Light Cone Consistency: Toward a Unified Theory of Consistency in Message-Passing Systems

Abstract: Every distributed system -- databases, networks, postal services, CPU caches -- is a message-passing system. Every message-passing system is a growing causal log observed by a set of observers. We present Light Cone Consistency (LCC), a framework that describes every known consistency model as a configuration of three constraints on each observer's visible sub-DAG: causal closure $C(\mathrm{deps})$, fork resolution $O(π)$, and timeliness $R(δ)$, plus an orthogonal return-value function $F$. We map 85 configurations, covering all 50+ named models from Viotti and Vukolic's taxonomy, with caveats for fork-based and probabilistic models. We show that three impossibility results of distributed computing -- CAP, FLP, and AFC -- each constrain exactly one pair of parameters, and prove they are minimal and independent. Our central result is the observation that these three constraints are fully entangled: violation of any one surface cascades to the other two, because restoring any parameter requires messages -- and those messages are subject to all three constraints. The three parameters and their pairwise impossibility surfaces form a fully connected triangle. Every distributed system must exit the triangle by relaxing at least one parameter. The triangle activates only when the system is in use: $C \neq \mathrm{none}$, $O \neq \mathrm{trivial}$, or $R \neq \mathrm{absent}$ each introduces a constraint that exposes the system to the surfaces. A system that demands nothing -- or writes far slower than its propagation delay -- is trivially linearizable. We identify open problems including a conjectured fourth surface (log locality), undiscovered constraints, and the universality of the safety-liveness fork as the consequence of crossing any boundary.

• The paper's main contribution is the formulation of the Light Cone Consistency (LCC) framework using causal closure, fork resolution, and timeliness to characterize consistency in message-passing systems.
• It maps well-known models like linearizability, causal, and eventual consistency to specific configurations within its parameter space, demonstrating completeness against existing frameworks.
• It reveals the inherent safety-liveness tradeoffs in distributed systems by leveraging impossibility results (CAP, FLP, AFC) structured as a 'consistency triangle'.

Light Cone Consistency: A Unified Structural Theory for Consistency in Message-Passing Systems

Introduction and Motivation

The paper "Light Cone Consistency: Toward a Unified Theory of Consistency in Message-Passing Systems" (2605.09114) introduces the Light Cone Consistency (LCC) framework to formalize and mechanistically elucidate the space of consistency models in distributed systems. It approaches every distributed (message-passing) system as a causal Directed Acyclic Graph (DAG) and proposes a concise parameterization—causal closure $C$, fork resolution $O$, and timeliness $R$—to capture the core structural properties that define known and theoretical consistency models. This parametrization is shown to be complete with respect to existing formal frameworks and directly structurally connects the known impossibility results (CAP, FLP, AFC) as entangled boundaries in this parameter space—what the authors term the "consistency triangle".

LCC Framework Definition

At its core, LCC maps each observer’s knowledge in a message-passing system as a sub-DAG of observed messages. All standard consistency properties are recast as combinations of three visibility constraints:

• Causal closure ($C$(deps)): Determines which dependencies (ancestors) must be visible before a message is considered visible. Scope varies from none, per-key, per-session, to full explicit closure.
• Fork resolution ($O$($T$)): Formalizes to what degree concurrency (forks in the DAG) must be serialized into a total order. Scope ranges from none (partial order), per-key, per-session, per-observer, to global total order.
• Timeliness ($R(\delta)$): Specifies bounds (possibly absent) on message propagation time into each observer’s visible sub-DAG. Ranges from immediate to unbounded to absent (no liveness guarantee).

An orthogonal, fourth axis is the return-value function $F$, which dictates how returns are computed from an observer’s visible sub-DAG (e.g., "latest," "any concurrent," deterministic merge).

All consistency models in the taxonomy of Viotti and Vukolić can be represented as configurations over these axes. The framework’s expressiveness subsumes that of Burckhardt’s abstract executions, exceeding it by permitting configurations with no delivery and per-observer fork resolution.

Mapping of Consistency Models and Expressiveness

The framework’s completeness is established via a mapping from Burckhardt’s core relations—visibility, arbitration, returns-before, session order—to corresponding $C$, $O$, $O$0, and $O$1 constraints. Notably, $O$2 abstracts liveness; $O$3 and $O$4 together generate all relevant sub- and total orders of causality and arbitration. This allows the enumeration of 85 distinct configurations, covering all known but also many unnamed, potentially new models.

