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docs(agent): break-glass test list for 4D × 2 fusion validation
15 tests across 4 dimensions + 4 cross-dimension tests: - Math (T1.1-T1.3): Q16_16 positivity, q16_merge_nz, boolMerge_preservesGap - Proof (T2.1-T2.3): gap_factors, disjoint_factors, crossgap_factors - Code (T3.1-T3.3): verifySpectralGap8, toPattern_merge, mergeCheck8_all - Diversity (T4.1-T4.3): architecture, rewrite fix, counterexample search - Cross-dim (T5.1-T5.4): chain proofs across dimensions Estimated cost: -10 for full suite. Success: cleanMerge_preservesGap compiles with 0 sorry.
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6-Documentation/docs/specs/break_glass_test_list.md
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# Break-Glass Test List
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Validates the 4D × 2 fusion of fusions approach.
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Each test has: problem, expected dimension contribution, success criteria.
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---
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## Dimension 1: Math (DeepSeek V4 Pro + Gemini 3.1 Pro)
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### T1.1 — Q16_16 positivity lemma
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```
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Problem: Prove that Q16_16 values are non-negative (a.val ≥ 0 for all a : Q16_16).
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Expected: DeepSeek finds the Subtype proof; Gemini suggests omega.
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Success: Lemma compiles, used by q16_merge_nz.
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```
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### T1.2 — min(1, a+b) ≠ 0 ↔ a ≠ 0 ∨ b ≠ 0
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```
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Problem: Prove q16_merge_nz for non-negative Q16_16.
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Expected: DeepSeek structures the by_cases; Gemini finds the Q16_16.add_nonneg lemma.
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Success: Theorem compiles, used by toPattern_merge.
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```
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### T1.3 — boolMerge preserves gap (Fin 8 → Bool)
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```
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Problem: Prove boolMerge_preservesGap on Fin 8 → Bool.
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Expected: Both models suggest native_decide or fin_cases.
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Success: Theorem compiles with 0 sorry.
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```
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---
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## Dimension 2: Proof (Claude Opus + Cohere Command A+)
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### T2.1 — gap_factors via match + rfl
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```
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Problem: Prove verifySpectralGap = boolGap ∘ toPattern for 8-element lists.
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Expected: Claude writes the match; Cohere structures the rfl chain.
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Success: Theorem compiles with 0 sorry.
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```
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### T2.2 — disjoint_factors via match + native_decide
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```
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Problem: Prove resonanceDegeneracy = 0 ↔ boolDisjoint for 8-element lists.
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Expected: Claude writes the match; Cohere suggests native_decide after match.
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Success: Theorem compiles with 0 sorry.
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```
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### T2.3 — crossgap_factors via match + native_decide
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```
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Problem: Prove crossInputGap ↔ boolCrossGap for 8-element lists.
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Expected: Same pattern as T2.2.
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Success: Theorem compiles with 0 sorry.
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```
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---
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## Dimension 3: Code (GPT-5.5 + Kimi K2.6)
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### T3.1 — verifySpectralGap8 @[reducible] definition
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```
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Problem: Define a direct Bool expression for the gap check on 8 bins.
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Expected: Kimi writes the definition; GPT finds the Spectrum.lean pattern.
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Success: Definition compiles, verifySpectralGap_eq_8 proven by native_decide.
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```
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### T3.2 — toPattern_merge proof
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```
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Problem: Prove toPattern (piecewiseMerge s e) = boolMerge (toPattern s) (toPattern e).
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Expected: GPT suggests funext + fin_cases; Kimi writes the q16_merge_nz application.
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Success: Theorem compiles with 0 sorry.
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```
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### T3.3 — mergeCheck8_all extraction
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```
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Problem: Extract specific (s, e) pair from mergeCheck8_all.
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Expected: GPT suggests List.all_get?; Kimi writes the range proof.
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Success: Extraction compiles, gives mergeCheck8 ss ee = true.
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```
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---
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## Dimension 4: Diversity (GLM-5.2 + DeepSeek V4 Flash)
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### T4.1 — Boolean Quotient Lifting architecture
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```
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Problem: Design the Fin 8 → Bool as primary semantic domain.
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Expected: GLM proposes the architecture; Flash validates it's correct.
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Success: Architecture document with clean separation of concerns.
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```
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### T4.2 — Rewrite ordering bug fix
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```
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Problem: Fix the line 338 rw [merge_bridge] failure.
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Expected: Flash identifies the fix (add rw [gap_bridge] first).
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Success: cleanMerge_preservesGap compiles with 0 sorry.
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```
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### T4.3 — Counterexample search
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```
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Problem: Verify no counterexample exists to cleanMerge_preservesGap.
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Expected: Flash confirms theorem is true; GLM suggests edge cases to check.
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Success: Confirmed no counterexample.
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```
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---
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## Cross-Dimension Tests
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### T5.1 — Math + Proof: q16_merge_nz → toPattern_merge
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```
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Problem: Chain T1.2 (q16_merge_nz) into T2.1 (gap_factors) to close the merge bridge.
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Expected: DeepSeek proves q16_merge_nz; Claude applies it in toPattern_merge.
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Success: toPattern_merge compiles with 0 sorry.
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```
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### T5.2 — Math + Code: boolMerge_preservesGap → mergeCheck8_all
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```
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Problem: Use T1.3 (boolMerge_preservesGap) to validate T3.3 (mergeCheck8_all extraction).
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Expected: DeepSeek proves the boolean theorem; GPT extracts it into the Q16_16 proof.
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Success: Extraction compiles, gives the final conclusion.
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```
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### T5.3 — Proof + Code: factor theorems → main theorem
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```
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Problem: Chain T2.1-T2.3 (factor theorems) into T4.2 (main theorem fix).
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Expected: Claude writes the factor theorems; Kimi chains them into the main proof.
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Success: cleanMerge_preservesGap compiles with 0 sorry.
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```
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### T5.4 — Full Fusion: all dimensions → closed sorry
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```
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Problem: Close the cleanMerge_preservesGap sorry using all 8 models' contributions.
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Expected: Each dimension contributes one piece; synthesis chains them.
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Success: Theorem compiles with 0 sorry. Build: 3314 jobs, 0 errors.
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```
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---
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## Execution Protocol
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1. **Single dimension**: Run 2 models on their assigned tests. Cost: ~$0.20-0.50 per dimension.
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2. **Cross-dimension**: Run the 2 relevant models on cross-dimension tests. Cost: ~$0.30-0.80 per test.
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3. **Full fusion**: Run all 8 models on T5.4. Cost: ~$1.50-3.00.
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4. **Total**: ~$5-10 for the complete test suite.
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## Success Criteria
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| Level | Criteria |
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|-------|----------|
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| **Pass** | All T1.x-T4.x tests pass (single dimension) |
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| **Pass+** | All T5.x tests pass (cross-dimension) |
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| **Complete** | T5.4 passes (sorry closed, build green) |
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