Human Anchor: A Cross-Layer Authority Invariant for Many-Agent AI Systems

Advanced AI may eventually exist as very large populations of persistent, tool-using, delegated agents, making per-agent human supervision an inadequate scaling assumption. This paper formalizes Human Anchor as a cross-layer authority invariant intended to preserve effective independent human refusal over high-impact and irreversible authority transitions. The formal core defines a Human-Revisable Authority Region and proves that if every transition available to a specified AI coalition without fresh independent Human Anchor authorization preserves that region, then no finite unanchored execution by the coalition can leave it. The theorem schema has no explicit dependence on total finite agent population, including the modeled grand coalition, although verification and implementation difficulty may still scale sharply with system size. The paper extends the invariant to dynamic authority-bearing changes, including identities, credentials, issuers, delegation, tools, policies, restart mechanisms, substrates, and actuators. A Human-Anchor Authority-Sound Simulation states the conditions under which the abstract invariant transfers to a real authority system. A dependency-closed epoch bridge prevents new protected authority from becoming active while the previous model-to-reality relation is stale and the next relation has not yet been validated. The paper further develops resource-side complete mediation, Anti-Bypass authority reduction, timing before causal lock-in, and explicit limit conditions for external unmediated authority domains. A separate many-agent implication shows that if conditional shared-catastrophe hazard remains bounded below by a positive constant, long-run collective survival probability tends to zero without requiring independence. Under explicit payoff conditions, reciprocal Human Anchor can be individually rational for survival-valuing agents, motivating its interpretation as a possible mutual-survival infrastructure rather than only a human-over-AI control mechanism. The paper does not claim that arbitrary superintelligence is controllable, that verification complexity is independent of agent count, or that Human Anchor guarantees civilization survival. Its purpose is to make the assumptions behind effective human refusal explicit, formal, and falsifiable. AIS-HA (AI’s Human Anchor) is the paper’s operational criterion for a conjunctive judgment over structural refusal, boundary/path coverage, human independence/effectiveness, authority observability, and timing.