The Geometry of U.S.–China Cooperation

A two-part systems analysis of where America and China can create mutual strength, using verified data, correlation mapping, nonlinear joint-gain scoring, and scenario simulation instead of ideology or opinion.

Image @ PYURA ANSHUMAN

PART I

Beyond Rivalry: How I Built a Mathematical Map of U.S.–China Win-Win Cooperation

For a long time, most conversations about the United States and China have been trapped inside one frame:

competition.

Who leads in AI? Who controls semiconductors? Who dominates manufacturing? Who wins the next geopolitical century?

Those questions matter.

But they are incomplete.

I wanted to ask a different question:

Where can the U.S. and China work together in a way that makes both stronger?

Not sentimentally.

Not diplomatically.

Mathematically.

I wanted to move away from narrative and build a systems model that asks:

Which cooperation domains create mutual gain,
global spillover,
and manageable strategic risk?

This is important because U.S.–China relations are not just bilateral. They are embedded inside the operating system of the world economy.

The U.S. and China are the world’s two largest economies, with 2024 GDP of about $28.75 trillion for the U.S. and $18.74 trillion for China, according to World Bank data.

Their trade relationship also remains enormous. USTR estimates U.S. goods and services trade with China at $658.9 billion in 2024.

So I began from one premise:

If these two systems only compete, the world absorbs the friction. If they cooperate in the right domains, the world absorbs the stability.

The question is how to identify those domains objectively.

Step 1: I Reframed the Question

Most U.S.–China analysis begins with conflict domains:

Semiconductors
Taiwan
AI
Trade deficits
Military balance
Export controls
Supply chains

But I wanted to build the opposite map.

Not:

Where do they clash?

But:

Where does cooperation create joint system strength?

That changed the entire structure of the analysis.

A good cooperation domain must satisfy five conditions:

1. The U.S. gains.
2. China gains.
3. The world system gains.
4. Strategic risk is manageable.
5. Feasibility is not zero.

This is why I did not want a simple opinion piece.

I wanted a model.

Step 2: I Chose 12 Cooperation Domains

I selected 12 areas where U.S.–China cooperation could plausibly matter at global scale:

This set gave me a broad enough system.

It included public goods, macroeconomic stability, frontier technology, and security-sensitive domains.

Step 3: I Identified Verified Data Anchors

The model needed to be grounded in real-world data.

So I used public, credible sources.

For macro scale, I used World Bank GDP data for the U.S. and China.

For bilateral trade exposure, I used USTR’s official U.S.–China trade summary, which reported $658.9 billion in goods and services trade in 2024.

For value-chain interdependence, I used OECD TiVA conceptually because TiVA tracks origins of value added in exports, imports, and final demand, which is more useful than gross trade alone.

For clean energy, I used IEA-linked investment data showing China at roughly $675 billion in clean-energy investment in 2024 and the U.S. as a major clean-energy investment node.

For AI, I used Stanford University AI Index 2025, which reported U.S. private AI investment at $109.1 billion in 2024, nearly 12 times China’s $9.3 billion.

For climate, I used the Global Carbon Project, which projected fossil CO₂ emissions at 37.4 billion tonnes in 2024, up 0.8% from 2023.

These were not all the data we would eventually need for a full empirical paper, but they were sufficient to build the first objective framework.

Step 4: I Defined the Scoring Variables

For each domain, I scored seven variables on a normalized scale from 0 to 1.

This structure mattered because some domains are valuable but nearly impossible.

For example, semiconductors have enormous mutual value, but also very high strategic sensitivity.

Climate has massive global spillover and lower direct military risk.

AI safety has huge future importance, but trust friction is high.

So the model had to reward benefit while punishing risk.

Step 5: I Built the Nonlinear Joint-Gain Function

A simple average would not work.

If a domain gives large benefit to one side and almost none to the other, cooperation will collapse.

