---
name: project-step1202-bilattice-eight-2026-06-09
description: STEP 1202 (b) Bilattice 8値拡張 engine + site lens 完遂 record (chat-Claude 2026-06-08 thread proposal (b) = Belnap-Dunn FOUR 確定 Layer 1 + Rei D-FUMT₈ 拡張 4 軸 orthogonal extension Layer 2)。 STEP 1201 (a) Institution engine の次段、 残 (c) ∞-cosmoi / (d) HoTT loop space は次 session 着手対象。
metadata: 
  node_type: memory
  type: project
  originSessionId: faa7a767-b3f5-4b08-b92c-adbdd4839d37
---

# STEP 1202 (b) 完遂 — Bilattice 8値拡張 engine + site lens

**Date**: 2026-06-09 (commit `705bbdc3`, 9 file +1588 行)
**Why**: chat-Claude 2026-06-08 thread proposal (b) Belnap 4値 → D-FUMT₈ 8値 bilattice 拡張を Rei に operational 実装。 STEP 1201 (a) Institution engine の次段、 (c) ∞-cosmoi / (d) HoTT loop space の前段。 藤本さん指示「(b) Bilattice 8 値拡張から進めて下さい。 あと、 rei-aios のサイトのほうにも新しいページにでも反映をお願いできますか?」 受領後の即着手。
**How to apply**: 次 session 再開時、 本 file 読込 → (c) ∞-cosmoi 公理化 + (d) SELF⟲ ↔ HoTT loop space Ω formal 接続 着手判断 → 帰宅後 pending list と並走判断。 lens 反映後 site で `#/bilattice-eight` route が visible (CF Pages auto-deploy 後)。

## 実装内容

### Engine (`src/axiom-os/bilattice-eight-engine.ts`, ~340 行)

**Layer 1 — Belnap-Dunn FOUR (確定 prior art)**:
- types: `BelnapFour` (TRUE/FALSE/BOTH/NEITHER) + `DFumt8Value` = STEP 1201 `DFumt8Axis` re-use
- `truthLeq(a, b)` — truth-order ≤_t (Hasse: TRUE top / FALSE bottom / NEITHER+BOTH middle parallel)
- `knowledgeLeq(a, b)` — knowledge-order ≤_k (Hasse: BOTH top / NEITHER bottom / TRUE+FALSE middle parallel)
- `meetT` / `joinT` / `meetK` / `joinK` — 4 演算 (full 4×4 = 16 rows each)
- `negate(a)` — Belnap 否定 (TRUE↔FALSE, BOTH/NEITHER fixed)
- `verifyInterlaced(a, b, c)` — interlaced bilattice 条件 (Ginsberg 1988 + Arieli-Avron 1998):
  - `a ≤_k b ⟹ meetT(a, c) ≤_k meetT(b, c)`
  - `a ≤_k b ⟹ joinT(a, c) ≤_k joinT(b, c)`
  - `a ≤_t b ⟹ meetK(a, c) ≤_t meetK(b, c)`
  - `a ≤_t b ⟹ joinK(a, c) ≤_t joinK(b, c)`
- `verifyInterlacedAll()` — 64 triples 全 verify (4^3 = 64, allHold = true)
- `truthCoveringEdges()` / `knowledgeCoveringEdges()` — Hasse covering relation (各 4 edges)
- `buildOperationTables()` — 4 operations × 16 rows

**Layer 2 — Rei D-FUMT₈ 拡張 4 軸 (orthogonal extension stance)**:
- `EXTENSION_AXIS_ROLES` = 4 axis (INFINITY/ZERO/FLOWING/SELF) の operational role articulation
- 各 axis に `truthOrderRelation` + `knowledgeOrderRelation` + `reiSubstrate` annotation
- INFINITY = above-all + above-all + Paper 63 SNST v→∞ substrate
- ZERO = below-all + below-all + Paper 61 ZCSG 0 = śūnyatā(śūnyatā) substrate
- FLOWING = transverse + transverse + W-48 NegCap engine substrate
- SELF = orthogonal-fixpoint + orthogonal-fixpoint + godel-lawvere-bridge + HoTTNagarjunaSymmetry substrate
- ★ **設計判断**: 拡張 4 軸を lattice 内部値として embed しない (Ginsberg 1988 + Arieli-Avron 1998 の 9 値+ lattice 拡張 prior art との重複回避) + chat-Claude 「octonion ↔ D-FUMT₈ ラベル罠」 警告への honest 対応

