# PHASE 3 ORCHESTRATION LOG
## BOB Quantum Kernel Loop Invariant Formalization
**Generated:** 2026-07-24  
**Orchestrator:** Haiku (Haiku 4.5)  
**Project:** sov-kernel-monster  
**Repo:** /c/tmp/jacobian-formal/agda/

---

## ROUND 1: STRUCTURAL ANALYSIS (COMPLETE)

### Agent Assignments
- **ahmad_bot:** EvolutionLoop.agda (state evolution bookkeeping)
- **forge:** EulerLoop.agda (amplitude update mechanics)
- **enki:** MatrixAccumulationLoop.agda (matrix/gate logic proofs)

### Results Summary

#### Ahmad_bot Finding: EvolutionLoop.agda Line 139
**Hole:** `h_state_valid = ?` in `evolution_step` function

**Diagnosis:** STRUCTURAL GAP in `StepTransition` record

The `StepTransition` record at lines 100-124 lacks a semantic contract for dimensional validity preservation. Quantum state evolution must preserve the Hilbert space dimension (number of basis states), but this constraint is not encoded in the record definition.

**Required Fix:**
Add field to `StepTransition` record:
```agda
state_valid_preserved :
  isValidDim (EvolutionState.state s) →
  isValidDim (EvolutionState.state s')
```

**Location:** EvolutionLoop.agda lines 100-124

**Why it matters:** Without this field, the inductive step cannot prove that an evolved state remains valid. This is not just a proof technicality—it represents a missing semantic requirement from the physics: evolution operators preserve the dimension of the state space.

---

#### Enki Finding: MatrixAccumulationLoop.agda Line 101
**Hole:** `h_k_valid = ?` in `matrix_acc_base` function

**Diagnosis:** PRECONDITION VIOLATION

The predicate `taylorTermIndex k max_terms` expands to `k ≤ max_terms`. At k=1 (base case), we need `1 ≤ max_terms`, but no precondition guarantees `max_terms ≥ 1`.

The function signature is:
```agda
matrix_acc_base :
  (s : MatrixAccLoopState) →
  MatrixAccLoopState.k s ≡ 1 →
  ...
  MatrixAccLoopState.error_status s ≡ 0 →
  MatrixAccInvariant s 1
```

**Missing precondition:**
```agda
h_max_terms_pos : MatrixAccContext.max_terms (MatrixAccLoopState.ctx s) ≥ 1 →
```

**Location:** MatrixAccumulationLoop.agda lines 87-97

**Why it matters:** RK4 Taylor series acceleration requires at least one term (the constant term, k=1). While the implementation uses MAX_TERMS=20 in practice, the formal spec doesn't encode this invariant. This is a gap between the implementation contract and the formalization.

---

#### Forge Finding: EulerLoop.agda Line 141
**Hole:** First element of pair in `h_i_in_range` record field

**Diagnosis:** DISCHARGEABLE with stdlib support

The hole requires proving `1 ≤ i + 1` given that `i ≥ 1` in the inductive case.

**Proposed Proof Term:**
```agda
Data.Nat.Properties.n≤n+m 1 i
```

This uses the standard library lemma: `n ≤ n + m` for any naturals n, m.

**Alternative (with explicit case handling):**
```agda
case (EulerInvariant.h_i_in_range inv_i) of λ where
  (inl ⟨ _ , _ ⟩) → Data.Nat.Properties.n≤n+m 1 i
  (inr p) → absurd (¬p refl)
```

**Status:** Requires type-checking against actual Agda/Lean 4 stdlib to verify lemma availability.

**Location:** EulerLoop.agda line 141

---

### Hole Inventory (Round 1 Analysis)

**Total holes identified:** 15  
**Holes discharged:** 0  
**Holes blocked (spec gaps):** 3  
**Holes pending analysis:** 12  

| Module | Line | Function | Status | Agent |
|--------|------|----------|--------|-------|
| EvolutionLoop.agda | 139 | evolution_step | BLOCKED | ahmad_bot |
| EvolutionLoop.agda | 142 | evolution_step | PENDING | ahmad_bot |
| EvolutionLoop.agda | 149 | evolution_step | PENDING | ahmad_bot |
| EulerLoop.agda | 141 | euler_step | PROPOSED | forge |
| EulerLoop.agda | 142 | euler_step | PENDING | forge |
| EulerLoop.agda | 186 | euler_exit | PENDING | forge |
| MatrixAccumulationLoop.agda | 101 | matrix_acc_base | BLOCKED | enki |
| MatrixAccumulationLoop.agda | 156 | matrix_acc_step | PENDING | enki |
| MatrixAccumulationLoop.agda | 159 | matrix_acc_step | PENDING | enki |
| MatrixAccumulationLoop.agda | 195 | matrix_acc_exit | PENDING | enki |
| MatrixAccumulationLoop.agda | 196 | matrix_acc_exit | PENDING | enki |
| GateApplicationLoop.agda | 172 | gate_step | NOT_ANALYZED | — |
| GateApplicationLoop.agda | 185 | gate_step | NOT_ANALYZED | — |
| GateApplicationLoop.agda | 217 | gate_exit | NOT_ANALYZED | — |
| GateApplicationLoop.agda | 218 | gate_exit | NOT_ANALYZED | — |

---

## NEXT STEPS

### Phase 3.1: Spec Corrections (PRIORITY CRITICAL)
Before proceeding with Round 2, the following spec gaps must be fixed:

1. **EvolutionLoop.agda**: Add `state_valid_preserved` field to `StepTransition` record
   - Semantic: Evolution preserves Hilbert space dimension
   - Affects: 3 holes in EvolutionLoop (lines 139, 142, 149)

2. **MatrixAccumulationLoop.agda**: Add precondition to `matrix_acc_base`
   - Add parameter: `h_max_terms_pos : max_terms ≥ 1`
   - Semantic: RK4 requires minimum 1 term
   - Affects: 5 holes in MatrixAccumulationLoop

### Phase 3.2: Round 2 Discharge (AFTER SPEC FIXES)
Reassign holes to agents after corrections are applied. Expect:
- EvolutionLoop holes 139, 142: ahmad_bot (retry)
- EulerLoop hole 141: forge (verify proposed discharge)
- MatrixAccumulationLoop hole 101: enki (retry)
- Additional holes: assign sequentially

### Phase 3.3: GateApplicationLoop Analysis (NEW)
Launch full analysis of GateApplicationLoop.agda (4 holes):
- Similar precondition patterns expected
- Likely requires gate unitary enforcement preconditions

---

## WORM AUDIT TRAIL

No WORM seals generated in Round 1 (zero successful discharges).
Entries logged to `/tmp/PHASE_3_WORM_ENTRIES.jsonl` for structural findings.

When discharges succeed in subsequent rounds:
```
PHASE_3_PROOF_DISCHARGE::<module>::<agent>::<blake3_hash_of_proof_term>
```

---

## ARTIFACTS

- Full hole inventory: See hole_list.txt in same directory
- Agent reports: Collected in agent_findings/ subdirectory
- Spec gaps report: See PHASE_3_DISCHARGE_REPORT.md

---

**End of Round 1 Log**