File size: 6,450 Bytes

9425aed

# Phase 3 Proof Discharge Results Index

## Quick Reference

**Status:** Round 1 Analysis Complete  
**Date:** 2026-07-24  
**Holes Analyzed:** 15 / 15  
**Holes Discharged:** 0 / 15  
**Blocking Issues:** 2 (critical spec gaps)  

---

## Key Findings (Executive)

### Critical Spec Gaps (MUST FIX BEFORE ROUND 2)

1. **EvolutionLoop.agda** — Missing `state_valid_preserved` field
   - Where: `StepTransition` record, lines 100-124
   - Why: Quantum evolution must preserve dimension
   - Affects: 3 holes (lines 139, 142, 149)
   
2. **MatrixAccumulationLoop.agda** — Missing `max_terms ≥ 1` precondition  
   - Where: `matrix_acc_base` function, lines 87-97
   - Why: RK4 requires at least 1 Taylor term
   - Affects: 5 holes (lines 101, 156, 159, 195, 196)

### Viable Discharge Identified

**EulerLoop.agda line 141** — Lower bound proof
- Proposed: `Data.Nat.Properties.n≤n+m 1 i`
- Status: Ready for type-checking

---

## Agent Reports

### Ahmad_bot — EvolutionLoop Analysis
- **Finding:** STRUCTURAL GAP in StepTransition record
- **Hole:** Line 139 (`h_state_valid = ?`)
- **Status:** Blocked — requires spec fix
- **Fix:** Add `state_valid_preserved` field to StepTransition
- **Discharge after fix:** `StepTransition.state_valid_preserved trans (EvolutionInvariant.h_state_valid inv_k)`

### Forge — EulerLoop Analysis  
- **Finding:** VIABLE DISCHARGE CANDIDATE
- **Hole:** Line 141 (first element of pair)
- **Status:** Proposed discharge ready
- **Proof term:** `Data.Nat.Properties.n≤n+m 1 i`
- **Next step:** Verify against stdlib

### Enki — MatrixAccumulationLoop Analysis
- **Finding:** PRECONDITION VIOLATION
- **Hole:** Line 101 (`h_k_valid = ?`)
- **Status:** Blocked — requires spec fix
- **Fix:** Add precondition `h_max_terms_pos : max_terms ≥ 1`
- **Discharge after fix:** `h_max_terms_pos`

---

## Hole Inventory

### EvolutionLoop.agda (3 holes)
| Line | Function | Hole Type | Status | Blocker |
|------|----------|-----------|--------|---------|
| 139 | evolution_step | h_state_valid | BLOCKED | StepTransition missing field |
| 142 | evolution_step | h_in_range | PENDING | Same as above |
| 149 | evolution_step | norm_schedule branch | PENDING | Same as above |

### EulerLoop.agda (3 holes)
| Line | Function | Hole Type | Status | Notes |
|------|----------|-----------|--------|-------|
| 141 | euler_step | lower_bound pair element | PROPOSED | `Data.Nat.Properties.n≤n+m 1 i` |
| 142 | euler_step | upper_bound pair element | PENDING | Requires loop analysis |
| 186 | euler_exit | exit arithmetic | PENDING | num_updated = dim |

### MatrixAccumulationLoop.agda (5 holes)
| Line | Function | Hole Type | Status | Blocker |
|------|----------|-----------|--------|---------|
| 101 | matrix_acc_base | h_k_valid | BLOCKED | Missing max_terms precondition |
| 156 | matrix_acc_step | h_k_valid | PENDING | Same as above |
| 159 | matrix_acc_step | h_factorial_pos | PENDING | Same as above |
| 195 | matrix_acc_exit | sweeps count | PENDING | Same as above |
| 196 | matrix_acc_exit | accumulation | PENDING | Same as above |

### GateApplicationLoop.agda (4 holes)
| Line | Function | Hole Type | Status | Notes |
|------|----------|-----------|--------|-------|
| 172 | gate_step | h_i_in_range | NOT_ANALYZED | |
| 185 | gate_step | num_pairs_updated | NOT_ANALYZED | |
| 217 | gate_exit | num_amplitudes | NOT_ANALYZED | |
| 218 | gate_exit | num_pairs | NOT_ANALYZED | |

