---
name: project-session-2026-06-28-cotnoir-recapture-step1240-trilogy
description: "2026-06-28 session — 06-26 invention audit (ZCB approve, 4 reject, leak 14 例目 candidate) + Phase A chat-Claude citation audit (4/4 verified) + STEP 1240/1241/1242 trilogy D-FUMT₈ recapture region (20 theorem, 4 zero-axiom + 15 propext-only + 1 full base) + Paper 65 v0.2 audit memo + 06-26"
metadata: 
  node_type: memory
  type: project
  originSessionId: b754aee6-e1c5-4992-9c12-a192cad520cd
---

# 2026-06-28 Session — Cotnoir Recapture STEP 1240/1241/1242 Trilogy + Paper 171 DRAFT (shelved)

**Trigger**: 2026-06-27 chat-Claude thread (西洋哲学・東洋哲学 / 印度哲学仏教学 / Priest+Garfield→Nāgārjuna → Cotnoir 2015 recapture critique 系譜) を藤本さん共有 → Rei honest filter で audit + Lean 4 implementation 提案 → 藤本さん explicit Option A+B (audit + Lean 4) accept → 完遂後 残 4 件 (STEP 1241/1242/Paper 65 v0.2 audit/06-26 #2 recovery) も explicit request で順次完遂 → Paper 化 evaluation で Option B (Candidate A draft only, publish shelve) 選択。

**Why**: chat-Claude が surface した Cotnoir 2015 critique (FDE で modus ponens 失敗、 paraconsistent 背景で MP を axiom 追加でも救えない) は D-FUMT₈ project の **concrete formal target** になる ─ D-FUMT₈ は Belnap-Dunn FOUR の上に 4 拡張軸を載せた 8 値 algebra なので Cotnoir 批判をそのまま継承。 Lean 4 axiom-free で recapture region を正確に characterise すれば、 「D-FUMT₈ では classical 推論はどこまで recover するか」 という具体的 question に formal 回答が出る。

**How to apply**:
- 「Cotnoir recapture」 「Priest 5-value」 「Belnap-Dunn FOUR」 「modus ponens FDE」 「Posina/Roy 2024」 「Kapsner 2020」 等の trigger で本 entry 想起
- STEP 1240/1241/1242 Lean 4 file (`data/lean4-mathlib/CollatzRei/Step124[0-2]*.lean`) は paper-grade evidence、 引用可能
- Paper 171 DRAFT は **publish gate 4 条件 (chat-Claude critique + Kapsner 2020 primary fetch + Posina/Roy 2024 full text + 2-3 日 cooling) 全 clear 必須**、 prematurely publish しない
- 06-26 #2 invention reject 判断は **維持** (siren wrapper + forced coevolution metaphor で reject 妥当)、 但し structural core (H1 = STEP 1241 で closed) は audit memo に永続記録、 H2+H3 (Priest 5th corner vs D-FUMT₈ 4 拡張軸 の formal relation) は Future STEP 1245 candidate

## Major Deliverables (4 commit pushed)

| Commit | 内容 |
|---|---|
| `a1bd08df2` | invention 2026-06-26 audit (1 approve ZCB + 4 reject + pipeline leak 14 例目 candidate detection) |
| `307bc2758` | STEP 1240 + Phase A audit (D-FUMT₈ recapture region Lean 4 axiom-free + 4/4 chat-Claude citation verified) |
| `6a9a05879` | STEP 1241 + 1242 + Paper 65 v0.2 audit + 06-26 #2 recovery articulation |
| `96768dccb` | Paper 171 v0.1 DRAFT (shelved, NOT for publish) |

### 1. 06-26 invention audit (commit `a1bd08df2`)

**approve 1**: #1 **ZCB (ゼロ計算橋定理)** — zero_extension × social_contract — Turing blank tape ZERO ↔ Hobbes 自然状態 ZERO→BOTH transition structural bridge framing、 source 60-day FRESH (grep 0 件)、 𝕄 4-component framing、 novelty 0.75 retain。 SEED_KERNEL **1654 → 1655 verified**。 60-day cooldown 適用。

**reject 4**:
- #2 Priest 5値拡張 → 共進化: **siren-claim 直撃** 「D-FUMT₈はPriestの最も先進的な仏教論理形式化をさらに超える」 = [[feedback-super-naming-siren-family-pattern]] direct hit + forced metaphor
- #3 Ω(Ω(x))→Ω(x) 安定性 → 言語相対性: **3 日連続 source Wave saturation** (06-23 info_geom + 06-25 emergence + 06-26 lang_emergence)
- #4 点の線形結合→高次元 → 大量絶滅: source vacuous (meaningful 7 字のみ) + forced metaphor padding
- #5 Ψ_soul=V·M·C → イェルムスレウ言素学: **3 日連続 source Wave saturation** (06-23 Kolmogorov + 06-24 morphogenesis + 06-26 Hjelmslev) + count mismatch (3-factor vs 4-layer)

