Geometric Dynamics of Human Olfactory Identity

Human olfactory identity is conventionally modeled through static molecular ngerprints or nite biomarker subsets extracted from volatile organic compound populations. However, molecular concentrations exhibit strong temporal instability, high-dimensional redundancy, and extended collective correlations, making isolated biomarker representations structurally fragile. In the present work, biological identity is reformulated as a dynamical geomet- ric phenomenon emerging from correlated collective organization inside a reduced biological manifold. Starting from high-dimensional molecular congurations, we construct a normalized covariance geometry whose spectral decomposition reveals strong dimensional collapse and the emergence of a low-dimensional collective con- guration space. Within this manifold, biological states evolve as continuous trajectories rather than isolated molecular snapshots. Structural similarity is dened through normal- ized geometric operators, inducing intrinsic geodesic distances over the population. The framework introduces geodesic drift, acceleration, curvature, and connement dynamics as fundamental descriptors of biological stability. A central result of the analysis is the emergence of stable structural basins associ- ated with persistent biological identities. Under perturbation, biological trajectories undergo basin transitions accompanied by curvature amplication, metastability, hysteresis, and geodesic instability. Critically, the analysis shows that topologi- cal basin transitions can occur before complete observable molecular degradation becomes macroscopically detectable. The framework therefore suggests that biological pathology may correspond to geometric instability inside a collective manifold rather than to isolated molecu- lar abnormalities. This opens the possibility of predictive geometric diagnostics based on structural deformation and topological instability preceding conventional biomarker emergence. All results presented in this work emerge directly from the internal geometric and spectral organization of the biological population without supervised classication, externally imposed biomarkers, or phenomenological tting procedures.