Noteworthy examples include:

• Linearizability: $O$5, $O$6, $O$7.
• Causal Consistency: $O$8, $O$9, $R$0.
• Eventual Consistency: $R$1, $R$2, $R$3.

The framework easily expresses "degenerate" models such as fire-and-forget messaging, as well as scenarios where guarantees are relaxed (e.g., CRDTs, Dynamo, Raft) for performance or availability.

Impossibility Surfaces and the Consistency Triangle

A central contribution is synthesizing the classical impossibility results—CAP (causal closure vs. availability under partition), FLP (consensus impossibility in async with a crash), and AFC (arbitration-free consistency)—as distinct pairwise boundaries on the $R$4 parameter space. These results are shown to be (1) minimal, (2) independent, and (3) structurally entangled:

• CAP constraints $R$5: Maintaining causal closure under network partition precludes timeliness;
• FLP constraints $R$6: Fork resolution (global ordering) cannot be achieved within bounded time in asynchronous systems with faults;
• AFC constraints $R$7: Full closure and global ordering cannot be implemented in an available (wait-free) manner, absent a serializing authority.

These boundaries do not form independent "facets" but, rather, a fully connected triangle. Any violation of one induces a cascade to the others: restoring any parameter requires message exchanges—subject to all constraints—propagating the impossibility. Thus, every non-trivial system must exit the triangle by relaxing at least one parameter.

Structural Consequences: Safety-Liveness Fork and Holographic Divergence

The authors formalize that entering the regime bounded by the consistency triangle forces a fundamental systemic choice: either safety or liveness must be sacrificed:

• Proceeding without required resolution (safety loss) leads to holographic divergence: observers maintain mutually irreconcilable but locally consistent sub-DAGs.
• Waiting for resolution (liveness loss) may result in deadlock or indefinite blocking.

This "safety–liveness fork" is conjectured to be a universal consequence for any (future) impossibility boundaries in the configuration space, not only the three known surfaces.

Open Problems and Future Directions

Several open technical directions are articulated:

• Log locality: Conjectured as a fourth impossibility surface, attaching a physical location to serialization points for total orderings, manifesting as real-time (relativistic) lower bounds.
• Missing logic and physics projections: Combinatorial explosion of metadata for causality and ordering vs. timeliness is noted as an avenue for new impossibility theorems.
• Universality conjecture: Formalizing that every boundary, including future ones (e.g., probabilistic, quantum-relativistic constraints), will enforce a safety-liveness tradeoff.

These conjectures call for formalization of boundaries involving system-wide parameters (node count, throughput, metadata), and model extensions to encompass Byzantine/fork-based and probabilistic consistency regimes.

Implications for the Theory and Practice of Distributed Systems

The LCC framework imposes a highly structural, parameterized lens on the design and analysis of distributed consistency. It offers:

• A universal model for expressing, reasoning, and extending taxonomies of consistency, consolidation of the logic and physics of distributed operation, and mechanistic mapping between known paradigms.
• A blueprint for protocol design: Systematic identification of unavoidable tradeoff loci and principled choices for where to relax strong guarantees (e.g., Paxos/Raft/Kafka/CRDTs).
• Foundational groundwork for developing new theoretical impossibility results, synthetic models, or practical protocols that make explicit where and how they escape the triangle.
• A call for unification: The message-passing DAG language demystifies consistency and impossibility into a single, observer-centric framework, inviting cross-domain applicability from distributed databases to networks, CPU caches, replicated ledgers, and beyond.

Conclusion

By reducing consistency to a triad of entangled, parameterized message visibility constraints, the Light Cone Consistency framework unifies the space of distributed system guarantees and constrains their boundaries by logically and physically grounded impossibility results. The entanglement of $R$8, $R$9, and $C$0—the "consistency triangle"—structures both the taxonomy and the tradeoff landscape. This perspective catalyzes rigorous exploration of new impossibility surfaces, deeper theory surrounding causal and concurrency metadata, and principled systems engineering in the presence of fundamentally inescapable tradeoffs.