What makes something matter to an agent? In reinforcement learning systems, the answer is fixed by an external designer through a reward function; in living beings, it emerges from a single demand: remaining viable. This work proposes G-EMV, a geometric architecture of homeostatic orientation in which this criterion of relevance emerges from the structure of the agent itself, without being specified from outside. The state is defined over three survival domains (physical, resource, and social), each governed by two independent opponent forces, one of gain and one of loss. From them, two separable quantities are derived: position (their difference) and tension (their sum), so that two states with identical position may differ in their internal load. Through agent simulations, the work shows that several non-trivial adaptive phenomena emerge from this geometry without specific programming, each depending on a distinct structural mechanism and verified by ablation. The model also admits an affective interpretation, whose validation with human subjects lies beyond the scope of this work.