Deterministic State-Space Governance of LLMs via Multi-Objective Optimization Envelopes and Jacobian Steering

As Large Language Models (LLMs) transition toward autonomous agentic roles, quantifying and mitigating the uncertainty induced by adversarial drift becomes critical. Traditional categorical guardrails fail to capture the continuous, non-binary nature of state-space divergence during complex reasoning tasks. We introduce the Multi-Objective Optimization Envelope (MOE), a statistical framework for geometric governance that quantifies alignment risk and provides deterministic trajectory correction. By utilizing Data Envelopment Analysis (DEA), we construct a convex relaxation of the model's optimal reasoning-safety frontier. We empirically demonstrate that adversarial drift manifests as severe distributional variance, quantifiable as a Mahalanobis-scaled Efficiency Deficit (mean $\beta=3.36$). To neutralize this uncertainty, MOE applies Projected Subgradient Steering, actively bounding the agent's generative trajectory within the safe operational envelope. This continuous control mechanism ensures deterministic alignment under adversarial conditions without degrading the predictive reasoning utility of the base model.