So I used a nonlinear multiplicative structure:

Jᵢ = (B_USᵢ^α × B_CNᵢ^β × Sᵢ^γ × Cᵢ^δ × Fᵢ^θ) / (1 + Rᵢ^η + Tᵢ^λ)

Where:

The reason for using multiplication in the numerator is simple:

If either side gains very little, the joint-gain score falls sharply.

The reason for using risk and trust in the denominator is also simple:

Even high-value cooperation fails 
if strategic risk and mistrust become too large.

This is more realistic than a linear model.

A cooperation domain must survive both incentive logic and geopolitical friction.

Step 6: I Chose the Baseline Exponents

For the baseline model, I used:

α = 1.0
β = 1.0
γ = 1.2
δ = 1.1
θ = 1.0
η = 1.4
λ = 1.2

Why?

Because I wanted global spillover and complementarity to matter slightly more than ordinary bilateral benefit.

I also wanted strategic risk to penalize more strongly than trust friction, because some domains are structurally dangerous even if diplomatic mood improves.

That is why semiconductors still remain difficult even in a better political scenario.

The technology is simply too strategic.

Step 7: I Built the Correlation Matrix

After scoring each domain, I represented each one as a vector:

Domain Vector = [US Benefit, China Benefit, Spillover, Complementarity, 
Feasibility, Risk, Trust]

Then I compared the domains using cosine similarity:

Corr(i,j) = (Vᵢ · Vⱼ) / (||Vᵢ|| ||Vⱼ||)

This shows which cooperation areas naturally cluster together.

For example:

Climate + clean energy + food security + health

Cluster X: because they share public-good characteristics.

Trade + supply chains + financial stability + critical minerals

Cluster Y: because they stabilize global economic flows.

AI safety + semiconductors + space + science

Cluster Z: because they involve advanced technology, dual-use risk, and strategic trust issues.

This correlation matrix does not tell us who is morally right.

It tells us which domains share structural profiles.

That is the point.

Step 8: I Built the First Baseline Score Table

The initial normalized table looked like this:

Image @ PYURA ANSHUMAN

These inputs are not presented as final truth.

They are a transparent modeling layer.

The point is to show how the analysis was constructed.

Step 9: The First Major Finding

The model produced one important early conclusion:

The highest-value domains are not automatically the best 
cooperation domains.

Semiconductors are a perfect example.

They score extremely high in mutual benefit and complementarity.

But they also score extremely high in strategic risk and trust friction.

So their final cooperation score is pulled down.

This is the central mathematical insight:

Strategic sensitivity can overpower economic value.

That is why the strongest cooperation areas are not necessarily the most glamorous technologies.

They are often the domains where mutual benefit is high and security leakage is manageable.

That sets up Part II.

PART II

The Cooperation Matrix: What the Numbers Suggest America and China Should Work On Together

In Part I, I explained the model.

I did not want to ask whether America or China is stronger.

I wanted to ask:

Where does cooperation make both stronger?

So I built a nonlinear joint-gain function and a correlation matrix across 12 cooperation domains.

The model used verified anchors from GDP, trade, clean energy, AI investment, emissions, and value-chain data.

Now comes the more important question:

What did the model suggest?

The First Output: Cooperation Clusters

The correlation matrix produced three broad cooperation clusters.

Cluster 1: Planetary Stability

Climate
Clean energy
Food security
Health security

These domains cluster together because they have:

• high global spillover
• direct benefit to both countries
• lower military leakage risk
• strong public-good characteristics

This is the easiest cooperation basket to justify.

Both countries are exposed to climate risk, food-system instability, health shocks, and energy-transition pressures.

The Global Carbon Project’s 2024 emissions estimate shows why this matters. Fossil CO₂ emissions are still rising globally, reaching a projected 37.4 billion tonnes in 2024.

This is not a symbolic area.

It is a planetary operating constraint.

Cluster 2: System Stability

Financial stability
Trade stabilization
Supply-chain resilience
Critical minerals

This cluster is about preventing shocks from cascading through the world economy.

The U.S. and China remain deeply linked through trade. USTR’s 2024 estimate of $658.9 billion in goods and services trade shows that decoupling is much easier to say than to execute.

