Capability alone is insufficient to legitimize autonomous action. Traditional approaches rooted in the science of behavior emphasize measuring outcomes such as accuracy, efficiency, latency, and robustness, treating observed effects as the ultimate standard of evaluation. Yet behavior alone cannot answer the deeper governance question: should the system act now, at what scope, and under which safeguards? For this, a complementary discipline — the science of intention — is required, one that treats intent as a computable, runtime object with provenance, constraints, and reversibility guarantees. Behavior tells us what is likely to happen; intention tells us why it is justified to happen and under what conditions. Together, these sciences form a dual lens: behavior provides efficacy, while intention provides legitimacy. We propose a geometric view of intention in which the curvature of the causal trajectory — spanning purpose, policy, plan, action, and outcome — becomes a live constraint on authorization. Smooth, low-curvature trajectories reflect reversible, traceable, and convergent execution, where autonomy may scale safely. High-curvature trajectories reflect costly reversals, broken traces, or abrupt semantic pivots, where autonomy must pause or shrink. Just as in physics mass curves spacetime, here misalignment loads curve the manifold of intention, bending the path of decisions and slowing authorization. The least-curvature route functions as an ethical geodesic: the safest rollout of intent under evidence. This analogy renders prudence not as a rhetorical aspiration but as a measurable runtime law that governs when systems may accelerate and when they must hesitate. For AGI, the advantage of this framework lies in transforming hesitation, rollback, and de-escalation into first-class capabilities. The runtime authorization gate Authorizationʳ = Wʳ · iFlwʳ · μʳ, modulated by intention curvature κᵢ constrained to a safe band, ensures that autonomy expands only where causal integrity remains intact. By coupling readiness, intention flow, and causal closure with geometric prudence, AGI systems earn the right to act not merely through raw capability but through evidence of alignment. In practice, this integration allows autonomy to contract under drift, uncertainty, or adversarial shocks, and to re-expand as reversibility and traceability recover. Systems that sustain smooth and auditable causal paths are not only effective in behavior but also wise in intention, embodying legitimacy as well as performance.