Topoethics: Individual Absolute Value through Nonlinear Dynamics and Topological Mixing

Version 2 Updates: Added experimental results to empirically support the theoretical framework. Included corresponding source code for the simulations to ensure reproducibility. Updated the manuscript to reflect these additions and refine the discussion. Abstract:We introduce Topoethics—the study of ethical consequences that arise from the topological structure of causal dynamics—and propose a mathematical framework establishing the non-negligibility of every individual existence within a deterministic chaotic model of history. Human actions are formalized as discrete impulses in a non-autonomous dynamical system on a smooth manifold. Under explicitly stated axioms—positive maximal Lyapunov exponent and topological mixing—we show that (i) every impulse induces an irreversible bifurcation of the global state vector, (ii) the resulting information is permanently embedded in the system topology rather than attenuated to zero, and (iii) the scale disparity between macroscopic human actions and Planck-scale physical resolution precludes signal truncation. We address five principal counter-arguments—noise attenuation, historical homeostasis, justification of irreversible state reduction, floating-point truncation, and macroscopic fatalism—and refute each within the framework. Ethics is reinterpreted as an engineering requirement: managing systemic indeterminacy within bounded basins of attraction, with a clear separation between the physical causality layer (L1/L2) and the institutional application layer (L7).