OECD TiVA matters here because gross trade does not fully show supply-chain dependence. TiVA tracks where value is actually created and how it moves through exports, imports, and final demand.

This cluster is not about friendship.

It is about preventing system shock.

Cluster 3: Future Stability

AI safety
Scientific research
Space and climate observation
Semiconductors

This is the most interesting but also the most difficult cluster.

The gains are huge.

The risks are also huge.

Stanford AI Index shows why AI matters structurally. In 2024, U.S. private AI investment reached $109.1 billion, while China’s reached $9.3 billion, but China remains highly active in AI publications and patenting.

This creates complementarity.

The U.S. has frontier capital, model ecosystems, cloud infrastructure, universities, and major AI firms.

China has deployment scale, industrial AI capacity, manufacturing depth, and research volume.

But the trust problem is severe.

AI safety cooperation is therefore necessary and difficult at the same time.

The Preliminary Ranking

Using the nonlinear scoring framework, the likely ranking of cooperation domains looked like this:

This ranking does not mean semiconductors are unimportant.

It means they are difficult to cooperate on directly.

That is a very different conclusion.

The Most Important Inference

The key result was this:

Semiconductors may be the highest-value domain,
but not the highest-cooperation domain.

Why?

Because the denominator explodes.

Strategic Risk + Trust Friction

If risk and mistrust become too high, even enormous economic benefit cannot generate stable cooperation.

That is the logic of the model.

Scenario Simulation

Then I tested three geopolitical scenarios.

Scenario 1: Low Trust

Assumptions:

Feasibility decreases by 25%
Trust friction increases by 25%
Strategic risk increases by 10%

Under this scenario, only low-security public-good cooperation survives.

Likely surviving domains:

Food security
Health
Climate monitoring
Financial crisis communication

This is the world where rivalry dominates.

Cooperation does not disappear.

But it retreats into narrow survival corridors.

Scenario 2: Managed Competition

Assumptions:

Feasibility baseline
Trust friction baseline
Strategic risk baseline

This is the most realistic near-term scenario.

Likely strongest domains:

Climate
Clean energy
Financial stability
Health
Food security
Trade stabilization

This is where I think U.S.–China cooperation has the highest probability of real implementation.

Not because the two countries trust each other deeply.

But because the cost of not coordinating is high.

Scenario 3: Strategic Reset

Assumptions:

Feasibility increases by 25%
Trust friction decreases by 25%
Strategic risk decreases by 10%

In this scenario, more advanced domains become possible:

AI safety
Clean energy
Trade stabilization
Supply chains
Scientific research
Climate

But even here, semiconductors remain difficult.

Why?

Because the dual-use nature of advanced chips does not vanish simply because diplomatic mood improves.

This is why some domains are structurally cooperative, while others are structurally contested.

What the Numbers Really Say

The model suggests three cooperation bundles.

Bundle 1: Stabilize the Planet

Climate
Clean energy
Food security
Health security

This is the highest legitimacy bundle.

It produces mutual benefit while reducing global risk.

Bundle 2: Stabilize the System

Financial stability
Trade stabilization
Supply-chain shock prevention
Critical minerals transparency

This bundle prevents global shocks.

It is less idealistic and more pragmatic.

Bundle 3: Stabilize the Future

AI safety
Scientific standards
Space and climate observation
Limited semiconductor guardrails

This is the hardest but most important long-term bundle.

It does not require full technological trust.

It requires guardrails.

My Final Conclusion

The U.S. and China do not need to cooperate everywhere.

That is unrealistic.

They should cooperate where:

systems are shared
collapse risk is mutual
security leakage is manageable
global spillover is large

They will continue competing where sovereignty is strategic.

That is normal.

The real question is whether they can build enough cooperation architecture around shared risks to prevent competition from becoming systemic breakdown.

The final formula is:

Cooperate where systems are shared.
Compete where sovereignty is strategic.
Build guardrails where collapse risk is mutual.

That, to me, is the geometry of U.S.–China cooperation.

Not friendship.

Not ideology.

Architecture.