# Rapid Convergence Criteria - Detailed

**Purpose**: In-depth explanation of 5 rapid convergence criteria
**Impact**: Understanding when 3-4 iterations are achievable

---

## Criterion 1: Clear Baseline Metrics ⭐ CRITICAL

### Definition

V_meta(s₀) ≥ 0.40 indicates strong foundational work enables rapid progress.

### Mathematical Basis

```
ΔV_meta needed = 0.80 - V_meta(s₀)

If V_meta(s₀) = 0.40: Need +0.40 → 3-4 iterations achievable
If V_meta(s₀) = 0.10: Need +0.70 → 5-7 iterations required
```

**Assumption**: Average ΔV_meta per iteration ≈ 0.15-0.20

### What Strong Baseline Looks Like

**Quantitative metrics exist**:
- Error rate, test coverage, build time
- Measurable via tools (not subjective)
- Baseline established in <2 hours

**Success criteria are clear**:
- Target values defined (e.g., <3% error rate)
- Thresholds for convergence known
- No ambiguity about "done"

**Initial taxonomy comprehensive**:
- 70-80% coverage in iteration 0
- 10-15 categories/patterns documented
- Most edge cases identified

### Examples

**✅ Bootstrap-003 (V_meta(s₀) = 0.48)**:
```
- 1,336 errors quantified via MCP query
- Error rate: 5.78% calculated automatically
- 10 error categories (79.1% coverage)
- Clear targets: <3% error rate, <2 min MTTR
- Result: 3 iterations
```

**❌ Bootstrap-002 (V_meta(s₀) = 0.04)**:
```
- Coverage: 72.1% (but no patterns documented)
- No clear test patterns identified
- Ambiguous "done" criteria
- Had to establish metrics first
- Result: 6 iterations
```

### Impact Analysis

| V_meta(s₀) | Iterations Needed | Hours | Reason |
|------------|-------------------|-------|--------|
| 0.60-0.80 | 2-3 | 6-10h | Minimal gap to 0.80 |
| 0.40-0.59 | 3-4 | 10-15h | Moderate gap |
| 0.20-0.39 | 4-6 | 15-25h | Large gap |
| 0.00-0.19 | 6-10 | 25-40h | Exploratory |

---

## Criterion 2: Focused Domain Scope ⭐ IMPORTANT

### Definition

Domain described in <3 sentences without ambiguity.

### Why This Matters

**Focused scope** → Less exploration → Faster convergence

**Broad scope** → More patterns needed → Slower convergence

### Quantifying Focus

**Metric**: Boundary clarity ratio
```
BCR = clear_boundaries / total_boundaries

Where boundaries = {in-scope, out-of-scope, edge cases}
```

**Target**: BCR ≥ 0.80 (80% of boundaries unambiguous)

### Examples

**✅ Focused (Bootstrap-003)**:
```
Domain: "Error detection, diagnosis, recovery, prevention for meta-cc"

Boundaries:
✅ In-scope: All meta-cc errors
✅ Out-of-scope: Infrastructure failures, user errors
✅ Edge cases: Cascading errors (handle as single category)

BCR = 3/3 = 1.0 (perfectly focused)
```

**❌ Broad (Bootstrap-002)**:
```
Domain: "Develop test strategy"

Boundaries:
⚠️ In-scope: Which tests? Unit? Integration? E2E?
⚠️ Out-of-scope: What about test infrastructure?
⚠️ Edge cases: Multi-language support? CI integration?

BCR = 0/3 = 0.00 (needs scoping work)
```

### Scoping Technique

**Step 1**: Write 1-sentence domain definition
**Step 2**: List 3-5 explicit in-scope items
**Step 3**: List 3-5 explicit out-of-scope items
**Step 4**: Define edge case handling

**Example**:
```markdown
## Domain: Error Recovery for Meta-CC

**In-Scope**:
- Error detection and classification
- Root cause diagnosis
- Recovery procedures
- Prevention automation
- MTTR reduction

**Out-of-Scope**:
- Infrastructure failures (Docker, network)
- User mistakes (misuse of CLI)
- Feature requests
- Performance optimization (unless error-related)

**Edge Cases**:
- Cascading errors: Treat as single error with multiple symptoms
- Intermittent errors: Require 3+ occurrences for pattern
- Error prevention: In-scope if automatable
```

---

## Criterion 3: Direct Validation ⭐ IMPORTANT

### Definition

Can validate methodology without multi-context deployment.

### Validation Complexity Spectrum

**Level 1: Retrospective** (Fastest)
- Use historical data
- No deployment needed
- Example: 1,336 historical errors

**Level 2: Single-Context** (Fast)
- Test in one environment
- Minimal deployment
- Example: Validate on current project

**Level 3: Multi-Context** (Slow)
- Test across multiple projects/languages
- Significant deployment overhead
- Example: 3 project archetypes

**Level 4: Production** (Slowest)
- Real-world validation required
- Months of data collection
- Example: Monitor for 3-6 months

### Time Impact

| Validation Level | Overhead | Example Iterations Added |
|------------------|----------|--------------------------|
| Retrospective | 0h | +0 (Bootstrap-003) |
| Single-Context | 2-4h | +0 to +1 |
| Multi-Context | 6-12h | +2 to +3 (Bootstrap-002) |
| Production | Months | N/A (not rapid) |

### When Retrospective Validation Works

**Requirements**:
1. Historical data exists (session logs, error logs)
2. Data is representative of current/future work
3. Metrics can be calculated from historical data
4. Methodology can be applied retrospectively

**Example** (Bootstrap-003):
```
✅ 1,336 historical errors in session logs
✅ Representative of typical development work
✅ Can classify errors retrospectively
✅ Can measure prevention rate via replay

Result: Direct validation, 0 overhead
```

---

## Criterion 4: Generic Agent Sufficiency 🟡 MODERATE

### Definition

Generic agents (data-analyst, doc-writer, coder) sufficient for execution.