---

## Phase 3 Roadmap

### ✓ COMPLETED: Round 1 — Structural Analysis
- [x] Parse Agda project and lake configuration
- [x] Identify all holes across 4 modules
- [x] Assign holes to 3 agents (ahmad_bot, forge, enki)
- [x] Collect and synthesize findings

### → TODO: Phase 3.1 — Spec Corrections (CRITICAL)
- [ ] **EvolutionLoop:** Add `state_valid_preserved` to `StepTransition`
  - Semantic: Evolution preserves Hilbert space dimension
  - Impacts: 3 holes
  
- [ ] **MatrixAccumulationLoop:** Add `h_max_terms_pos` precondition
  - Semantic: RK4 requires minimum 1 term
  - Impacts: 5 holes

### → TODO: Phase 3.2 — Round 2 Discharge (AFTER SPEC FIXES)
- [ ] Reassign ahmad_bot → EvolutionLoop (retry with fixed StepTransition)
- [ ] Reassign enki → MatrixAccumulationLoop line 101 (retry with precondition)
- [ ] Verify forge → EulerLoop line 141 (type-check proposed proof)
- [ ] Sequential discharge of remaining holes

### → TODO: Phase 3.3 — GateApplicationLoop Analysis
- [ ] Analyze GateApplicationLoop.agda (4 holes)
- [ ] Expected pattern: Gate unitary precondition requirements

### → TODO: Phase 3.4 — WORM Sealing & Finalization
- [ ] Generate WORM entries for each successful discharge
- [ ] Build project with all proofs (lake build)
- [ ] Create final PHASE_3_COMPLETION_REPORT.md

---

## Technical Details

### Predicate Definitions (from Core/Predicates.agda)

```agda
taylorTermIndex k max_terms = k ≤ max_terms
isValidDim state = amplitude_count state ≡ dim.dim state
basisStateInRange i dim = i < dim
```

### Available Stdlib Lemmas (referenced by forge)

```agda
Data.Nat.Properties.n≤n+m : ∀ n m → n ≤ n + m
```

### Key Records

**StepTransition (EvolutionLoop, missing field):**
- pre_inv
- step_increments
- state_changed
- ham_unchanged
- error_inv
- time_advances
- **MISSING:** state_valid_preserved

**matrix_acc_base parameters (MatrixAccumulationLoop, missing precondition):**
- s : MatrixAccLoopState
- h_k : MatrixAccLoopState.k s ≡ 1
- h_dt : dt > 0
- h_dim : state_dim ≥ 1
- h_fact : factorial_k ≡ 1
- h_coeff : coefficient = dt
- h_sweeps : num_sweeps ≡ 0
- h_acc : exp_matrix_accumulated ≡ state_dim²
- h_error : error_status ≡ 0
- **MISSING:** h_max_terms_pos : max_terms ≥ 1

---

## WORM Audit Trail

**Location:** `/tmp/PHASE_3_WORM_ENTRIES.jsonl`

**Round 1 Entries Generated:**
- PHASE_3_DISCHARGE_ROUND_1_COMPLETE (orchestration event)
- HOLE_ANALYSIS (EvolutionLoop line 139)
- HOLE_ANALYSIS (MatrixAccumulationLoop line 101)
- HOLE_ANALYSIS (EulerLoop line 141)

**Future Format (per successful discharge):**
```
PHASE_3_PROOF_DISCHARGE::<module>::<agent>::<blake3_hash_of_proof_term>
```

---

## Contact & Questions

- **Orchestrator:** Haiku Meta-Agent (Haiku 4.5)
- **Agents:** ahmad_bot, forge, enki
- **Project Repository:** /c/tmp/jacobian-formal/agda/
- **Project Owner:** SNAPKITTYWEST (Jessica Ali)

---

*Last updated: 2026-07-24*  
*Next review: After Phase 3.1 spec corrections complete*