This notebook presents a computational model for the classic Distributed Firing Squad Problem (FSSP), trained using the Wolfram Language's capabilities for cellular automata and graph theory. Rather than simply reproducing a known solution, this simulation serves as a didactic tool to explore the fundamental challenges of achieving "simultaneity" and "consensus" in distributed systems, an adopted focus of the Open Atomic Ethernet project.

Our approach to FSSP does not leave anything up to academic exercise. It is a re-examination of the foundational axioms of distributed computing, particularly the Forward-In-Time-Only (FITO) thinking that dominates conventional networking. As our research shows, a system's reliance on sequential, irreversible state transitions and the illusion of a global timeline is a primary cause of silent data corruption and catastrophic failures.

This simulation justifies several essential DÆDÆLUS principles. The model operates entirely without a global clock. Synchronization is an developing property of local interactions, not an imposition from a centralized time source. Rejection of global time conveniently pro-positions our critique that "Simultaneity is impossible in theory. It will therefore be problematic in practice." The system's behavior is governed by simple, deterministic local rules, reminiscent of our belief that "fully verifiable algorithms like spanning trees, failure routing, and healing must be done with local-only information." Local-first causality contrasts sharply with complex global coordination protocols that often fail under real-world conditions.

In the simulation, the final "Fire" state F is a form of local, irreversible commitment. The process of reaching this state illustrates the inductive ballet of information exchange required for even a simple form of consensus. It sets the antecedent for how fragile this process is and why we advocate for protocols that are reversible at the transactional level. As the illusion of atomicity would have it, "Atomicity is a constraint, not an assumption."

The use of the Wolfram Language allows us to treat this simulation not just as a model, but as a formal specification. By encoding the system's logic directly into executable code, we can prove properties about its behavior, such as the time required for all cells to fire, with mathematical certainty. Formal verification through computation fortifies our "Code as Proof" methodology and our commitment to using tools like Mathematica to "create executable whitepapers with computation and code."

This notebook, along with our other work in this space, is a step towards architecturally proceeding with a new class of networks where reliability is not an optional add-on but a foundational, provable property of the protocol itself. We invite the Wolfram Community to be a-part from this model and contribute to the conversation about the future of distributed systems.