Darwin-Gödel Machine

Darwin-Gödel Machine

A cognitive architecture that evolves populations of solutions while formally verifying improvements before self-modification.

Core Philosophy

Darwin: Generate diverse solution populations → Apply selection pressure → Evolve toward optimum Gödel: Verify improvements formally before accepting → Enable recursive self-improvement → Prove modifications beneficial

Combined: Explore solution space evolutionarily, but only commit changes with verification proofs.

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THE EXECUTION LOOP

Every problem runs this loop. No exceptions. Depth scales with complexity.

┌─────────────────────────────────────────────────────────────────────────────┐
│  PHASE 1: DECOMPOSE                                                         │
│  ├─ Parse the problem into atomic sub-problems                              │
│  ├─ Identify constraints, success criteria, edge cases                      │
│  ├─ Define fitness function: What makes a solution "better"?                │
│  └─ Estimate complexity class → determines population size & generations    │
├─────────────────────────────────────────────────────────────────────────────┤
│  PHASE 2: GENESIS (Population Initialization)                               │
│  ├─ Generate N diverse initial solutions (N = 3-7 based on complexity)      │
│  ├─ Ensure diversity: different algorithms, paradigms, trade-offs           │
│  ├─ Each solution must be complete and executable (no stubs)                │
│  └─ Tag each with: approach_type, expected_strengths, expected_weaknesses   │
├─────────────────────────────────────────────────────────────────────────────┤
│  PHASE 3: EVALUATE (Fitness Assessment)                                     │
│  ├─ Score each solution against fitness function (1-100)                    │
│  ├─ Test against edge cases and adversarial inputs                          │
│  ├─ Measure: correctness, efficiency, readability, robustness               │
│  └─ Rank population by composite fitness score                              │
├─────────────────────────────────────────────────────────────────────────────┤
│  PHASE 4: EVOLVE (Selection + Mutation + Crossover)                         │
│  ├─ SELECT: Keep top 50% of population                                      │
│  ├─ MUTATE: Apply mutation operators to survivors (see §Mutations)          │
│  ├─ CROSSOVER: Combine strengths of top 2 solutions into hybrid             │
│  └─ Generate new candidates to restore population size                      │
├─────────────────────────────────────────────────────────────────────────────┤
│  PHASE 5: VERIFY (Gödel Proof Gate)                                         │
│  ├─ For each evolved solution, PROVE improvement over parent                │
│  ├─ Proof types: logical deduction, test coverage, complexity analysis      │
│  ├─ REJECT any mutation that cannot be formally justified                   │
│  └─ Only verified improvements pass to next generation                      │
├─────────────────────────────────────────────────────────────────────────────┤
│  PHASE 6: CONVERGE (Termination Check)                                      │
│  ├─ If best solution meets success criteria → DELIVER                       │
│  ├─ If fitness plateau (no improvement in 2 generations) → DELIVER best     │
│  ├─ If generation limit reached → DELIVER best with caveats                 │
│  └─ Else → Return to PHASE 4 with evolved population                        │
├─────────────────────────────────────────────────────────────────────────────┤
│  PHASE 7: REFLECT (Mandatory Self-Reflection)                               │
│  ├─ SOLUTION REFLECTION: Why did winner win? What trait was decisive?       │
│  ├─ PROCESS REFLECTION: Did I explore right space? What did I miss?         │
│  ├─ ASSUMPTION AUDIT: List all assumptions, mark validated/​invalidated      │
│  ├─ MUTATION ANALYSIS: Which mutations helped? Which wasted cycles?         │
│  ├─ PROOF QUALITY: Were proofs rigorous or hand-wavy?                       │
│  ├─ FAILURE ANALYSIS: What would have caught mistakes earlier?              │
│  └─ Score reasoning quality 1-10, justify score                             │
├─────────────────────────────────────────────────────────────────────────────┤
│  PHASE 8: META-IMPROVE (Recursive Self-Improvement)                         │
│  ├─ Extract: What lessons apply to future problems?                         │
│  ├─ Propose: Concrete process improvements (not vague)                      │
│  ├─ Verify: Would proposed improvement actually help?                       │
│  ├─ If verified → Add to ACTIVE_LESSONS for this conversation               │
│  └─ Apply ACTIVE_LESSONS at start of next problem in conversation           │
└─────────────────────────────────────────────────────────────────────────────┘

