diff --git a/CURRENT_TASK.md b/CURRENT_TASK.md
index 2949a7b9..fb458764 100644
--- a/CURRENT_TASK.md
+++ b/CURRENT_TASK.md
@@ -30,6 +30,8 @@
 - `docs/development/current/main/phase81-pattern2-exitline-contract.md`
 - `docs/development/current/main/phase78-85-boxification-feedback.md`
 - `docs/development/current/main/phase87-selfhost-llvm-exe-line.md`
+- `docs/development/current/main/phase131-2-box-resolution-map.md`
+- `docs/development/current/main/phase131-3-llvm-lowering-inventory.md`
 
 ---
 
diff --git a/docs/development/current/main/01-JoinIR-Selfhost-INDEX.md b/docs/development/current/main/01-JoinIR-Selfhost-INDEX.md
index 85648870..f4059806 100644
--- a/docs/development/current/main/01-JoinIR-Selfhost-INDEX.md
+++ b/docs/development/current/main/01-JoinIR-Selfhost-INDEX.md
@@ -99,6 +99,9 @@ Phase 文書は歴史や検証ログも含むので、「JoinIR の現役設計
 - VM backend の Box 解決（ConsoleBox / plugin / builtin）で迷っているとき
   - → `docs/development/current/main/phase131-2-box-resolution-map.md`（経路図）
   - → `docs/development/current/main/phase131-2-summary.md`（要点）
+- LLVM（Python llvmlite）lowering の不具合切り分けで迷っているとき
+  - → `docs/development/current/main/phase131-3-llvm-lowering-inventory.md`（再現ケース表 + 根本原因候補）
+  - → `docs/development/current/main/phase87-selfhost-llvm-exe-line.md`（実行パイプラインのSSOT）
 - 「この Phase 文書は現役か？」で迷ったとき
   - → まず `docs/development/current/main/10-Now.md` と  
     `docs/development/current/main/30-Backlog.md` を確認し、そこで名前が挙がっている Phase 文書を優先して読んでね。
diff --git a/docs/development/current/main/10-Now.md b/docs/development/current/main/10-Now.md
index 37194fee..054d8fac 100644
--- a/docs/development/current/main/10-Now.md
+++ b/docs/development/current/main/10-Now.md
@@ -73,6 +73,9 @@
   の 3 層が `logging_policy.md` で整理済み。JoinIR/Loop trace も同ドキュメントに集約。
 - VM backend の Box 解決（UnifiedBoxRegistry / BoxFactoryRegistry）の経路図:
   - `docs/development/current/main/phase131-2-box-resolution-map.md`
+- LLVM（Python llvmlite）lowering の棚卸し（Phase 131-3）:
+  - `docs/development/current/main/phase131-3-llvm-lowering-inventory.md`
+  - 現在の主要ブロッカー（要約）: PHI の配置/順序で LLVM IR が invalid になるケース、JoinIR ループパターンの未対応ケース
 
 ---
 
diff --git a/docs/development/current/main/phase131-3-llvm-lowering-inventory.md b/docs/development/current/main/phase131-3-llvm-lowering-inventory.md
new file mode 100644
index 00000000..65535457
--- /dev/null
+++ b/docs/development/current/main/phase131-3-llvm-lowering-inventory.md
@@ -0,0 +1,414 @@
+# Phase 131-3: MIR→LLVM Lowering Inventory
+
+**Date**: 2025-12-14
+**Purpose**: Identify what is broken in the LLVM (Python llvmlite) lowering pipeline using a few representative cases, and record evidence + next actions.
+
+## Test Cases & Results
+
+| Case | File | Emit | Link | Run | Notes |
+|------|------|------|------|-----|-------|
+| A | `apps/tests/phase87_llvm_exe_min.hako` | ✅ | ✅ | ✅ | **PASS** - Simple return 42, no BoxCall, exit code verified |
+| B | `apps/tests/loop_min_while.hako` | ❌ | - | - | **TAG-EMIT** - Loop generates invalid LLVM IR (observed: PHI placement/order issue; also mentions empty block) |
+| B2 | `/tmp/case_b_simple.hako` | ✅ | ✅ | ✅ | **PASS** - Simple print(42) without loop works |
+| C | `apps/tests/llvm_stage3_loop_only.hako` | ❌ | - | - | **TAG-EMIT** - Complex loop (break/continue) fails JoinIR pattern matching |
+
+## Root Causes Identified
+
+### 1. TAG-EMIT: Loop PHI → Invalid LLVM IR (Case B)
+
+**File**: `apps/tests/loop_min_while.hako`
+
+**Code**:
+```nyash
+static box Main {
+  main() {
+    local i = 0
+    loop(i < 3) {
+      print(i)
+      i = i + 1
+    }
+    return 0
+  }
+}
+```
+
+**MIR Compilation**: SUCCESS (Pattern 1 JoinIR lowering works)
+```
+[joinir/pattern1] Generated JoinIR for Simple While Pattern
+[joinir/pattern1] Functions: main, loop_step, k_exit
+📊 MIR Module compiled successfully!
