Causal Non-Interference: Formal Definition and Core Theorems

We provide a formal definition of Causal Non-Interference (CNI) — a security property for governed AI systems that extends classical non-interference (Goguen & Meseguer 1982) by replacing information-flow security levels with identifiability states derived from causal structure. A system satisfies CNI if and only if signals in the non-identifiable state Ψ cannot produce changes in observable institutional state that are causally attributable to those signals. We prove four core results: (1) the Rooted Admissibility Invariant (RAI-Γ) is sufficient for strict CNI; (2) the CVG Separation Invariant (VALID ≠ MANDATE) is a logical consequence of CNI, not an independent axiom; (3) the Audit Illusion is formally a CNI violation through identifiability-state misclassification; and (4) the Structural Limit Theorem is the causal-geometric characterisation of precisely the condition under which strict CNI is non-trivially binding. The four standard ML deployment strategies — shadow, canary, A/B, interleaved — correspond to the four levels of the identifiability lattice, yielding the first formal safety criterion for deployment strategy selection grounded in causal structure rather than operational heuristics. Version 1.1 incorporates §5a (Probe Stability Amendments): three new formal objects — the Visibility Function V(ΔA, t), probe-induced drift δθ(ΔA, t, λ), and the Probe Stability Threshold Δθ_max — formalise the maximum tolerable actor-adaptation drift during a probe episode and provide both a pre-activation design constraint and a runtime enforcement mechanism (the Probe Stability Violation monitor). These objects provide a partial formal response to Open Question Q2 (decidability of id_state at runtime) within the bounded context of active probe episodes. Three open questions remain: CNI compositionality across system boundaries (Q1), full decidability of id_state outside probe episodes (Q2), and probabilistic extension for stochastic AI systems (Q3).