Life–Intelligence Theorem: Temporal Meta-Control, Finite- Horizon Viability, and Epigenetic Intelligence

Living systems face a temporal trade-off between retaining information long enough to exploit environmental regularities and remaining responsive when predictive conditions change. We formulate this stability–plasticity problem as a finite-horizon control problem with explicit temporal, resource, and viability constraints. The formal results are deliberately separated. Theorem 1 is a spectral result for the scalar first-order fixed-controller subclass: strong convexity and sufficient separation of regime-specific optima imply disjoint acceptable spectral-risk sublevel sets. Proposition 1 transfers that separation to viability only when a risk-to-survival calibration is independently established; an affine stationary hazard model provides an exact case in which the spectral-risk and viability sets coincide. Proposition II addresses a different question: conditional on the existence and accessibility of a successful adaptive policy, it bounds finite-horizon survival in terms of adapted hazard, transition hazard, reconfiguration latency, switching frequency, and resource feasibility. These results do not establish that all living systems require temporal meta-control, nor do they exclude richer fixed nonlinear, recurrent, robust, or multiscale controllers. We then propose Epigenetic Intelligence as a falsifiable biological instantiation in which molecular memory systems, including, as candidates, repetitive-element/LINE-1-associated regulation, may modulate the kinetics, persistence, thresholds, or weighting of subsequent responses. The framework therefore separates a tractable mathematical result about temporal filtering from the empirical hypothesis that living systems can regulate the dynamics by which environmental information reshapes biological state.