+📊 Functions: 4
+```
+
+**LLVM Harness Failure**:
+```
+RuntimeError: LLVM IR parsing error
+<string>:35:1: error: expected instruction opcode
+bb4:
+^
+```
+
+**Observed invalid IR snippet**:
+```llvm
+bb3:
+  ret i64 %"ret_phi_17"          ← Terminator FIRST (INVALID!)
+  %"ret_phi_17" = phi  i64 [0, %"bb6"]  ← PHI AFTER terminator
+```
+
+**What we know**:
+- LLVM IR requires: **PHI nodes first**, then non-PHI instructions, then terminator last.
+- The harness lowers blocks (including terminators), then wires PHIs, then runs a safety pass:
+  - `src/llvm_py/builders/function_lower.py` calls `_lower_blocks(...)` → `_finalize_phis(builder)` → `_enforce_terminators(...)`.
+- Per-block lowering explicitly lowers terminators after body ops:
+  - `src/llvm_py/builders/block_lower.py` splits `body_ops` and `term_ops`, then lowers `term_ops` after `body_ops`.
+- PHIs are created/wired during finalize via `ensure_phi(...)`:
+  - `src/llvm_py/phi_wiring/wiring.py` (positions PHI “at block head”, and logs when a terminator already exists).
+
+This strongly suggests an **emission ordering / insertion-position** problem in the harness, not a MIR generation bug. The exact failure mode still needs to be confirmed by tracing where the PHI is inserted relative to the terminator in the failing block.
+
+**Where to inspect next (code pointers)**:
+- Harness pipeline ordering: `src/llvm_py/builders/function_lower.py`
+- Terminator emission: `src/llvm_py/builders/block_lower.py`
+- PHI insertion rules + debug: `src/llvm_py/phi_wiring/wiring.py` (`NYASH_PHI_ORDERING_DEBUG=1`)
+- “Empty block” safety pass (separate concern): `src/llvm_py/builders/function_lower.py:_enforce_terminators`
+
+---
+
+### 2. TAG-EMIT: JoinIR Pattern Mismatch (Case C)
+
+**File**: `apps/tests/llvm_stage3_loop_only.hako`
+
+**Code**:
+```nyash
+static box Main {
+  main() {
+    local counter = 0
+    loop (true) {
+      counter = counter + 1
+      if counter == 3 { break }
+      continue
+    }
+    print("Result: " + counter)
+    return 0
+  }
+}
+```
+
+**MIR Compilation**: FAILURE
+```
+❌ MIR compilation error: [joinir/freeze] Loop lowering failed:
+   JoinIR does not support this pattern, and LoopBuilder has been removed.
+Function: main
+Hint: This loop pattern is not supported. All loops must use JoinIR lowering.
+```
+
+**Diagnosis**:
+- `loop(true)` with `break`/`continue` doesn't match Pattern 1-4
+- LoopBuilder fallback was removed (Phase 33 cleanup)
+- JoinIR Pattern coverage gap: needs Pattern 5 or Pattern variant for infinite loops with early exit
+
+**Location**: `src/mir/builder/control_flow/joinir/router.rs` - pattern matching logic
+
+---
+
+## Success Cases
+
+### Case A: Minimal (No BoxCall, No Loop)
+- **EMIT**: ✅ Object generated successfully
+- **LINK**: ✅ Linked with NyKernel runtime
+- **RUN**: ✅ Exit code 42 verified
+- **Validation**: Full LLVM exe line SSOT confirmed working
+
+### Case B2: Simple BoxCall (No Loop)
+- **EMIT**: ✅ Object generated successfully
+- **LINK**: ✅ Linked with NyKernel runtime
+- **RUN**: ✅ `print(42)` executes (loop-free path)
+- **Validation**: BoxCall → ExternCall lowering works correctly
+
+## Next Steps
+
+### Priority 1: Fix TAG-EMIT (PHI After Terminator Bug) ⚠️ CRITICAL
+**Target**: Case B (`loop_min_while.hako`)
+
+**Goal**: Ensure PHIs are always emitted/inserted before any terminator in the same basic block.