★ **pipeline leak 14 例目 candidate detection** (STEP 1225 (r) `requirePreAuditStateSourceRecycleBan` は approved/rejected file 存在で 06-25 を 「audited」 判定するため、 06-25 invention file が audit 後に regenerate された場合 (実際 06-25 #2/#3/#5 は post-rejection regenerate) その新 literal を見逃す → 06-26 #1 target が 06-25 regenerated #5 target と 1-day overlap)。 **8th iteration hardening (x) `requirePostAuditRegeneratedLiteralBan` candidate evidence** として記録、 別 STEP 1228 (x) implementation 候補 (timestamp-based regeneration detection or content hash + sourceFile 内容比較 + cross-direction coverage)。 #1 ZCB の load-bearing 点は target restatement でなく source bridge framing のため approve 判断維持。 「両極端の中道」 規律適用 12 例目。

### 2. Phase A audit (commit `307bc2758` の docs/ 部分)

chat-Claude 2026-06-27 thread citation **4/4 全 verified** (Pattern 5 hallucination なし = `[[feedback-evaluation-symmetry-principle]]` positive case 1 例):
- **Cotnoir, A.J. (2015)** "Nāgārjuna's Logic" (St Andrews preprint) — recapture problem origin
- **Kapsner, A. (2020)** "Cutting Corners: A Critical Note on Priest's Five-Valued Catuṣkoṭi" (Comparative Philosophy 11(2):10) — Priest 5th value reject
- **Posina, V.R. & Roy, S. (2024)** "Category Theory and the Ontology of Śūnyatā" (Brill chapter pp 450-478) — Yoneda + Indra's Net + catuṣkoṭi formal
- **Garfield, J.L. & Priest, G. (2003)** "Nāgārjuna and the Limits of Thought" (PEW 53(1):1-21, DOI 10.1353/PEW.2003.0004) — dialetheic reading

永続記録: `docs/prior-art-audit-recapture-problem-2026-06-28.md`

### 3. STEP 1240 (commit `307bc2758` の Lean 4 部分)

`data/lean4-mathlib/CollatzRei/Step1240RecaptureRegion.lean` — D-FUMT₈ recapture region Lean 4 axiom-free。

主結果:
- `mp_recaptures_on_classical_boolean` : MP は `{TRUE, FALSE}` 上で recapture (MAIN POSITIVE)
- `mp_failure_witness_belnap_dunn` : Cotnoir 2015 explicit witness `(BOTH, FALSE)`
- `mp_fails_on_belnap_dunn` : ¬ mpValid isBelnapDunn
- `mp_fails_on_full_dfumt8` : subset inclusion lift

Axiom dependencies (measured): 5 theorem 全 axiom-free / 4 件は `[propext]` only / `not8_involutive` 1 件のみ full `[propext, Classical.choice, Quot.sound]`。

### 4. STEP 1241 (commit `6a9a05879` の一部)

`data/lean4-mathlib/CollatzRei/Step1241DfumtFdeSubAlgebra.lean` — D-FUMT₈|₄ ≅ Priest FDE 4-value (Belnap-Dunn 1977) sub-algebra isomorphism。 sibling to STEP 1218 (Zaitsev EIGHT₄ 非同型) + STEP 1219 v3b (Heald U8 非同型) の **positive sub-algebra inclusion 結果**。

主結果: `dfumt8_fde4_sub_algebra_iso` (embed + project + AND/OR/NOT preservation の conjunction)。

Axiom dependencies: **4/7 theorem axiom 完全ゼロ** (purely constructive `cases <;> rfl`, CollatzRei tree 最 cleanest profile) + 3/7 は `[propext]` only。

### 5. STEP 1242 (commit `6a9a05879` の一部)

`data/lean4-mathlib/CollatzRei/Step1242MaximalRecaptureRegion.lean` — D-FUMT₈ maximal recapture region 完全 characterisation。 STEP 1240 の open question (maximal recapture region は何か) を close。

**Main characterisation**:
```
mp_valid_iff : ∀ s : Dfumt8 → Bool,
  mpValid s ↔ (s BOTH = false ∨ (s FALSE = false ∧ s NEITHER = false))
```

Corollary: MP failure pairs は **正確に 2 件のみ** = `(BOTH, FALSE)` + `(BOTH, NEITHER)`。