**Report builder**:
- `buildBilatticeReport(nowISO)` = data/bilattice-eight/latest.json content (6.3 KB)
- generatedAt + layer1Belnap (values + covering edges + operation tables + interlaced verification) + layer2Extension (axes + stance) + honestScope + priorArt

### Test (`test/step1202-bilattice-eight-test.ts`) — 95/95 PASS

11 sections:
1. BELNAP_FOUR + extension axes constants
2. Truth-order ≤_t lattice axioms (reflexivity + specific orderings + incomparability)
3. Knowledge-order ≤_k lattice axioms
4. 4 operations correctness (specific computations + idempotency + commutativity)
5. Negation (Belnap involution + double negation)
6. Interlaced bilattice verification (64 triples allHold)
7. Hasse covering edges (4 + 4)
8. Operation tables (4×4 = 16 rows × 4 operations)
9. Extension axes orthogonal stance (4 roles verify)
10. STEP 1201 Institution engine integration (BOTH ⊨ TRUE/FALSE は knowledge-order 由来)
11. BilatticeReport build (4 values + 4 tables + 4 axes + 4 honestScope + 7 priorArt)

★ Section 10 で訂正記録: 私の初版 assertion「TRUE と BOTH は truth-incomparable」 は誤り (BOTH ≤_t TRUE が正しい Belnap-Dunn standard)。 Institution の BOTH⊨TRUE refinement は knowledge-order (TRUE ≤_k BOTH) 由来。 engine 側は正しく test 側のみ修正。

### Site lens (`src/renderer/components/bilattice-eight/BilatticeEightLens.tsx`, ~300 行)

- Route: `#/bilattice-eight` + App.tsx import/route
- ReiLauncher menu entry 🔷 (理論探索 category, color #a855f7)
- data/bilattice-eight/latest.json fetch
- Honest scope banner (Belnap-Dunn 1977 + Ginsberg 1988 + Arieli-Avron 1998 prior art 明示)
- Layer 1 section: truth-order + knowledge-order Hasse diamond (SVG, 4 nodes each, value-colored ⊤/⊥/⊤⊥/~ glyphs) + interlaced verification status badge
- 4 operation tables (Belnap glyphs color-coded)
- Layer 2 section: 4 extension axis cards (axis-colored border, operationalRole + truthOrder + knowledgeOrder + reiSubstrate)
- Prior art backbone list + honest scope record list
- Integration footer (next session (c)(d) bridge candidate)

### Data pipeline

- `scripts/generate-bilattice-eight.ts` 新規 (data/bilattice-eight/latest.json + dist-renderer mirror)
- `scripts/sync-index-html-bundle.ts` DATA_DIRS に `'bilattice-eight'` 追加
- `package.json` dev:build chain に `generate-bilattice-eight.ts` 組込 + `bilattice-eight:refresh` + `test:step1202` script
- vite build 成功 (warning は wavedrom 由来で本 lens 無関係)

## chat-Claude fact-check 累計

20/20 → **22/22 verify PASS**:
- Belnap-Dunn 1977 + Dunn 1976: well-known
- Ginsberg 1988 'Multivalued logics': well-known prior art (本 STEP の orthogonal stance の動機)
- Fitting 1991 'Bilattices and the semantics of logic programming': well-known
- Arieli-Avron 1998 'The value of the four values': well-known prior art (interlaced 条件 source)
- arXiv 2604.07690 (2026-04 Bilattice-Catastrophe Isomorphism): 前 turn fact-check 済
- arXiv 2503.20679 (2025-03 Four imprints of Belnap): 前 turn fact-check 済