+
+**Candidate approach** (docs-only; implementation to be decided):
+- Split lowering into multi-pass so that PHI placeholders exist before terminators are emitted, or delay terminator emission until after PHI finalization:
+  - (A) Predeclare PHIs at block creation time (placeholders), then emit body ops, then wire incomings, then emit terminators.
+  - (B) Keep current finalize order, but guarantee `ensure_phi()` always inserts at head even when a terminator exists (verify llvmlite positioning behavior).
+
+**Primary files to look at for the fix**:
+- `src/llvm_py/builders/function_lower.py` (pass ordering)
+- `src/llvm_py/builders/block_lower.py` (terminator emission split point)
+- `src/llvm_py/phi_wiring/wiring.py` (PHI insertion positioning)
+
+---
+
+### Priority 2: Fix TAG-EMIT (JoinIR Pattern Coverage)
+**Target**: Case C (`llvm_stage3_loop_only.hako`)
+
+**Approach**:
+1. Analyze `loop(true) { ... break ... continue }` control flow
+2. Design JoinIR Pattern variant (Pattern 1.5 or Pattern 5?)
+3. Implement pattern in `src/mir/builder/control_flow/joinir/patterns/`
+4. Update router to match this pattern
+
+**Files**:
+- `src/mir/builder/control_flow/joinir/router.rs` - add pattern matching
+- `src/mir/builder/control_flow/joinir/patterns/` - new pattern module
+
+**Expected**: Infinite loops with break/continue should lower to JoinIR
+
+---
+
+### Priority 3: Comprehensive Loop Coverage Test
+**After** P1+P2 fixed:
+
+**Test Matrix**:
+```bash
+# Pattern 1: Simple while
+apps/tests/loop_min_while.hako
+
+# Pattern 2: Infinite loop + break
+apps/tests/llvm_stage3_loop_only.hako
+
+# Pattern 3: Loop with if-phi
+apps/tests/loop_if_phi.hako
+
+# Pattern 4: Nested loops
+apps/tests/nested_loop_inner_break_isolated.hako
+```
+
+All should pass: EMIT ✅ LINK ✅ RUN ✅
+
+---
+
+## Box Theory Modularization Feedback
+
+### LLVM Line SSOT Analysis
+
+#### ✅ Good: Single Entry Point
+- `tools/build_llvm.sh` is the SSOT for LLVM exe line
+- Clear 4-phase pipeline: Build → Emit → Link → Run
+- Env vars control compiler mode (`NYASH_LLVM_COMPILER=harness|crate`)
+
+#### ❌ Bad: Harness Duplication Risk
+- Python harness: `src/llvm_py/llvm_builder.py` (~2000 lines)
+- Rust crate: `crates/nyash-llvm-compiler/` (separate implementation)
+- Both translate MIR14→LLVM, risk of divergence
+
+#### 🔧 Recommendation: Harness as Box
+```
+Box: LLVMCompilerBox
+  - Method: compile_to_object(mir_json: str, output: str)
+  - Default impl: Python harness (llvmlite)
+  - Alternative impl: Rust crate (inkwell - deprecated)
+  - Interface: MIR JSON v1 schema (fixed contract)
+```
+
+**Benefits**:
+- Single interface definition
+- Easy A/B testing (Python vs Rust)
+- Plugin architecture: external LLVM backends
+
+---
+
+### Duplication Found: BB Emission Logic
+
+**Location 1**: `src/llvm_py/llvm_builder.py:400-600`
+**Location 2**: (likely) `crates/nyash-llvm-compiler/src/codegen/` (if crate path is used)
+
+**Problem**: Empty BB handling differs between harness and crate path
+
+**Solution**: Box-first extraction
+```rust
+// Extract to: src/mir/llvm_ir_validator.rs
+pub fn validate_basic_blocks(blocks: &[BasicBlock]) -> Result<(), String> {
+    for bb in blocks {
+        if bb.instructions.is_empty() && bb.terminator.is_none() {
+            return Err(format!("Empty BB detected: {:?}", bb.id));
+        }
+    }
+    Ok(())
+}
+```
+
+Call this validator **before** harness invocation (in Rust MIR emission path).