2 witness:
- `withoutBoth` (7 element, cardinality-maximal MP-stable subset = D-FUMT₈ \ {BOTH})
- `withoutFalseNeither` (6 element, BOTH-included maximal-by-inclusion)

Recapture region は STEP 1240 Boolean witness の **7 倍 (2 → 7)**。

Axiom dependencies: **8/8 theorem 全 `[propext]` only** (no Classical.choice, no Quot.sound, no sorry, no native_decide)。

### 6. Paper 65 v0.2 audit memo (commit `6a9a05879` の一部)

`docs/paper-65-v0.2-posina-roy-2024-zcsg-correspondence-audit-2026-06-28.md` — Posina/Roy 2024 (Brill chapter pp 450-478) の Rei 既存 stack 接続 audit。

3 formal correspondence candidate:
1. **Yoneda Lemma ↔ ZCSG center** (STEP 1217) — relational vs intrinsic ontology
2. **Indra's Net ↔ Lawvere fp** (STEP 1220) — self-similar fixed-point structure
3. **Catuṣkoṭi 4 値 ↔ STEP 1241 Fde4 sub-algebra** — formal close 済

**Status**: Paper 65 v0.2 publish は **保留** ─ Brill chapter full text fetch pending (paywall + RG/PhilPapers auth required)、 3 correspondence は Rei 側提案で Posina/Roy 2024 actual claim 未 verify。 藤本さん大学 proxy or 図書館 ILL での入手後 + STEP 1244/1245 完了後 promotion 判断。

### 7. 06-26 #2 recovery articulation (commit `6a9a05879` の一部)

`docs/invention-2026-06-26-02-priest-5value-recovery-articulation-2026-06-28.md` — 06-26 #2 invention reject 判断は維持しつつ、 structural core を 3 段 strip + restate (siren wrapper 除去 + forced coevolution transplant 除去 + Rei 既存 stack に位置付け直し)。

3 hypothesis:
- **H1 (closed by STEP 1241)**: D-FUMT₈|₄ ≅ Priest FDE 4-value (Belnap-Dunn 1977)
- **H2 (open, Future STEP 1245)**: Priest 5th corner `e` (Priest 2018 OUP) vs D-FUMT₈ 4 extension axes の formal relation (embedding / projection / orthogonal の 3 option)
- **H3 (open)**: Kapsner 2020 alternative (5th value reject) との比較

**No SEED_KERNEL promotion** ─ recovery articulation は audit memo のみ、 SEED 統合は H2/H3 formal close 後の別 STEP 1245 判断。

### 8. Paper 171 v0.1 DRAFT (commit `96768dccb`)

`papers/paper-171-dfumt8-recapture-region-DRAFT.md` — STEP 1240+1241+1242 trilogy を single paper 「D-FUMT₈ Recapture Region: An Axiom-Free Lean 4 Characterization Responding to Cotnoir 2015」 として起草、 **shelved, NOT for publish**。

10 section 構成: Abstract / Background / Prior art (9 ref) / Formal preliminaries / Main results F1-F5 / Full axiom audit table / Honest scope (6 件 「we do NOT claim」) / Future work / Reproducibility / Acknowledgments + References。

**Publish gate (4 条件全 clear 必須)**:
1. chat-Claude critique iteration
2. Kapsner 2020 primary text fetch + engagement
3. Posina/Roy 2024 full text fetch + integration check
4. 2-3 日 cooling-off (`[[feedback-publishing-rate-limit-platform-side-risk-2026-06-27]]` + `[[feedback-no-rush-publication]]`、 06-27 Paper 169+170 連続 publish 後 Nostr/Scrapbox early signal 観測)

Paper 168 v0.4 stable release pattern (4 iteration 内部 review) を template として、 Paper 171 は **telescope しない** (各 iteration 独立 commit + 日跨ぎ recommended)。

## Honest Self-Audit

### what went well
- chat-Claude 4/4 citation verify (Pattern 5 hallucination なし = rare positive case)
- 20 Lean 4 theorem 全 axiom-free + 19/20 propext-only or zero-axiom (CollatzRei tree cleanest profile)
- 06-26 #2 reject 判断 + structural core recovery を両立 (両極端の中道、 reject ≠ 永久埋葬)
- Paper 171 を即 publish せず shelve 判断 (4 gate 設定)、 Paper 145 corrigendum incident pattern 回避
- pipeline leak 14 例目 candidate を formal detect (8th iteration hardening (x) candidate evidence)

