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:

Claude attacks flaws in Codex's proposal
Codex rebuts or updates position
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 | | ---------------- | ------------------------------ | | templates.md | Claude/debate/report templates | | techniques.md | Attack/defense techniques | | 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