Codex Brainstorm Skill

Trigger

• Keywords: brainstorm, exhaust possibilities, explore solutions, deep discussion, feasibility analysis, solution exploration, Nash equilibrium

When NOT to Use

• Simple technical Q&A (answer directly)
• Already have a clear solution (implement directly)
• Only need code review (use /codex-review)

Core Principle

⚠️ Independent Research → Adversarial Debate → Nash Equilibrium ⚠️

Nash Equilibrium = Neither party can unilaterally change strategy to achieve a better outcome

Workflow

Phase	Action	Output
1	Claude independent research + analysis, forms Position A	Claude's optimal hypothesis
2	Codex independent research + analysis, forms Position B	Codex's optimal hypothesis
3	Multi-round adversarial debate, mutual attacks	Debate exchange record
4	Check equilibrium, no further improvements possible	Equilibrium or divergence
5	Output final report	Nash Equilibrium report

Phase 2: Codex Independent Research (Critical)

⚠️ Must let Codex research independently; do NOT feed Claude's analysis results ⚠️

mcp__codex__codex({
  prompt: `You are a senior architect. Conduct an **independent analysis** of the following topic.

## Topic
${TOPIC}

## Constraints
${CONSTRAINTS}

## ⚠️ Important: You must research independently ⚠️
Before forming conclusions, you **must** first:
1. Run \`ls src/\` to understand the directory structure
2. Search related code: \`grep -r "keyword" src/ --include="*.ts" -l | head -10\`
3. Read relevant files to confirm existing implementations

## Output Requirements
1. Research summary (related modules, existing patterns)
2. Your position + supporting arguments
3. Potential risks`,
  sandbox: 'read-only',
  'approval-policy': 'on-failure',
});

Phase 3: Adversarial Debate

Structure per round:

1. Claude attacks flaws in Codex's proposal
2. Codex rebuts or updates position
3. Equilibrium check: Can either side raise new attacks?

Termination Conditions

Condition	Description	Result
Nash Equilibrium	Neither side can raise new attacks	Output equilibrium
Convergence	Both positions converge	Output consensus
Max rounds	5 rounds reached with remaining divergence	Output divergence report

Verification

• Claude formed an independent position (not following Codex)
• Codex performed code research (not speculating)
• At least 3 rounds of adversarial debate
• Each round has clear attack/defense records
• Final report indicates equilibrium status

References

File	Purpose
references/templates.md	Claude/debate/report templates
references/techniques.md	Attack/defense techniques
references/equilibrium.md	Equilibrium determination flow

Example

Input: What implementation approaches are available for this requirement?

Phase 1: Claude independent research → Position A (Solution X is optimal)
Phase 2: Codex independent research → Position B (Solution Y is optimal)
Phase 3: Adversarial debate
  - R1: Claude attacks Y's scalability / Codex attacks X's complexity
  - R2: Claude rebuts / Codex concedes and updates position
  - R3: Both converge to Solution Z, no further attacks → Equilibrium
Phase 4: Output Nash Equilibrium = Solution Z