Decoupling Correctness from Policy: A Deterministic Causal Structure for Multi-Agent Systems

TL;DR

The paper addresses the challenge of decoupling system correctness from agent policy in asynchronous, multi-agent systems. It introduces the Deterministic Causal Structure (DCS), a policy-agnostic invariant that manifests as a unique Provenance Directed Acyclic Graph (Provenance DAG) governing the causal history. The authors present a minimal axiomatic framework and prove existence, uniqueness, policy-agnostic invariance, observational equivalence, and axiom minimality (Theorems A–C and related results), arguing that DCS provides a stronger structural guarantee than value-convergence models like CRDTs. They discuss a two-layer model of correctness, the Correctness-as-a-Chassis paradigm, and outline practical implications, including safe policy evolution, formal verifiability, and composable systems, with future work toward Byzantine resilience and a prototype framework.

Abstract

In distributed multi-agent systems, correctness is often entangled with operational policies such as scheduling, batching, or routing, which makes systems brittle since performance-driven policy evolution may break integrity guarantees. This paper introduces the Deterministic Causal Structure (DCS), a formal foundation that decouples correctness from policy. We develop a minimal axiomatic theory and prove four results: existence and uniqueness, policy-agnostic invariance, observational equivalence, and axiom minimality. These results show that DCS resolves causal ambiguities that value-centric convergence models such as CRDTs cannot address, and that removing any axiom collapses determinism into ambiguity. DCS thus emerges as a boundary principle of asynchronous computation, analogous to CAP and FLP: correctness is preserved only within the expressive power of a join-semilattice. All guarantees are established by axioms and proofs, with only minimal illustrative constructions included to aid intuition. This work establishes correctness as a fixed, policy-agnostic substrate, a Correctness-as-a-Chassis paradigm, on which distributed intelligent systems can be built modularly, safely, and evolvably.

Figures (9)

• Figure 1: The core principle of Structure-Policy Decoupling. This illustrates how, for the exact same set of generated events, different operational policies (such as message ordering, batching, or reordering) all result in the construction of the identical, unique Deterministic Causal Structure (DCS). The correctness of the causal history is thus decoupled from the infrastructural mechanics of its delivery.
• Figure 2: The internal structure of a Contribution. The immutable causal history is "soldered" into the data structure itself via the parents field, which contains the unique RIDs of its direct predecessors. This forms an unbreakable, verifiable causal chain.
• Figure 3: Violation of Axiom \ref{['ax:fairness']} (Weak Fairness). The failure to deliver a contribution to all relevant agents results in permanently divergent local states ($M_u^* \neq M_v^*$), breaking the guarantee of value convergence.
• Figure 4: Violation of Axiom \ref{['ax:semilattice']} (Join-Semilattice). Without a commutative and idempotent merge operation (e.g., using an "overwrite" logic), the final state becomes dependent on the arbitrary message arrival order, thus violating determinism.
• Figure 5: Violation of Axiom \ref{['ax:uniqueness']} (Contribution as an Immutable Fact). If the uniqueness of a rid is not guaranteed, two different contributions ($\delta_A$ and $\delta_B$) can claim the same identity. This makes the global graph ill-defined and violates structural determinism.

Theorems & Definitions (11)

• Definition 1: Contribution
• Theorem 1: Existence, Uniqueness, and Constructibility of the DCS
• Theorem 2: The Decoupling Invariant: Policy-Agnosticism
• Proposition 1: Observational Equivalence
• Theorem 3: Axiom Minimality
• Proposition 2: Separation from CRDTs
• Lemma 1: State Monotonicity
• Lemma 2: Order and Duplicate Irrelevance on Directed Sets
• Lemma 3: Decomposability and Traceability
• Lemma 4: Eventual Propagation