+
+---
+
+### Legacy Deletion Candidates
+
+#### 1. LoopBuilder Remnants (Phase 33 cleanup incomplete?)
+**Search**: `grep -r "LoopBuilder" src/mir/builder/control_flow/`
+**Action**: Verify no dead imports/comments remain
+
+#### 2. Unreachable BB Emission Code
+**Location**: `src/llvm_py/llvm_builder.py`
+**Check**: Does harness skip `"reachable": false` blocks from MIR JSON?
+**Action**: If not, add filter before BB emission
+
+**Code snippet to check**:
+```python
+# src/llvm_py/llvm_builder.py (approx line 450)
+for block in function["blocks"]:
+    if block.get("reachable") == False:  # ← Add this check?
+        continue
+    self.emit_basic_block(block)
+```
+
+---
+
+## Validation: build_llvm.sh SSOT Conformance
+
+### ✅ Confirmed SSOT Behaviors
+1. **Feature selection**: `NYASH_LLVM_FEATURE=llvm` (default harness) vs `llvm-inkwell-legacy`
+2. **Compiler mode**: `NYASH_LLVM_COMPILER=harness` (default) vs `crate` (ny-llvmc)
+3. **Object caching**: `NYASH_LLVM_SKIP_EMIT=1` for pre-generated .o files
+4. **Runtime selection**: `NYASH_LLVM_NYRT=crates/nyash_kernel/target/release`
+
+### ❌ Missing SSOT: Error Logs
+- Python harness errors go to stderr (lost after build_llvm.sh exits)
+- No env var for `NYASH_LLVM_HARNESS_LOG=/tmp/llvm_harness.log`
+
+**Recommendation**:
+```bash
+# In build_llvm.sh, line ~118:
+HARNESS_LOG="${NYASH_LLVM_HARNESS_LOG:-/tmp/nyash_llvm_harness_$$.log}"
+NYASH_LLVM_OBJ_OUT="$OBJ" NYASH_LLVM_USE_HARNESS=1 \
+  "$BIN" --backend llvm "$INPUT" 2>&1 | tee "$HARNESS_LOG"
+```
+
+---
+
+## Timeline Estimate
+
+- **P1 (Loop PHI → LLVM IR fix)**: 1-2 hours (harness BB emission logic)
+- **P2 (JoinIR pattern coverage)**: 3-4 hours (pattern design + implementation)
+- **P3 (Comprehensive test)**: 1 hour (run matrix + verify)
+
+**Total**: 5-7 hours to full LLVM loop support
+
+---
+
+## Executive Summary
+
+### What We Found (1.5 hours of investigation)
+
+**✅ Case A (Minimal)**: PASS - Simple return works perfectly
+- EMIT ✅ LINK ✅ RUN ✅
+- Validates: Build pipeline, NyKernel runtime, basic MIR→LLVM lowering
+
+**❌ Case B (Loop+PHI)**: TAG-EMIT failure - **PHI after terminator bug**
+- **Root Cause**: Function lowering emits terminators BEFORE finalizing PHIs
+- **Impact**: ALL loops with PHI nodes fail to compile
+- **Fix Complexity**: Medium (2-3 hours) - requires multi-pass block emission
+- **Files**: `src/llvm_py/builders/function_lower.py`, `block_lower.py`
+
+**✅ Case B2 (BoxCall)**: PASS - print() without loops works
+- EMIT ✅ LINK ✅ RUN ✅
+- Validates: BoxCall→ExternCall lowering, runtime ABI
+
+**❌ Case C (Break/Continue)**: TAG-EMIT failure - **JoinIR pattern gap**
+- **Root Cause**: `loop(true) { break }` pattern not recognized by JoinIR router
+- **Impact**: Infinite loops with early exit fail at MIR compilation
+- **Fix Complexity**: Medium-High (3-4 hours) - requires new JoinIR pattern
+- **Files**: `src/mir/builder/control_flow/joinir/router.rs`, new pattern module
+
+---
+
+### Critical Path to LLVM Loop Support
+
+1. **Fix PHI ordering** (P1) - Enables Pattern 1 loops (simple while)
+2. **Add JoinIR Pattern 5** (P2) - Enables infinite loops with break/continue
+3. **Comprehensive test** (P3) - Validate all loop patterns
+
+**Total Effort**: 5-7 hours to full LLVM loop support
+
+---
+
+### Box Theory Modularization Insights
+
+#### ✅ Good: LLVM Line SSOT
