gh-yaleh-meta-cc-claude/skills/methodology-bootstrapping/reference/convergence-criteria.md

Convergence Criteria

How to know when your methodology development is complete.

Standard Dual Convergence

The most common pattern (used in 6/8 experiments):

Criteria

Converged when ALL of:
1. M_n == M_{n-1}        (Meta-Agent stable)
2. A_n == A_{n-1}        (Agent set stable)
3. V_instance(s_n) ≥ 0.80
4. V_meta(s_n) ≥ 0.80
5. Objectives complete
6. ΔV < 0.02 for 2+ iterations (diminishing returns)

Example: Bootstrap-009 (Observability)

Iteration 6:
  V_instance(s₆) = 0.87 (target: 0.80) ✅
  V_meta(s₆) = 0.83 (target: 0.80) ✅
  M₆ == M₅ ✅
  A₆ == A₅ ✅
  Objectives: All 3 pillars implemented ✅
  ΔV: 0.01 (< 0.02) ✅

→ CONVERGED (Standard Dual Convergence)

Use when: Both task and methodology are equally important.

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Meta-Focused Convergence

Alternative pattern when methodology is primary goal (used in 1/8 experiments):

Criteria

Converged when ALL of:
1. M_n == M_{n-1}        (Meta-Agent stable)
2. A_n == A_{n-1}        (Agent set stable)
3. V_meta(s_n) ≥ 0.80    (Methodology excellent)
4. V_instance(s_n) ≥ 0.55 (Instance practically sufficient)
5. Instance gap is infrastructure, NOT methodology
6. System stable for 2+ iterations

Example: Bootstrap-011 (Knowledge Transfer)

Iteration 3:
  V_instance(s₃) = 0.585 (practically sufficient)
  V_meta(s₃) = 0.877 (excellent, +9.6% above target) ✅
  M₃ == M₂ == M₁ ✅
  A₃ == A₂ == A₁ ✅

  Instance gap analysis:
  - Missing: Knowledge graph, semantic search (infrastructure)
  - Present: ALL 3 learning paths complete (methodology)
  - Value: 3-8x onboarding speedup already achieved

  Meta convergence:
  - Completeness: 0.80 (all templates complete)
  - Effectiveness: 0.95 (3-8x validated)
  - Reusability: 0.88 (95%+ transferable)

→ CONVERGED (Meta-Focused Convergence)

Use when:

• Experiment explicitly prioritizes meta-objective
• Instance gap is tooling/infrastructure, not methodology
• Methodology has reached complete transferability (≥90%)
• Further instance work would not improve methodology quality

Validation checklist:

• Primary objective is methodology (stated in README)
• Instance gap is infrastructure (not methodology gaps)
• V_meta_reusability ≥ 0.90
• Practical value delivered (speedup demonstrated)

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Practical Convergence

Alternative pattern when quality exceeds metrics (used in 1/8 experiments):

Criteria

Converged when ALL of:
1. M_n == M_{n-1}        (Meta-Agent stable)
2. A_n == A_{n-1}        (Agent set stable)
3. V_instance + V_meta ≥ 1.60 (combined threshold)
4. Quality evidence exceeds raw metric scores
5. Justified partial criteria
6. ΔV < 0.02 for 2+ iterations

Example: Bootstrap-002 (Testing)

Iteration 5:
  V_instance(s₅) = 0.848 (target: 0.80, +6% margin) ✅
  V_meta(s₅) ≈ 0.85 (estimated)
  Combined: 1.698 (> 1.60) ✅

  Quality evidence:
  - Coverage: 75% overall BUT 86-94% in core packages
  - Sub-package excellence > aggregate metric
  - Quality gates: 8/10 met consistently
  - Test quality: Fixtures, mocks, zero flaky tests
  - 15x speedup validated
  - 89% methodology reusability

  M₅ == M₄ ✅
  A₅ == A₄ ✅
  ΔV: 0.01 (< 0.02) ✅

→ CONVERGED (Practical Convergence)

Use when:

• Some components don't reach target but overall quality is excellent
• Sub-system excellence compensates for aggregate metrics
• Diminishing returns demonstrated
• Honest assessment shows methodology complete

Validation checklist:

• Combined V_instance + V_meta ≥ 1.60
• Quality evidence documented (not just metrics)
• Honest gap analysis (no inflation)
• Diminishing returns proven (ΔV trend)

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System Stability

All convergence patterns require system stability:

Agent Set Stability (A_n == A_{n-1})

Stable when:

• Same agents used in iteration n and n-1
• No new specialized agents created
• No agent capabilities expanded

Example:

Iteration 5: {coder, doc-writer, data-analyst, log-analyzer}
Iteration 6: {coder, doc-writer, data-analyst, log-analyzer}
→ A₆ == A₅ ✅ STABLE

