Grading the Graders: Verification Autonomy Levels (L0-L5) for LLM Reasoning

Large language models (LLMs) are increasingly paired with verifiers (step checkers, self-consistency filters, tool-based fact checkers, formal proof assistants) that claim to detect the model's errors. Yet the verification literature uses the word "level" to mean at least five different things: verification granularity, concept abstraction, risk tier, system-stack layer, and the epistemic source of the ground truth. We propose Verification Autonomy Levels (VAL), a meta-standard classifying verification schemes along a single axis: where does the verification spec come from, and what does the verdict guarantee? VAL ranges from L0 (LLM self-declaration, no deterministic anchor) through L2 (objective ground truth, correctness only) to L3/L4 (decidable systems with single-property or domain-level completeness), with L5 impossible in the unrestricted case. Central to VAL is the completeness blind spot: substitution- and sampling-based verifiers can confirm that proposed candidates hold, but cannot prove that no candidate was missed. We further identify a dichotomy the literature has not stated: completeness is reachable only for formally specifiable properties, while empirical open-world verification (fact-checking, diagnosis) caps at anchored correctness (L2). We document this across four domains (symbolic mathematics, behavior monitoring, medical diagnosis, and code generation) and in the strongest existing formal-verification baseline, whose authors note the verifier "focuses o