### Specialization Overhead

**Generic agents**: 0 overhead (use as-is)
**Specialized agents**: +1 to +2 iterations for design + testing

### When Specialization Adds Value

**10x+ speedup opportunity**:
- Example: coverage-analyzer (15 min → 30 sec = 30x)
- Example: test-generator (10 min → 1 min = 10x)
- Worth 1-2 iteration investment

**<5x speedup**:
- Use generic agents + simple scripts
- Not worth specialization overhead

### Examples

**✅ Generic Sufficient (Bootstrap-003)**:
```
Tasks:
- Analyze errors (generic data-analyst)
- Document taxonomy (generic doc-writer)
- Create validation scripts (generic coder)

Speedup from specialization: 2-3x (not worth it)
Result: 0 specialization overhead
```

**⚠️ Specialization Needed (Bootstrap-002)**:
```
Tasks:
- Coverage analysis (15 min → 30 sec = 30x with coverage-analyzer)
- Test generation (10 min → 1 min = 10x with test-generator)

Speedup: >10x for both
Investment: 1 iteration to design and test agents
Result: +1 iteration, but ROI positive overall
```

---

## Criterion 5: Early High-Impact Automation 🟡 MODERATE

### Definition

Top 3 automation opportunities identified by iteration 1.

### Pareto Principle Application

**80/20 rule**: 20% of automations provide 80% of value

**Implication**: Identify top 3 early → rapid V_instance improvement

### Identification Signals

**High-frequency patterns**:
- Appears in >10% of cases
- Example: File-not-found (18.7% of errors)

**High-impact prevention**:
- Prevents >50% of pattern occurrences
- Example: validate-path.sh prevents 65.2%

**High ROI**:
- Time saved / time invested > 5x
- Example: validate-path.sh = 61x ROI

### Early Identification Techniques

**Frequency Analysis**:
```bash
# Count error types
cat errors.jsonl | jq -r '.error_type' | sort | uniq -c | sort -rn

# Top 3 = high-frequency candidates
```

**Impact Estimation**:
```
If tool prevents X% of pattern Y:
- Pattern Y occurs N times
- Prevention: X% × N
- Impact: (X% × N) / total_errors
```

**ROI Calculation**:
```
Manual time: M min per occurrence
Tool investment: T hours
Expected uses: N

ROI = (M × N) / (T × 60)
```

### Example (Bootstrap-003)

**Iteration 0 Analysis**:
```
Top 3 by frequency:
1. File-not-found: 250/1,336 = 18.7%
2. MCP errors: 228/1,336 = 17.1%
3. Build errors: 200/1,336 = 15.0%

Automation feasibility:
1. File-not-found: ✅ Path validation (high prevention %)
2. MCP errors: ❌ Infrastructure (low automation value)
3. Build errors: ⚠️ Language-specific (moderate value)

Selected:
1. validate-path.sh: 250 errors, 65.2% prevention, 61x ROI
2. check-file-size.sh: 84 errors, 100% prevention, 31.6x ROI
3. check-read-before-write.sh: 70 errors, 100% prevention, 26.2x ROI

Total impact: 317/1,336 = 23.7% error prevention
```

**Result**: Clear automation path from iteration 0

---

## Criteria Interaction Matrix

| Criterion 1 | Criterion 2 | Criterion 3 | Likely Iterations |
|-------------|-------------|-------------|-------------------|
| ✅ (≥0.40) | ✅ Focused | ✅ Direct | 3-4 ⚡ |
| ✅ (≥0.40) | ✅ Focused | ❌ Multi | 4-5 |
| ✅ (≥0.40) | ❌ Broad | ✅ Direct | 4-5 |
| ❌ (<0.40) | ✅ Focused | ✅ Direct | 5-6 |
| ❌ (<0.40) | ❌ Broad | ❌ Multi | 7-10 |

**Key Insight**: Criteria 1-3 are multiplicative. Missing any = slower convergence.

---

## Decision Tree

```
Start
  │
  ├─ Can you achieve V_meta(s₀) ≥ 0.40?
  │    YES → Continue
  │    NO → Standard convergence (5-7 iterations)
  │
  ├─ Is domain scope <3 sentences?
  │    YES → Continue
  │    NO → Refine scope first
  │
  ├─ Can you validate without multi-context?
  │    YES → Rapid convergence likely (3-4 iterations)
  │    NO → Add +2 iterations for validation
  │
  └─ Generic agents sufficient?
       YES → No overhead
       NO → Add +1 iteration for specialization
```

---

**Source**: BAIME Rapid Convergence Criteria
**Validation**: 13 experiments, 85% prediction accuracy
**Critical Path**: Criteria 1-3 (must all be met for rapid convergence)