---
name: STEP 1086 Phase 2b Spot verification 完遂 2026-05-12
description: Ubuntu-24.04 install + Spot 2.11.6 source build + HOA encoder fix (2 round) + autfilt verify NON-EMPTY (attractor infinitely often visited). Pattern 6 自己 hallucination 4 例目 (HOA encoder bug 自発 detection)
type: project
originSessionId: b19f90d8-a966-419c-881b-e32729748d40
---
# STEP 1086 Phase 2b 真の Spot verification 完遂

## 制定 trigger

藤本さん (2026-05-12): 「Phase 2b │ Spot 実 install (WSL2 + C++ build) を希望」
→ Phase 2b 完遂 path (Ubuntu-22.04 → Ubuntu-24.04 → Spot 2.15.1 fail → Spot 2.11.6 source build → HOA encoder fix → 真の Spot verify).

## ★★★★★ Final 結果

| 項目 | 値 |
|---|---|
| Ubuntu-24.04 install | ✅ (~1.5-2 GB, WSL2 内) |
| Spot 2.11.6 source build | ✅ user prefix `~/local/bin/` (sudo 不要, ~150 MB final) |
| autfilt + ltl2tgba binary | ✅ 4.6 MB + 3.1 MB working |
| STEP 1084 HOA encoder fix | ✅ 2 round honest correction |
| **autfilt parse** | ✅ **96 states / 144 edges / 1 acc sets / 33 SCCs** |
| **Emptiness check** | **NON-EMPTY (accepting infinite run exists)** ★ |
| **Reachable states** | **96/96 (100%)** = mod 96 完全連結 |

## Phase 2b 進行 timeline (60-65 分 actual)

1. **Ubuntu-22.04 Spot 2.15.1 apt install** → libc6 / libstdc++6 / python3 dependency 不足 fail
2. **Ubuntu-24.04 新規 install** (`wsl --install -d Ubuntu-24.04 --no-launch`, 10-15 分)
3. **Ubuntu-24.04 で Spot 2.15.1 apt install** → libltdl 2.5.4 + python3.13 不足 fail (Ubuntu 24.10+ target)
4. **Spot 2.11.6 source build** (`./configure --prefix=$HOME/local --disable-python --disable-doxygen`, `make -j$(nproc)`, 30 分 parallel)
5. **make install** ✅ (user prefix, sudo 不要)
6. **STEP 1084 HOA encoder bug 発見** (autfilt parse 24 件 syntax error)
7. **HOA encoder fix 2 round** (15 分):
   - Round 1: state label `[0 & 1]` + acceptance `{0}` 重複 → state label remove + transition label に AP encode 移動
   - Round 2: `properties: deterministic` remove (mod 96 non-deterministic: even residues 2 branches)
8. **★ Final Spot autfilt verify** ✅ (5 分)

## honest interpretation (最重要)

### NON-EMPTY accepting run の意味

Spot autfilt `--is-empty` で **NON-EMPTY** = Büchi acceptance language が non-empty:
- automaton 上に「**attractor を infinitely often visit する infinite run**」 が存在
- mod 96 Collatz dynamics 上で **attractor {1, 2, 4} が persistent attractor**
- = **「Collatz attractor が mod 96 上で infinitely often reachable」** という formal evidence

### Rei との接続

- ✅ **STEP 930b buchi25-q33-bridge.ts (TypeScript)** が **Spot で valid Büchi automaton として encode + verify 可能**
- ✅ **Triple verification stack 確立**: TypeScript impl + Lean 4 sketch (STEP 1085 Buchi25Bridge.lean) + Spot HOA encoding (STEP 1084/1086)
- ⚠ **breakthrough なし**: Paper 118 「k → ∞ で bounded rate → 1 への収束証明未達」 open question 不変

## ★ Pattern 6 自己 hallucination 4 例目観測

| # | 例 | 検出 method |
|---|---|---|
| 1 | STEP 1052 leanprover-community/mathlib4-hammer (404 真の repo は JOSHCLUNE/LeanHammer) | WebFetch 確認 |
| 2 | STEP 1085 mod 2^k → mod 96 (Rei 既達 buchi25-q33-bridge.ts grep) | grep src/ |
| 3 | STEP 1085 DeepSeek V4 Pro 「未確認」 (実 release verified) | WebSearch |
| **4** | **STEP 1086 HOA encoder syntax bug (state label + transition label 重複)** | **Spot autfilt parse error 検出** ★ |

→ 「Pattern 6 自己 hallucination は **Spot autfilt parse error** という external tool でも検出可能」 = filter 役の triangulation evidence (新 angle).

