As AI systems evolve from reactive tools into persistent, planning-capable architectures, governance must extend beyond model outputs and individual actions to the world models that shape long-term behaviour. World models encode beliefs about people, resources, risks, relation- ships, and outcomes; they guide planning, justication, and future decision-making. Existing AI governance approachesrisk frameworks, content safety, and training-based alignmentdo not constrain how world models form and update beliefs about positive impact, nor how claims of benet are asserted and treated as fact. This paper introduces the Social Value Ledger (SVL): a runtime governance layer for AI world models that makes social and environmental value machine-checkable as epistemic state transitions. SVL governs how world models record commitments, register delivery events, and assert veried benet through explicit assertion typing, evidence requirements, refusal codes, and replayable receipts. SVL operates as a rst-class invariant alongside safety, consent, fairness, resource budgets, and Paris-aligned carbon guardrails. SVL does not advise users on procurement, ethics, or policy. It constrains what AI systems themselves may believe and claim about benet, independent of model family. By translating mature social value accounting practicessuch as the UK National TOMs frameworkinto world-model primitives, SVL provides a missing govern