| # Phase 3 Proof Discharge — Quick Start Guide |
|
|
| ## What Happened? |
|
|
| Round 1 orchestration of Phase 3 proof discharge for the BOB quantum kernel loop invariants formalization (Agda) is **complete**. Three specialized agents (ahmad_bot, forge, enki) analyzed 15 holes across 4 modules and identified critical structural gaps. |
| |
| ## Key Results (60-second summary) |
| |
| | Metric | Value | |
| |--------|-------| |
| | Holes Identified | 15 | |
| | Holes Discharged | 0 | |
| | Spec Gaps Found | 2 (critical) | |
| | Viable Discharges Proposed | 1 | |
| | Agents Deployed | 3 (running in parallel) | |
| |
| ### The Two Critical Issues |
| |
| **1. EvolutionLoop.agda** — Missing semantic contract |
| - **What:** `StepTransition` record lacks `state_valid_preserved` field |
| - **Why:** Quantum evolution must preserve Hilbert space dimension |
| - **Fix:** Add 1 field (~4 lines) |
| - **Impact:** Unblocks 3 holes |
| |
| **2. MatrixAccumulationLoop.agda** — Missing precondition |
| - **What:** `matrix_acc_base` doesn't require `max_terms ≥ 1` |
| - **Why:** RK4 Taylor series needs at least one term |
| - **Fix:** Add 1 parameter (~2 lines) |
| - **Impact:** Unblocks 5 holes |
|
|
| ### Viable Discharge Found |
|
|
| **EulerLoop.agda line 141:** Lower bound arithmetic proof ready for type-checking. |
|
|
| --- |
|
|
| ## Where to Find Everything |
|
|
| ### Main Reports (in this directory) |
| - **PHASE_3_RESULTS_INDEX.md** ← START HERE (executive summary) |
| - **PHASE_3_ORCHESTRATION_LOG.md** (detailed findings per agent) |
| - **PHASE_3_DISCHARGE_SUMMARY.txt** (full context) |
| |
| ### Supporting Artifacts |
| - `/tmp/PHASE_3_DISCHARGE_REPORT.md` (analysis) |
| - `/tmp/PHASE_3_WORM_ENTRIES.jsonl` (WORM audit trail) |
| |
| ### Source Code Locations |
| |
| **Files that need fixing:** |
| - `src/Invariants/EvolutionLoop.agda` (lines 100–124) |
| - `src/Invariants/MatrixAccumulationLoop.agda` (lines 87–97) |
| |
| **Proposed discharge:** |
| - `src/Invariants/EulerLoop.agda` (line 141) |
| |
| --- |
| |
| ## Next Steps (Priority Order) |
| |
| ### Phase 3.1: Apply Spec Corrections (BLOCKING) |
| |
| **In EvolutionLoop.agda**, add to `StepTransition` record (after `time_advances` field): |
| ```agda |
| state_valid_preserved : |
| isValidDim (EvolutionState.state s) → |
| isValidDim (EvolutionState.state s') |
| ``` |
| |
| **In MatrixAccumulationLoop.agda**, modify `matrix_acc_base` signature: |
| ```agda |
| matrix_acc_base : |
| (s : MatrixAccLoopState) → |
| MatrixAccLoopState.k s ≡ 1 → |
| MatrixAccContext.dt (MatrixAccLoopState.ctx s) > 0 → |
| MatrixAccContext.state_dim (MatrixAccLoopState.ctx s) ≥ 1 → |
| MatrixAccLoopState.factorial_k s ≡ 1 → |
| MatrixAccLoopState.term_coefficient s ≡ MatrixAccContext.dt (MatrixAccLoopState.ctx s) → |
| MatrixAccLoopState.num_hamiltonian_sweeps s ≡ 0 → |
| MatrixAccLoopState.exp_matrix_accumulated s ≡ MatrixAccContext.state_dim (MatrixAccLoopState.ctx s) * MatrixAccContext.state_dim (MatrixAccLoopState.ctx s) → |
| MatrixAccLoopState.error_status s ≡ 0 → |
| MatrixAccContext.max_terms (MatrixAccLoopState.ctx s) ≥ 1 → -- ADD THIS LINE |
| MatrixAccInvariant s 1 |
| ``` |
| |
| Then in `matrix_acc_base` body, replace line 101: |
| ```agda |
| { h_k_valid = h_max_terms_pos -- Changed from: ? |
| ``` |
| |
| ### Phase 3.2: Re-run Discharge (After fixes) |
| |
| 1. Run agents on fixed code: |
| - ahmad_bot → EvolutionLoop holes (retry) |
| - enki → MatrixAccumulationLoop hole 101 (retry) |
| - forge → EulerLoop line 141 (verify proposed proof) |
| |
| 2. Type-check proposed discharges via `lake build` |
| |
| 3. WORM-seal successful proofs |
| |
| ### Phase 3.3: Analyze Remaining Modules |
| |
| - GateApplicationLoop.agda (4 holes) — not yet analyzed |
| - Expected: Similar precondition patterns |
| |
| --- |
| |
| ## Technical Context |
| |
| ### The Formalization |
| |
| This is a Phase 2→3 progression of BOB's quantum kernel loop invariants in Agda: |
| |
| - **Phase 2** (completed): Defined 4 loop invariant structures + predicates |
| - **Phase 3** (in progress): Discharge 15 proof holes to validate invariants |
| |
| ### The Holes |
| |
| All 15 holes are placeholder `?` marks in proof terms. They represent: |
| - 3 base-case proofs (induction start) |
| - 5 inductive-step proofs (state preservation) |
| - 4 exit-condition proofs (postconditions) |
| - 3 auxiliary arithmetic proofs |
| |
| ### The Agents |
| |
| - **ahmad_bot:** Specializes in state evolution & bookkeeping (EvolutionLoop) |
| - **forge:** Specializes in numerical updates & bounds (EulerLoop) |
| - **enki:** Specializes in matrix algebra & Taylor series (MatrixAccumulationLoop) |
|
|
| --- |
|
|
| ## Why This Matters |
|
|
| The formalization bridges informal C/Fortran implementation and formal specification. The two spec gaps that surfaced are **semantic invariants** that the implementation silently assumes but the formalization must make explicit: |
|
|
| 1. **Dimension Preservation:** Quantum evolution respects the structure of the state space (core physics) |
| 2. **Taylor Series Bounds:** RK4 requires minimum 1 term (integration contract) |
|
|
| These aren't bugs—they're **correctness requirements** that formal verification makes visible. |
|
|
| --- |
|
|
| ## Questions? |
|
|
| See **PHASE_3_RESULTS_INDEX.md** for: |
| - Full technical details (predicate definitions, record structures) |
| - Per-agent findings and recommendations |
| - Complete hole inventory with status |
| - Phase 3 roadmap (Phases 3.1–3.4) |
| |
| --- |
| |
| **Status:** Ready for Phase 3.1 spec corrections |
| **Estimated time to completion:** 2–4 hours (after fixes applied) |
| **Next checkpoint:** Phase 3.2 (Round 2 discharge verification) |
| |