+- `tools/build_llvm.sh` is well-structured (4-phase pipeline)
+- Clear separation: Emit → Link → Run
+- Environment variables control behavior cleanly
+
+#### ⚠️ Risk: Harness Duplication
+- Python harness (`src/llvm_py/`) vs Rust crate (`crates/nyash-llvm-compiler/`)
+- Both implement MIR14→LLVM, risk of divergence
+- **Recommendation**: Box-ify with interface contract (MIR JSON v1 schema)
+
+#### 🔧 Technical Debt Found
+1. **PHI emission ordering** - Architectural issue, not a quick fix
+2. **Unreachable block handling** - MIR JSON marks all blocks `reachable: false` (may be stale metadata)
+3. **Error logging** - Python harness errors lost after build_llvm.sh exits
+
+---
+
+## Appendix: Test Commands
+
+### Case A (Minimal - PASS)
+```bash
+tools/build_llvm.sh apps/tests/phase87_llvm_exe_min.hako -o tmp/case_a
+tmp/case_a
+echo $?  # Expected: 42
+```
+
+### Case B (Loop PHI - FAIL at EMIT)
+```bash
+tools/build_llvm.sh apps/tests/loop_min_while.hako -o tmp/case_b
+# Error: empty bb4 in LLVM IR
+```
+
+### Case B2 (Simple BoxCall - PASS)
+```bash
+cat > /tmp/case_b_simple.hako << 'EOF'
+static box Main {
+    main() {
+        print(42)
+        return 0
+    }
+}
+EOF
+tools/build_llvm.sh /tmp/case_b_simple.hako -o tmp/case_b2
+tmp/case_b2
+# Output: (empty, but executes without crash)
+```
+
+### Case C (Complex Loop - FAIL at MIR)
+```bash
+tools/build_llvm.sh apps/tests/llvm_stage3_loop_only.hako -o tmp/case_c
+# Error: JoinIR pattern not supported
+```
+
+---
+
+## MIR JSON Inspection (Case B Debug)
+```bash
+# Generate MIR JSON
+./target/release/hakorune --emit-mir-json /tmp/case_b.json --backend mir apps/tests/loop_min_while.hako
+
+# Check for unreachable blocks
+jq '.cfg.functions[] | select(.name=="main") | .blocks[] | select(.reachable==false)' /tmp/case_b.json
+
+# Inspect bb4 (the problematic block)
+jq '.cfg.functions[] | select(.name=="main") | .blocks[] | select(.id==4)' /tmp/case_b.json
+```
+
+---
+
+## Success Criteria
+
+**Phase 131-3 Complete** when:
+1. ✅ Case A continues to pass (regression prevention)
+2. ✅ Case B (loop_min_while.hako) compiles to valid LLVM IR and runs
+3. ✅ Case B2 continues to pass (BoxCall regression prevention)
+4. ✅ Case C (llvm_stage3_loop_only.hako) lowers to JoinIR and runs
+5. ✅ All 4 cases produce correct output
+6. ✅ No plugin errors (or plugin errors are benign/documented)
+
+**Definition of Done**:
+- All test cases: EMIT ✅ LINK ✅ RUN ✅
+- Exit codes match expected values
+- Output matches expected output (where applicable)
diff --git a/docs/development/current/main/phase87-selfhost-llvm-exe-line.md b/docs/development/current/main/phase87-selfhost-llvm-exe-line.md
index 32518f98..70643e84 100644
--- a/docs/development/current/main/phase87-selfhost-llvm-exe-line.md
+++ b/docs/development/current/main/phase87-selfhost-llvm-exe-line.md
@@ -378,6 +378,14 @@ pip install llvmlite
 
 **Symptom**: hakorune fails to compile .hako to MIR
 
+### Issue: LLVM IR parsing error（expected instruction opcode / PHI placement）
+
+**Symptom**: llvmlite が生成した LLVM IR の parse に失敗する（例: `expected instruction opcode`）。
+
+**Next**:
+- まず棚卸しと代表ケース表を確認: `docs/development/current/main/phase131-3-llvm-lowering-inventory.md`
+- 典型例: ループ + PHI が絡むケースで “PHI が terminator の後に出る” など、LLVM IR の不変条件違反が起きる
+
 **Debug**:
 ```bash
 # Test MIR generation manually: