---
name: project-session-2026-07-26-evening-v3-draft-arc
description: "★★★★ 2026-07-26 evening continuation: γ-4 śūnyatā decision 3 段 protocol の 3 段目 (Paper 26 v3.0 draft 起草) 完了 arc。 PM session の Task 3 (段階 3 の 1 survivor identify) + Task 4 (Paper 26 v3 draft) + Task 5 (git commit) を実行。 (a) Lean 4 companion file 追加 (Paper26V3SurvivorDisplay.lean 10 theorem 全 axiom-free = 5 zero + 5 propext-Classical-Quot) → step 3 unique survivor を `bSwapBN` (Belnap 1977 非自明 automorphism {B↔N swap}) と axiom-free に identify + step 3→4 fail 理由 (involution → E∘E=id → 空亦復空 non-trivial の第 2 条件が全 x で false) axiom-free 説明。 (b) Paper 26 v3.0 draft 起草 (papers/paper-026-v3-shunyata-e-operator-belnap4-DRAFT.md 220 行) — v0.3 corrigendum abstract の 6 v3 予告全 grep verify + scope-change 注記 3 項目 (予告 path 不採用 / SAC-4 #4 root cause / v0.3 (5)(6) 継承) 明示、 Q1-Q6 verbatim table、 F1-F4 findings、 A3.1-A3.3 3 atomic claims、 6 non-claims、 B.5-B.10 background/methodology/prior art/related/deferred、 C.1 dual numbering v0.x/v3.x lineage 区別、 C.2 references (Belnap 1977 / Dunn 1976 / Font-Rivieccio 2011 / Priest-Garfield 2003 / Ganeri 2002 / Tanaka 2013 / MMK / v0.2 / v0.3)。 (c) git commit + push (次 step)。 publish は Q6 (II) protocol で藤本さん再判断待ち (feedback-no-rush-publication 準拠)。 累計: Lean 4 v3 evidence stack = 18 theorem all sorry/native_decide 全 0 (8 zero-axiom + 10 propext-Classical-Quot)、 3 段 protocol 全完了、 publish のみ pending。"
metadata: 
  node_type: memory
  type: project
  originSessionId: 8ea7ce66-a9a6-4ff8-8069-92d8a947516c
  modified: 2026-07-26T14:43:07.791Z
---

## 概要

2026-07-26 PM session の直接続き (evening continuation)。 藤本さん 「続きでお願い致します」 で再開、 PM session close 時に pending だった 3 段 protocol の残 tasks を完了。

## 前 session (PM) 状態 recap

PM session 終了時 Task 状態:
- Task 1 (§8 Q1-Q6 decisions): ✅ completed
- Task 2 (Track 2 256 enum reproduce): ⏸ partial-cross-check 完了、 hint 待ち
- Task 3 (Paper 26 v3 draft): ⏸ blocked
- Task 4 (Memory save Rule 4+5): ✅ completed
- Task 5 (Lean 4 implementation): ✅ completed
- Task 6 (Session memory save): ✅ completed
- **git commit 未実施 (帰宅後別判断)**

## Evening session 実行 tasks

| # | Task | Status |
|---|---|---|
| 1 | v0.2 spec 再 read + Q1-Q6 decisions 再確認 | ✅ completed |
| 2 | Lean 4 impl `#print axioms` 実測 | ✅ completed (8 theorem profile = 3 zero + 5 propext-Classical-Quot, cascade 256→16→4→1→0 confirmed) |
| 3 | 段階 3 の 1 survivor identify (companion file) | ✅ **completed** — bSwapBN identified axiom-free |
| 4 | Paper 26 v3 draft 起草 | ✅ **completed** — 220 行 |
| 5 | git commit + push | in_progress (evening close) |

## 主要 arc

### 1. Lean 4 impl `#print axioms` 実測 (Task 2)

`lake env lean CollatzRei/Paper26V3ShunyataEOperator.lean` を fresh run。 主 file 8 theorem の axiom profile 実測 confirmed:

| Theorem | Axioms |
|---|---|
| `bNeg_involutive` | ★ zero-axiom |
| `bDeMorgan_meet` | ★ zero-axiom |
| `bDeMorgan_join` | ★ zero-axiom |
| `shunyataOp_card` (256) | `[propext, Classical.choice, Quot.sound]` |
| `numSurvivorsLattice_eq_16` | `[propext, Classical.choice, Quot.sound]` |
| `numSurvivorsLatticeDeMorgan_eq_4` | `[propext, Classical.choice, Quot.sound]` |
| `numSurvivorsLatticeDeMorganNI_eq_1` | `[propext, Classical.choice, Quot.sound]` |
| **`numSurvivors_eq_0`** ★★★ | `[propext, Classical.choice, Quot.sound]` |

Cascade `#eval` 出力: `|ShunyataOp| = 256` → 16 → 4 → 1 → 0。 全 4 count 数 theorem 化済み。

### 2. Step 3 unique survivor identification (Task 3)

**発見**: step 3 の unique 1 survivor = **`bSwapBN`** (Belnap-Dunn FOUR の非自明 automorphism {B↔N swap})。

数学的 reasoning:
- Belnap 4 の lattice hom (meet + join 保存) → 16 survivors。 具体的候補: 4 constant functions + identity + 3 更なる candidates。
- + De Morgan commute → 4 survivors: `{const B, const N, identity, bSwapBN}` (constant T/F は ¬c ≠ c で reject)。
- + non-idempotent (∃ x, E(E(x)) ≠ E(x)) → **1 survivor**: `bSwapBN` のみ (const B/N/identity は全 x で E(E(x)) = E(x))。
- + shunyataShunyata non-trivial → **0 survivors**: bSwapBN は involution なので E∘E=id → 全 x で E(E(x)) = x → 第 2 条件 「E(E(x)) ≠ x」 が全 x で false。

これは **v0.3 corrigendum §A.3 (6) の "Aut(D-FUMT₈) = 2 elements only (identity + Belnap's own {B ↔ N} swap)" と同じ automorphism** = load-bearing convergence。

**実装** (`data/lean4-mathlib/CollatzRei/Paper26V3SurvivorDisplay.lean`, ~150 行):
- Section 1: bSwapBN 定義 + `#eval` function table display
- Section 2: bSwapBN 3 条件 (lattice + DeMorgan + notIdempotent) 満足 proof (`by cases <;> rfl` + `by decide` witness)
- Section 3: bSwapBN involutive + step 4 fail 説明
- Section 4: step 3 → step 4 transition constructive theorem
- Section 5: identity + constant B/N が step 3 で fail する baseline sanity

**Axiom profile (companion, 10 theorem)**:
- **5 完全 zero-axiom**: `bSwapBN_preservesLattice`, `bSwapBN_commutesWithNeg`, `bSwapBN_notIdempotent`, `bSwapBN_isStep3Survivor`, `bSwapBN_involutive`
- **5 propext-Classical-Quot**: `bSwapBN_fails_shunyataShunyata`, `step3_unique_survivor_fails_step4`, `identity_fails_notIdempotent`, `constB_fails_notIdempotent`, `constN_fails_notIdempotent`

**累計 evidence stack (main + companion) = 18 theorem all axiom-free** (8 zero + 10 propext-Classical-Quot / zero sorry / zero native_decide / zero user axioms)。

### 3. Paper 26 v3.0 draft 起草 (Task 4)

`papers/paper-026-v3-shunyata-e-operator-belnap4-DRAFT.md` (220 行) を起草。

**構成**:
- Title: "D-FUMT₈ Third Primitive as Śūnyatā Operator: Empirical Non-Existence on Belnap-Dunn FOUR Base (Lean 4 Axiom-Free)"
- Status header + **scope-change 3-item notice** (mandatory per Rule 5): (1) 予告 path 不採用 (2) SAC-4 #4 root cause (3) v0.3 (5)(6) 継承
- Authors (three-party OUKC) + License + Repo + Zenodo lineage (v1/v2/v0.2/v0.3/v3.0 TBD)
- **Abstract**: 主 negative result + 「Nāgārjuna 意図でなく one specific reading」 明示
- **Part A**:
  - **A.1 Findings** F1-F4 (cascade counts / bSwapBN identity / involution failure / semantic reading)
  - **A.2 Proofs**: 18 axiom-free theorem breakdown + verification commands
  - **A.3 Honest positioning**: A3.1-A3.3 3 atomic claims + **6 non-claims** (world-first / śūnyatā definability / Nāgārjuna intent / general reduction / v0.3 (5) glue 継承 / v0.3 (6) Fix(R) 継承)
  - **A.4 Required platform links**
- **Part B**:
  - **B.5 Background** (v0.3 decision tree + 5 中観 concepts mapping table)
  - **B.6 Methodology** (Q1-Q6 decisions verbatim table + filter definitions)
  - **B.7 Empirical scope** (v3.0 as-of, Track 2 cross-check status)
  - **B.8 Prior art audit** (Belnap 1977 / Dunn 1976 / Font-Rivieccio 2011 / Priest-Garfield 2003 / Aczel 1988 / Rutten 2000 / Ganeri 2002 / Priest 2018 / Tanaka 2013 / MMK)
  - **B.9 Related Rei stack references** (STEP 1207 / 1215 / 1218/1219/1220 / 1264 / Task 20 / v0.2 / v0.3)
  - **B.10 Deferred to v3.1**: 6 items (modal / higher-order / wider carrier / Fix(∅') / Track 2 / Full Part C)
- **Part C**:
  - **C.1 Version history** (dual numbering v0.x / v3.x lineage 区別、 mandatory scope-change item 3 詳細)
  - **C.2 References** (partial, full BibTeX deferred to v3.1)
  - **C.3 Acknowledgments** (藤本さん / chat-Claude / Rei)
- End + Publish protocol (Q6 (II) 藤本さん再判断待ち)

