Five worked examples of what the 3x3 methodology can find in practice are shown. The first two are simulated scenarios that demonstrate the analytical process end-to-end. The third is a real quantitative comparison. The fourth and fifth are deeper worked examples - future changes to the global food ecosystem and the SpaceX IPO.
1. A 30-to-90-day lead time on a supply chain regime change
The setting. A global container shipping company with significant exposure to a regional chokepoint. A regional conflict is escalating. The question is structural: what is the actual risk to the network?
What a tactical view finds. Reports of naval mobilization. A high-probability forecast of a shipping lane closure. Recommendations for convoy protection and route diversion.
What the 3x3 framework finds. The conflict is not the risk. The war-risk insurance pricing is the risk. By tracking the flow of energy, materials, money, and information through the system and modeling the contract renegotiation cycles of the war-risk market, the framework identifies a 30-to-90-day lead time on a regime change in insurance pricing — well before the conflict itself peaks.
The inflection point. A structural moment at which insurance pricing transitions from stable single-band rates to a multi-band surcharge structure.
The recommended response. A brief dispatched to pre-socialize a conflict surcharge with the client’s top global shippers — written to hold up across jurisdictions and lock in contract stability before the pricing transition hit.
Why this matters. The framework turns a tactical event (the conflict) into a structural prediction (the regime change in pricing) and a concrete operational response (the Charter). The lead time is the difference between reacting to a market that has already moved and acting before it moves.
2. A patent strategy that finds the holes
The setting. A research lab evaluating a competitive patent portfolio around a navigation technology. The standard question: how strong is this portfolio?
What standard tools do. Extract keywords from the claims. Find similar patents by topic. Categorize. No strategic insight.
What a world model does. Build a structural model of the patent’s claimed mechanism. The model reveals three things:
- The innovation’s core logic. The patent does not describe a static navigation system. It creates emergent adaptive intelligence by mechanizing the relationship between navigation contexts and instruction presentation. Multiple instruction options are generated for each navigation point, and the most contextually appropriate is selected in real time.
- The commercial reality. Four distinct market opportunities: consumer navigation with premium adaptive features, enterprise fleet management, accessibility applications, and autonomous vehicle integration.
- The strategic vulnerabilities. Critical missing claims in the original patent: learning algorithms, multi-user intelligence, safety optimization, and collaborative network effects. Each gap is both a competitive vulnerability and a continuation-patent opportunity.
What this enables. A continuation patent strategy built around the missing claim categories, with priority dates that preserve freedom to operate in the most commercially valuable segments.
3. A 5-out-of-5 score against frontier models on a perception task
The task. Classify five images as Earth or Mars surface scenes, using only the visual evidence. The test was run on a frontier LLM (ChatGPT 5.2) and another frontier LLM (Claude Sonnet 4.5), with the results compared against the 3x3 framework.
The result.
| Image | 3x3 | ChatGPT 5.2 | Claude Sonnet 4.5 |
|---|---|---|---|
| 1 | ✓ | ✓ | ✗ |
| 2 | ✓ | ✗ | ✓ |
| 3 | ✓ | ✓ | ✓ |
| 4 | ✓ | ✓ | ✗ |
| 5 | ✓ | ✓ | ✓ |
| Total | 5/5 | 4/5 | 3/5 |
The 3x3 framework classified all five correctly. ChatGPT 5.2 misclassified image 2 (a terrestrial dune with blue-sky context). Claude Sonnet 4.5 misclassified images 1 and 4.
Why the error mode matters. Both frontier models rely on object-level features — texture, color, surface appearance — and miss the contextual cues (atmosphere, scale, weathering) that distinguish Earth from Mars. The 3x3 framework’s structural prior — entities, behaviors, emergents, plus the 3x3 ontology — makes the contextual cues visible. The kind of error it avoids is exactly the kind of error that matters in high-stakes applications.
The full image-by-image analysis, with the 3x3 reasoning on each one, is in the Earth-vs-Mars image study →.
What these examples have in common
Each one demonstrates the same thing: a way of seeing the system as a system, not as a list.
- Example 1 turns a tactical event into a structural prediction.
- Example 2 turns a document into a mechanism model.
- Example 3 turns a perception task into a structural classification.
In each case, the value comes from the same place: the methodology forces completeness, and completeness changes the answer.
If you have a system you want to see that way, we should talk →.
Deeper worked examples
Example 4
Three business lines at three different maturity stages, seven sequential dependencies, three scenarios, probability-weighted expected value ~$725-925B against the $1.75T IPO price.
Example 5
Global food system (2026-2050) →
Inflection at Q4 2029 (70% confidence), with a Singapore sub-analysis showing what the global finding means for one specific actor.