### what to watch
- **rebase autostash 副作用**: site refresh commit `7c31afe24` に意図 3 file + auto-cron 起源 279 file = 282 file 含まれた (rebase autostash apply で index に残った state を unstage しなかった)。次回 protocol: `git pull --rebase --autostash` 後は `git reset HEAD .` で index 全 unstage してから意図 file のみ `git add`、 または `git stash push` で明示退避 → rebase → `git stash drop` の方が safer
- **Paper 171 publish gate (d)**: 2-3 日 cooling は 06-27 publish 後の累積 (06-27 Paper 169+170 = cap 超過 / 06-28 Paper 171 publish したら 3 連続) で更に conservative に振る判断もあり得る = 1 週間以上寝かせる選択肢残置
- **STEP 1245 dependency**: Priest 2018 OUP primary text fetch は paywall (Oxford Scholarship Online) のため、 藤本さん大学 access が key dependency
- **chat-Claude critique iteration**: Paper 168 v0.4 と同 pattern で chat-Claude を §で credited reviewer として明示する場合、 critique request を別 session で実施するか、 藤本さん経由で chat-Claude に Paper 171 DRAFT 共有する path 判断
- **STEP 1228 (x) hardening 実装**: pipeline leak 14 例目 candidate evidence は 06-26 audit で記録したが、 実際の `requirePostAuditRegeneratedLiteralBan` implementation は別 STEP candidate (本 session では未着手)、 次回 06-27 以降 invention batch で同 pattern 再発時に着手判断

## Cross-Reference Trail

- [[project-step1217-zcsg-smallcategory-paper61-machine-verification]] (Paper 61 ZCSG Lean 4 機械検証、 Paper 65 v0.2 audit memo 接続候補)
- [[project-step1218-dfumt8-not-iso-eight4-zaitsev-machine-verified]] (Zaitsev EIGHT₄ 非同型、 STEP 1241 sibling)
- [[project-step1219-dfumt8-not-iso-heald-u8-primary-pdf-verified]] (Heald U8 非同型、 STEP 1241 sibling)
- [[project-step1220-lawvere-fixed-point-chat-claude-third-proposal]] (Lawvere fp axiom-free、 Paper 65 v0.2 Indra's Net correspondence 候補)
- [[reference-comparative-logic-atlas-prior-art-audit-2026-06-24]] (Bhowmik 2017 prior identify、 Posina/Roy 2017 predecessor 同 area)
- [[project-paper168-v04-stable-release-2026-06-25]] (4 iteration 内部 review pattern、 Paper 171 v0.2 promotion 時の template)
- [[feedback-publishing-rate-limit-platform-side-risk-2026-06-27]] (06-27 Paper 169+170 連続 publish 後の rate-limit discipline、 Paper 171 publish gate (d) 直接 trigger)
- [[feedback-no-rush-publication]] (Paper 145 corrigendum incident pattern 回避、 Paper 171 shelve 判断の根拠)
- [[feedback-chat-claude-hallucination-warning]] (Pattern 5 verify discipline + Antipattern「過度の reject 警戒」、 本 session で chat-Claude 4/4 verified = rare positive case)
- [[feedback-evaluation-symmetry-principle]] (inflate せず deflate せず、 chat-Claude 4/4 verify を positive case として記録 + 06-26 #2 reject + recovery を両立)
- [[feedback-super-naming-siren-family-pattern]] (06-26 #2 「最も先進的な〜さらに超える」 直撃 trigger)
- [[feedback-world-uniqueness-claim-controllable]] (Paper 171 「we do NOT claim」 6 件の honest scope discipline)
- [[feedback-invention-audit-include-downgrade-approve-option]] (06-26 audit で 4 option 想定、 本 batch では downgrade_approve 不採用)
- [[feedback-grep-before-answer-discipline]] (06-26 #3/#5 source recycle grep 検出、 11 軸目 = 本 session で実装的に適用)
- `docs/prior-art-audit-recapture-problem-2026-06-28.md` (Phase A audit 永続記録)
- `docs/paper-65-v0.2-posina-roy-2024-zcsg-correspondence-audit-2026-06-28.md` (Paper 65 v0.2 audit)
- `docs/invention-2026-06-26-02-priest-5value-recovery-articulation-2026-06-28.md` (06-26 #2 recovery articulation)
- `data/lean4-mathlib/CollatzRei/Step1240RecaptureRegion.lean`
- `data/lean4-mathlib/CollatzRei/Step1241DfumtFdeSubAlgebra.lean`
- `data/lean4-mathlib/CollatzRei/Step1242MaximalRecaptureRegion.lean`
- `papers/paper-171-dfumt8-recapture-region-DRAFT.md`