Comprehending cell death is one of the central topics of biological science. Currently, the criteria for microbial cell death are purely experimental, based on PI staining and regrowth experiments. The debate on how “death” should be defined mathematically, and what mathematical properties the phenomenon of ‘death’ has, is largely untouched. In the present project, we aimed to develop a mathematical framework of cell death based on the controllability of cellular states [1]. We start by defining dead states as cellular states that are not returnable to the predefined "representative living states" regardless of the controllable parameters such as the gene expression level and external culture conditions. The definition requires a method to compute the restricted, global, and nonlinear controllability, for which no general theory exists. We have developed "The Stoichiometric Rays", a simple method to solve the controllability computation for catalytic reaction systems. This allows us to compute how the enzyme concentration should be modulated to control the metabolic state from a given state to a desired state. Using the stoichiometric rays, we have computed the controllability and hence the dead states of a simple toy model of cellular metabolism as well as a rather realistic in silico metabolic model of E. coli [2]. We have also quantified the boundary that divides the phase space into the live and dead states, called the “Separating Alive and Non-life Zone (SANZ) hypersurface” [3]. In this talk I will present our framework for cell death, including stoichiometric rays. I will also discuss possible connections of the cell death framework to related fields such as dynamical systems, resource theory [4], and viability theory [5]. [1]. Himeoka et al., (2024), arXiv., https://arxiv.org/abs/2403.02169. [2]. Boecker et al., (2021), Mol. Syst. Biol., 17 (12): e10504. [3]. The Sanzu hypersurface is derived from a mythical river in the Japanese Buddhist tradition, the Sanzu River that represents the boundary between the world of the living and the afterlife. [4]. Sagawa, (2022), “Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics”, Springer [5]. Aubin et al., (2011), “Viability Theory: New Directions”, Springer