**Rule 5 遵守**: v0.3 corrigendum abstract を `grep -n "v3\|version 3\|deferred to.*v3\|Paper 26 v3"` で verify、 6 v3 予告全 identify (continuous rotor / TurboQuant iliafed / P({t,f,x}) powerset / Cl(3,0) silicon / §C 7 elements / Mathlib CliffordAlgebra bridge)、 scope-change 注記 3 項目に反映。

## 3 段 protocol status

γ-4 = 龍樹の空 3 段 protocol:
- 段 1 (spec 詳細化): ✅ v0.2 spec (dfumt8-shunyata-e-operator-spec-2026-07-26.md) — PM session
- 段 2 (実装): ✅ Lean 4 main + companion (18 theorem axiom-free) — PM + evening session
- 段 3 (paper draft + publish): 🟡 **draft ✅ (evening session, 220 行)** / publish ⏸ 藤本さん再判断待ち (Q6 (II))

= **3 段 protocol 3/3 段完了、 publish のみ pending**。

## git commit 対象 files (Task 5)

**untracked (this session + PM session)**:
- `docs/spec/dfumt8-shunyata-base-structure-spec-2026-07-26-v01-REJECTED.md` (v0.1 archived, PM)
- `docs/spec/dfumt8-shunyata-e-operator-spec-2026-07-26.md` (v0.2 base spec, PM)
- `data/lean4-mathlib/CollatzRei/Paper26V3ShunyataEOperator.lean` (main Lean, PM)
- `data/lean4-mathlib/CollatzRei/Paper26V3SurvivorDisplay.lean` (companion Lean, evening)
- `papers/paper-026-v3-shunyata-e-operator-belnap4-DRAFT.md` (v3.0 draft, evening)

**modified**:
- `data/lean4-mathlib/CollatzRei.lean` (import 2 files 追加, evening: PM で main のみ、 evening で companion 追加 + comment 拡張)
- `memory/MEMORY.md` (累計 note update, evening)
- `memory/feedback_projection_self_audit_pattern.md` (Rule 4+5 追記, PM)
- `memory/project_session_2026-07-26_shunyata_e_operator_arc.md` (new, PM)
- `memory/project_session_2026-07-26_evening_v3_draft_arc.md` (new, evening — 本 file)

**除外**:
- data/ 内 auto-refresh files (arxiv, jquants, buddy, crypto, etc.) は本 session の commit に含めない (auto commit で別途処理)。

## 帰宅後 resume 用 pointer

- **Track 2 hint 到着後 action**: chat-Claude の 3 条件目 (非可縮) literal formal 定義を Rei `notIdempotent` と比較 → 段階 3 で 1 vs 0 discrepancy root cause 特定 → Paper 26 v3.1 で reflect
- **Zenodo v3.0 publish**: Q6 (II) 藤本さん再判断 → 承認あれば 11 platform publish script 起動 (Zenodo API User-Agent 既 fix 済)
- **v3.1 candidate work**: full Part C / Fix(∅') 探索 (fragment 拡張後) / modal signature Q1 (b) enumeration (feasibility 検討)

## Related

- [[project-session-2026-07-26-shunyata-e-operator-arc]] (PM session、 直接前身、 spec + Lean impl)
- [[project-session-2026-07-26-paper26v2-v03-corrigendum-arc]] (AM session、 v0.3 corrigendum + γ-4 decision 起点)
- [[project-dfumt8-shunyata-third-primitive-decision]] (γ-4 decision 永続 record)
- [[feedback-projection-self-audit-pattern]] (Rule 5 遵守で v0.3 grep verify 実行)
- [[feedback-critique-response-pattern]] SAC-4 discipline (evening session は SAC-4 発生無し、 前 sessions 5 回)
- [[feedback-zero-sorry-floor-not-ceiling]] (18 theorem 全遵守)
- [[feedback-no-rush-publication]] Q6 (II) publish pending 継承
- [[feedback-world-uniqueness-claim-controllable]] Paper 26 v3.0 6 non-claims 遵守
- Paper 26 v2 v0.3 corrigendum (Zenodo 10.5281/zenodo.21572459, immutable) — v3 予告 path 参照元、 grep verify 対象