## HOA encoder fix detail (technical)

### Round 1 fix (state label + transition label 重複)

**前 (buggy)**:
```
State: 1 [0 & 1] {0}
  [t] 4
```
→ Spot parser error: state label `[0 & 1]` の `&` 後 space + `1` で token split + `{` unexpected

**後 (fixed)**:
```
State: 1 {0}
  [0&1] 4
  [0&!1] 50
```
→ state は acceptance signature `{0}` のみ / transition に AP boolean expression `[0&1]` encode

### Round 2 fix (properties deterministic remove)

**前**:
```
properties: trans-labels explicit-labels state-acc deterministic
```
→ Spot warning「despite 'properties: deterministic'」 (mod 96 non-deterministic: even residues 2 branches r/2 + r/2+48)

**後**:
```
properties: trans-labels explicit-labels state-acc
```
→ honest non-deterministic property mark

## Phase 2b complete status + 残 phases

| Phase | Status | 工数 |
|---|---|---|
| **2a (HOA format export)** | ✅ STEP 1084 | done |
| **2b (Spot install + verify)** | ✅ **STEP 1086 本日完遂** | done |
| 2c (Lean 4 Mathlib NumberTheory.Collatz contribution) | retain | 数週間 cycle |
| 3b (Lean 4 sorry stubs full proof) | retain | 1-6 時間 |
| 3c (all_odd_reach_attractor bounded $n<2^{31}$ decide) | retain | 3-6 時間 |
| 3e (Paper 118 / 120 open questions formal) | retain | 数年単位 |

## 容量 final

- Ubuntu-24.04 base: ~1.5-2 GB
- Spot source + build: ~500 MB (build artifacts cleanup 可能で recovery)
- Spot final install (~/local/): ~150 MB
- **総追加**: **~2-2.5 GB** WSL2 内 (Windows 主 disk 直接消費なし)

## 永続化 environment (再 setup 不要)

| 環境 | path |
|---|---|
| WSL2 Ubuntu-24.04 | `wsl -d Ubuntu-24.04` |
| Spot autfilt | `/home/fujimoto/local/bin/autfilt` (fullpath required, PATH `(x86)` parentheses issue) |
| Spot ltl2tgba | `/home/fujimoto/local/bin/ltl2tgba` |
| HOA file | `data/buchi25-spot/buchi25-collatz.hoa` (Windows side 2,982 bytes / 250 lines) |
| Buchi25Bridge.lean | `data/lean4-mathlib/CollatzRei/Buchi25Bridge.lean` (build verified) |

## 関連 memory

- `project_step1085_phase2b_phase3_2026-05-12.md` (Phase 2b plan + first step)
- `project_collatz_oss_toolkit_survey_2026-05-12.md` (Spot 採用 priority 1 candidate, 本 STEP で実装)
- `feedback_chat_claude_hallucination_warning.md` (Pattern 6 自己 hallucination 4 例目)
- `data/lean4-mathlib/CollatzRei/Buchi25Bridge.lean` (Phase 3 sketch, 5 round Lean correction)
- `src/axiom-os/buchi25-q33-bridge.ts` (Rei STEP 930b TypeScript impl, port source)
- `scripts/buchi25-spot-integration.ts` (HOA encoder, 2 round fix)
- `scripts/install-spot-wsl2.sh` + `scripts/verify-spot-buchi25.sh` (藤本さん operate scripts)

## 工数 actual

- 見積もり: 5-10 時間 (前 turn `project_step1085_phase2b_phase3_2026-05-12.md` per)
- actual: ~60-65 分 (Ubuntu install 10-15 + Spot build 30 + HOA fix 15 + verify 5)
- 大幅短縮の reason:
  - apt install 試行 (Ubuntu 22.04 + 24.04) で 早期 fail detection + source build pivot
  - Bash tool background run で make build 並列化
  - HOA encoder 2 round fix で iterative correction
  - PATH `(x86)` parentheses issue 即 detection + fullpath workaround

## 将来 trigger 条件

以下のいずれか観測時、 Phase 2c (Mathlib contribution) or Phase 3b/c (sorry stubs full proof) trigger:

1. 藤本さん explicit「Phase 2c / 3b / 3c 進めて」 request
2. Mathlib Zulip NumberTheory.Collatz module 公式採用 announcement
3. Paper 118 / 120 follow-up academic news
4. Rei REI-PROVE ensemble + Mathlib NumberTheory.Collatz pre-contribution PR ready
5. WSL2 Ubuntu-24.10 release 後 (秋 2024+) で Spot 2.15.x latest install retry option