Meta-Agent Stability (M_n == M_{n-1})

Stable when:

• Same 5 capabilities in iteration n and n-1
• No new coordination patterns
• No Meta-Agent prompt evolution

Standard M₀ capabilities:

1. observe - Pattern observation
2. plan - Iteration planning
3. execute - Agent orchestration
4. reflect - Value assessment
5. evolve - System evolution

Finding: M₀ was sufficient in ALL 8 experiments (no evolution needed)

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Diminishing Returns

Definition: ΔV < epsilon for k consecutive iterations

Standard threshold: epsilon = 0.02, k = 2

Calculation:

ΔV_n = |V_total(s_n) - V_total(s_{n-1})|

If ΔV_n < 0.02 AND ΔV_{n-1} < 0.02:
  → Diminishing returns detected

Example:

Iteration 4: V_total = 0.82, ΔV = 0.05 (significant)
Iteration 5: V_total = 0.84, ΔV = 0.02 (small)
Iteration 6: V_total = 0.85, ΔV = 0.01 (small)
→ Diminishing returns since Iteration 5

Interpretation:

• Large ΔV (>0.05): Significant progress, continue
• Medium ΔV (0.02-0.05): Steady progress, continue
• Small ΔV (<0.02): Diminishing returns, consider converging

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Decision Tree

Start with iteration n:

1. Calculate V_instance(s_n) and V_meta(s_n)

2. Check system stability:
   M_n == M_{n-1}? → YES/NO
   A_n == A_{n-1}? → YES/NO

   If NO to either → Continue iteration n+1

3. Check convergence pattern:

   Pattern A: Standard Dual Convergence
   ├─ V_instance ≥ 0.80? → YES
   ├─ V_meta ≥ 0.80? → YES
   ├─ Objectives complete? → YES
   ├─ ΔV < 0.02 for 2 iterations? → YES
   └─→ CONVERGED ✅

   Pattern B: Meta-Focused Convergence
   ├─ V_meta ≥ 0.80? → YES
   ├─ V_instance ≥ 0.55? → YES
   ├─ Primary objective is methodology? → YES
   ├─ Instance gap is infrastructure? → YES
   ├─ V_meta_reusability ≥ 0.90? → YES
   └─→ CONVERGED ✅

   Pattern C: Practical Convergence
   ├─ V_instance + V_meta ≥ 1.60? → YES
   ├─ Quality evidence strong? → YES
   ├─ Justified partial criteria? → YES
   ├─ ΔV < 0.02 for 2 iterations? → YES
   └─→ CONVERGED ✅

4. If no pattern matches → Continue iteration n+1

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Common Mistakes

Mistake 1: Premature Convergence

Symptom: Declaring convergence before system stable

Example:

Iteration 3:
  V_instance = 0.82 ✅
  V_meta = 0.81 ✅
  BUT M₃ ≠ M₂ (new Meta-Agent capability added)

→ NOT CONVERGED (system unstable)

Fix: Wait until M_n == M_{n-1} and A_n == A_{n-1}

Mistake 2: Inflated Values

Symptom: V scores mysteriously jump to exactly 0.80

Example:

Iteration 4: V_instance = 0.77
Iteration 5: V_instance = 0.80 (claimed)
BUT no substantial work done!

Fix: Honest assessment, gap enumeration, evidence-based scoring

Mistake 3: Moving Goalposts

Symptom: Changing criteria mid-experiment

Example:

Initial plan: V_instance ≥ 0.80
Final state: V_instance = 0.65
Conclusion: "Actually, 0.65 is sufficient" ❌ WRONG

Fix: Either reach 0.80 OR use Meta-Focused/Practical with explicit justification

Mistake 4: Ignoring System Instability

Symptom: Declaring convergence while agents still evolving

Example:

Iteration 5:
  Both V scores ≥ 0.80 ✅
  BUT new specialized agent created in Iteration 5
  A₅ ≠ A₄

→ NOT CONVERGED (agent set unstable)

Fix: Run Iteration 6 to confirm A₆ == A₅

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Convergence Prediction

Based on 8 experiments, you can predict iteration count:

Base estimate: 5 iterations

Adjustments:

• Well-defined domain: -2 iterations
• Existing tools available: -1 iteration
• High interdependency: +2 iterations
• Novel patterns needed: +1 iteration
• Large codebase scope: +1 iteration
• Multiple competing goals: +1 iteration

Examples:

• Dependency Health: 5 - 2 - 1 = 2 → actual 3 ✓
• Observability: 5 + 0 + 1 = 6 → actual 6 ✓
• Cross-Cutting: 5 + 2 + 1 = 8 → actual 8 ✓

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Next: Read dual-value-functions.md for V_instance and V_meta calculation.