR available energies. We used the anti-k_T jet-detection algorithm for highlighting the main directions of flow in Au-Au collisions at CBM energies, thus obtaining structures of the events depending on the number of flow streams. The jet-finder algorithm identified domains in the y-ψ (rapidity-azimuthal angle) plane, where the number of charged particles, momenta and energy take higher values than in other areas of this plane. The anisotropic flow coefficients vn may offer information about the pressure gradients in the early stages of the collision and about the high-density nuclear matter properties. The observation of K⁺ mesons in heavy ion collisions is of interest since K⁺ mesons, due to their strangeness, have a mean free path that exceeds the dimensions of the "fireball". In the numerical calculations the interval of rapidity 0 < y < 0.8 is highlighted, for which the fluctuations of the antiparticle to particle ratio excitation functions show non-monotonic behavior in the 10-13 A GeV energy interval.

In order to describe the heavy ion collision dynamics which implies the formation of hot and very dense nuclear matter in the overlapping region of the two colliding nuclei, we used simulated numerical calculations for FAIR available energies. We used the anti-$k_T$ jet-detection algorithm for highlighting the main directions of flow in Au-Au collisions at CBM energies, thus obtaining structures of the events depending on the number of flow streams. The jet-finder algorithm identified domains in the y-$\psi$ (rapidity-azimuthal angle) plane, where the number of charged particles, momenta and energy take higher values compared to other areas of this plane. The anisotropic flow coefficients $v_n$ may offer information about the pressure gradients in the early stages of the collision and about the high-density nuclear matter properties. The observation of $K^{+}$ mesons in heavy ion collisions is of interest since $K^{+}$ mesons, due to their strangeness, have a mean free path that exceeds the dimensions of the “fireball”. In the numerical calculations the interval of rapidity $0<y<0.8$ is highlighted, for which the fluctuations of the antiparticle to particle ratio excitation functions show non-monotonic behavior in the 10–13 A GeV energy interval.