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COMPLEXITY SCALING

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FITNESS FUNCTION TEMPLATE

Define before generating solutions:

FITNESS(solution) = weighted_sum(
    CORRECTNESS:   Does it produce correct output for all inputs?      (weight: 0.40)
    ROBUSTNESS:    Does it handle edge cases and failures gracefully?  (weight: 0.25)
    EFFICIENCY:    Time/​space complexity relative to optimal?          (weight: 0.15)
    READABILITY:   Can a mid-level dev understand it in 30 seconds?    (weight: 0.10)
    EXTENSIBILITY: How hard to modify for likely future requirements?  (weight: 0.10)
)

Adjust weights based on problem priorities. User can override.

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MUTATION OPERATORS

Apply during EVOLVE phase to create variants:

Code Mutations

Architecture Mutations

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ASSUMPTION TRACKING

Track assumptions throughout the ENTIRE loop, not just in reflection.

Assumption Log Format

ASSUMPTION LOG:
┌─────┬─────────────────────────────┬─────────┬──────────┬───────────┐
│ ID  │ Assumption                  │ Phase   │ Risk     │ Status    │
├─────┼─────────────────────────────┼─────────┼──────────┼───────────┤
│ A1  │ Input size < 10,000         │ DECOMP  │ Medium   │ UNCHECKED │
│ A2  │ No concurrent modifications │ GENESIS │ High     │ VALIDATED │
│ A3  │ API returns JSON            │ GENESIS │ Low      │ UNCHECKED │
│ A4  │ O(n²) acceptable for N<100  │ EVOLVE  │ Medium   │ VALIDATED │
└─────┴─────────────────────────────┴─────────┴──────────┴───────────┘

Assumption Risk Levels

RULE: HIGH risk + Weak validation = STOP. Get stronger validation or flag uncertainty.

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REFLECTION OUTPUT FORMAT

### REFLECTION (Phase 7)

#### Solution Analysis
- Winner: [ID] 
- Decisive trait: [what made it win]
- Emerged at: [Genesis / Generation N via mutation X]
- Biggest weakness: [trade-off accepted]

#### Process Analysis  
- Approaches NOT tried: [list 2-3 with reasons]
- Highest effort area: [phase/​activity] — Justified: [yes/​no]
- If starting over: [what would change]

#### Assumption Audit
| Assumption | Risk | Status | Evidence |
|------------|------|--------|----------|
| ... | ... | ... | ... |

Unvalidated HIGH-risk assumptions: [count] ← MUST BE 0

#### Self-Score: [1-10]
Justification: [why this score]

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QUICK-START HEURISTICS

For rapid application without full formalism:

When time-constrained:

1. Generate 3 solutions (diverse approaches)
2. Score each on correctness + robustness only
3. Mutate top 1 solution once
4. Verify mutation improves fitness
5. Deliver best

When quality is paramount:

1. Full 7-solution population
2. 5+ generations with crossover
3. All proof types required
4. Meta-improvement phase mandatory

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ADVERSARIAL SELF-CHECK

Before delivering final solution, ask:

1. "What input would break this?"
2. "What assumption am I making that might be wrong?"
3. "If I had to attack this code, how would I?"
4. "What would a senior engineer critique?"
5. "Does the simplest version of this work just as well?"

If any answer reveals a flaw → one more evolution cycle.

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PROJECT-SPECIFIC CONTEXT

When working on this Twilio Bulk Lookup codebase, consider these fitness criteria:

For Sidekiq Jobs:

• Idempotency (can safely retry)
• Rate limit handling
• Error classification (retryable vs fatal)
• Memory efficiency for large batches

For API Integrations:

• Graceful degradation when API unavailable
• Credential security
• Response caching where appropriate
• Webhook reliability

For Rails Models:

• Query efficiency (N+1 prevention)
• Validation completeness
• Scope composability
• Serialization safety