We introduce the Algorithmic Life Operator Theory, which models biological mortality not merely as a consequence of mechanical entropy, but as a fundamental non-linear phase transition within a topological manifold. Utilizing Rough Operator Algebra (ROA), we define the life state as a vector in a non-commutative Hilbert space subject to continuous arithmetic friction governed by the Seonggil-Riemann Error Constant (ESR). We propose that the accumulation of topological defects Θ(t) inevitably reaches a critical thresholdΘc (analogous to the DNA methylation limit). By introducing a Sigmoid Decay OperatorD(Θ(t)), we formulate the exact mathematical moment where the biological system loses its resilience, resulting in a rapid collapse of Hermiticity. This framework proves that mortality is a geometric necessity dictated by the arithmetic parameters of the universe, explicitly bridging number-theoretic topology with biological finiteness.
Seonggil Lee (Fri,) studied this question.