Net Balances and Hidden Dynamics in Reaction Networks: Internal Excursions, Stoichiometric-Kernel Fluxes, and the Limits of Endpoint Observation

Net-zero changes in measured chemical concentrations do not imply the absence of internal reaction activity. Endpoint observations may conceal transient intermediates, catalytic turnover, cyclic fluxes, and temporally unresolved excursions. This interdisciplinary preprint develops a quantitative framework for distinguishing two forms of hidden dynamics: temporal cancellation along a reaction trajectory and stoichiometric invisibility associated with nonzero fluxes in the kernel of the stoichiometric matrix. Temporal cancellation is characterized through the path length, endpoint displacement, and a cancellation index chi, whereas stoichiometrically invisible activity is analyzed through a Moore–Penrose pseudoinverse decomposition of the reaction-flux vector and an invisible-flux fraction eta. A non-identifiability result shows that identical endpoint data can be compatible with arbitrarily different internal trajectories unless additional kinetic or temporal information is available. The framework is illustrated using the analytically solvable consecutive reaction A → I → P, in which the intermediate concentration vanishes at both endpoints while reaching a positive internal maximum. The implications for experimental sampling, reaction-network analysis, steady-state fluxes, and mechanistic interpretation are discussed. The mathematical ingredients and the underlying chemical concepts are classical. The contribution of this work is a unified conceptual and diagnostic framework rather than a claim of a new kinetic law.