Toward a Brain-in-a-Vat Experiment for AI Agents: Background Independence, Accessible Algebras, and Formal Limits on Meta-World Inference

This position paper formulates an experimental translation of the brain-in-a-vat scenario for artificial agents inside a background-independent relational framework. The substrate is a group-field theory whose perturbative expansion generates combinatorial spacetime histories; a test agent is a subcomplex of such a history, and its entire empirical access is carried by a declared algebra of boundary observables together with the state induced on it. This reformulation converts two previously stipulated conditions into results. Hypotheses differing only by a relational-clock reparameterization induce identical accessible states, so external pausing, checkpointing, rate change, re-execution, and hardware migration are unidentifiable in principle rather than by assumption. Hypotheses differing by an irrelevant operator at the accessible resolution have distinguishability suppressed by a power of the resolution ratio, which converts world matching from an engineering aspiration into a measurable exponent and a sample-complexity statement. The exact identification bound survives generalization: equal accessible states fix equal-prior binary discrimination at chance, and the approximate bound becomes a trace-distance ceiling over the accessible algebra that reduces to the earlier total-variation ceiling when the algebra is abelian. Accessible information across a hypothesis family is bounded by a Holevo quantity that constrains every protocol rather than ranking policies. The paper retains a graded epistemic protocol, a factorial experimental design, and precautionary ethical constraints. The substrate is a declared ontology, not an established physics of cognition; consciousness, epistemic birth, and metaphysical access remain unresolved.