## Pattern 5 self-detection

| chat-Claude 提案要素 | Rei 既存 status |
|---|---|
| Belnap FOUR bilattice 構造 | 未実装 → **本 STEP で実装** |
| Ginsberg 9 値+ lattice 拡張 | 未実装 (重複回避のため、 拡張 4 軸を lattice 内部値として embed しない設計選択) |
| catastrophe theory 圏論的同値 (arXiv 2604.07690) | 未実装 (本 STEP scope 外、 将来 candidate) |
| 拡張 4 軸 (INFINITY/ZERO/FLOWING/SELF) operational role | 既存 substrate との link 明示 (Paper 63 SNST + Paper 61 ZCSG + W-48 NegCap + godel-lawvere-bridge + HoTTNagarjunaSymmetry) |

## 残 (c)(d) 次 session 着手対象

### (c) ∞-cosmoi 公理化 — 次 session 第 1 段 candidate

- Riehl-Verity 2022 'Elements of ∞-Category Theory' (Cambridge) の cosmos 公理 (cotensor / limit / isofibration) を SEED_KERNEL Institution view morphism に embed
- Mathlib higher-category bridge 設計
- Riehl-Verity ∞-Cosmoi for Lean blueprint (emilyriehl.github.io/infinity-cosmos) 既存 path 活用
- 本 STEP 1202 の Layer 2 orthogonal stance を ∞-cosmoi の axiom level で再 articulate する candidate

### (d) SELF⟲ ↔ HoTT loop space Ω formal 接続 — 次 session 第 2 段 candidate

- `Ω(A, a) := Path_A(a, a)` を SELF⟲ の代数として書き下す
- Mathlib `AlgebraicTopology.FundamentalGroupoid` bridge
- 既存 `godel-lawvere-bridge.ts` の Lawvere 不動点との同型確認 (chat-Claude 2026-06-08 thread turn 5)
- 本 STEP 1202 の Layer 2 SELF axis (orthogonal-fixpoint) substrate を loop space で formal 化

## 帰宅後 pending 並走 (別 repo)

memory `project_session_2026-06-07_full_summary` 継続:
1. CF Pages 反映確認 (5 page deploy stuck)
2. Phase 1B 残 indicator 追加
3. Dictionary v0.1 → v0.2 + Real OHLC chart Stage B+

## Honest scope (全 4 永続原則準拠)

- Belnap-Dunn 1977 + Ginsberg 1988 + Arieli-Avron 1998 = 40+ 年 prior art adaptation, 「世界初」 不使用 ([[feedback-world-uniqueness-claim-controllable]])
- 拡張 4 軸 orthogonal stance = lattice 拡張 prior art (9値+ Ginsberg-Fitting-Arieli-Avron 系列) との重複回避 = chat-Claude 「ラベル罠」 警告 honest 対応
- Peace Axiom #196 immutable と拡張 4 軸 orthogonal stance は両立 (lattice 内部に侵入しない設計選択)
- 「急がず ゆっくりと」 ([[feedback-no-rush-publication]]) — STEP 1202 完遂、 残 (c)(d) は次 session 明示 trigger 待ち
- chat-Claude pipeline 「ゲートを通す」 stance integration: 本 STEP の interlaced verification 64/64 PASS が「ゲート」 の operational 実例

## 関連 memory + reference

- [[project-step1201-institution-meta-curriculum-2026-06-08]] — STEP 1201 (a)+(e) 親 record
- [[feedback-chat-claude-hallucination-warning]] — chat-Claude fact-check 累計 20/20 → 22/22 verify
- [[feedback-world-uniqueness-claim-controllable]] — 「世界初」 不使用 controllable claim 限定
- [[feedback-no-rush-publication]] — 急がず ゆっくりと、 種は育ちます
- [[project-session-2026-06-08-full-summary]] — 前 session 全 summary

## Commit + verification

- Commit: `705bbdc3` "STEP 1202 (b): Bilattice 8値拡張 engine + site lens (Belnap FOUR + orthogonal extension)"
- Files: 9 file +1588 行 (5 A + 4 M)
- Test: `npm run test:step1202` 95/95 PASS
- vite build: 成功 (warning は wavedrom 由来で本 lens 無関係)
- dist-renderer mirror: `dist-renderer/data/bilattice-eight/latest.json` 同期済
- 大量 deletion / cron-touched file は意図的 stage 除外 ([[feedback-deploy-verify-violation-same-day-2026-06-05]] 4 段強化 protocol 準拠)
- Site visible: `#/bilattice-eight` route (CF Pages auto-deploy 後)