The Consistency Bound: Cognitive Ownership and the Limits of Shared World Models in Multi-Agent Autonomous Systems

The Predictive Organization Bound (POB) showed that the fractional reduction in waste a factory control policy can achieve is bounded by the predictive information (Iₚred) its world model holds about the future; the Embodiment Bound (PE) showed that Iₚred is itself capped by sensing hardware. Both wrote "the world model" as a single coherent object. In any real autonomous system it is not: many agents, sensors, and models compete to maintain a shared representation of reality, and that representation can become inconsistent — a race condition in knowledge. This paper asks whether the ownership discipline that keeps Rust's view of memory consistent generalizes to keep a multi-agent system's view of reality consistent. It makes beliefs a first-class type, Belief = (value, confidence, provenance, timestamp), and defines a cognitive borrow checker enforcing three disciplines, each the knowledge-domain image of a memory hazard Rust prevents: freshness lifetimes (a belief used past its predictive half-life is a use-after-free), single-writer-xor-many-observers mutation (unsynchronized writes are a data race), and confidence-weighted fusion over provenance (last-writer-wins is a lost ownership transfer). The usable predictive information is Iconsistent = Iₚred − Lₛtale − Lᵣace − Lfusion+, and delivered value obeys ΔV ≤ Φ· (1 − 2^ (−2 Iconsistent/dₑff) ) — POB's ceiling with the coherent-model assumption replaced by a measured consistency efficiency χ. The bound is presented honestly as a specialisation of POB (itself a specialisation of the Touchette–Lloyd limits of control), not a new inequality; the contribution is isolating the three consistency losses and the Rust discipline that closes each. On seeded simulations with bootstrap confidence intervals: a belief's predictive value decays with age and its freshness lifetime tracks the world's mixing time (taufresh = 0. 50 tauₘix) ; a belief race destroys predictive information at equal mean age (Lᵣace = 0. 049 0. 044, 0. 055 bits at 20 writers, surviving a nonlinear readout) and the borrow check recovers it; confidence-weighted fusion's value over a provenance-blind average grows with sensor heterogeneity (0 to 2. 94 bits) ; a fixed 0. 95 confidence gate delivers its promised safety only when calibrated (0. 985 vs 0. 927 GO-safety, overconfident violating the contract) ; a predictive borrow check prevents collisions in proportion to the predictive horizon (recovers-iff tauₚ >= m, 0 to 100%) ; uncoordinated decision races scale with agent count (5 agents lose 22% of decisions, 50 lose 84%; the borrow check loses 0%) ; and full cognitive ownership recovers chi = 0. 998 0. 996, 1. 001 of the POB ceiling with no regime exceeding the bound. On recorded data (an 862-sensor freeway network) beliefs about real flow have a finite lifetime (taufresh approx. 16 h), inverse-variance fusion of real heterogeneous sensors beats last-writer-wins by 0. 75 bits, and the ceiling is never violated (0/6). Two of the seven simulation results (fusion optimality, the additive composition of Gaussian losses) are identities, reported as consistency checks rather than tests. All core plants are synthetic apart from the recorded-data grounding; a real multi-agent closed-loop trace remains the decisive open test. The broader, explicitly speculative programme it instantiates (the Predictive Reality Hypothesis) is developed separately and is not relied upon for any claim here. Code and figures: see the supplementary archive.