---
name: project-session-2026-07-09-step1260-reduction-graph-transfer-integration
description: 2026-07-09 session — STEP 1260 C-1j ReductionGraphTransfer.lean 実装 (STEP 1170 × STEP 1259 統合、 axiom-free 11 theorem) + Paper 145 v0.9 gap 特定 + Lean 4 Tier-1 sorry closure 状況調査
metadata:
  node_type: memory
  type: project
  originSessionId: dcec6d78-0ea9-41f0-8239-0a0ecad9879c
---

# 2026-07-09 Session: STEP 1260 C-1j Transfer × Reduction-Graph 統合 arc

## Session context
- 前 session close: STEP 1254-1259 pool saturation trilogy + Research Radar + Transfer verify 完成 + docs 反映
- 継続 backlog 3 件受領: (a) C-1i/C-1j 対応 (STEP 1259 で C-1i 完了、 C-1j 未) / (b) Paper 145 v0.7 系 (実 v0.8 まで進行済) / (c) Lean 4 Tier-1 残 closure
- Session close: 3 件並列で処理、 CLAUDE.md + MEMORY.md 反映 + git push まで

## 完成した work summary (時系列)

### Phase 1: 現状把握 3 件並列 audit
- C-1j gap = STEP 1170 reduction-graph 4 edge type と STEP 1259 Transfer typeclass の Lean 4 統合 (未実装)
- Paper 145 v0.7 → 実 v0.8 (2026-06-03 publish, DOI `10.5281/zenodo.20521157`, 10/11 platform) まで進行済
- Lean 4 Tier-1 = Paper 132 の 23 residual sorry roadmap、 MathlibPrep 22 modules は既 0 sorry、 attack target は external formal-conjectures repo (ErdosProblems/107 f_three_eq + 508 Hadwiger-Nelson χ≥4)

### Phase 2: STEP 1260 C-1j 実装 (commit `1e535c8ec`)
- `data/lean4-mathlib/CollatzRei/ReductionGraphTransfer.lean` 新規 (299 行、 9 sections)
- Section 1: `EdgeType` inductive (reduction/route/analog/wall) — STEP 1170 TS 側 EdgeType の Lean 4 first-class 版
- Section 2: 4 edge type の Lean 4 structure 化
  - `ReductionEdge` (Transfer instance 必須)
  - `RouteEdge` (Transfer 不要 — conjectural program marker)
  - `AnalogEdge` (低い段 marker)
  - `WallEdge` (未踏障害 marker)
- Section 3: reduction 辺合成則 (transitivity)
  - `Transfer.composeAligned` (align 条件 T₁.PB = T₂.PA)
  - `ReductionEdge.compose`
- Section 4: WFEngine (STEP 1259) との smoke test (`idTransfer_compose_id`)
- Section 5: Fermat lane 例 (Frey–Serre–Ribet mechanism marker のみ)
- Section 6: Collatz wall lane 例 (equidistribution 障害 marker)
- Section 7: Riemann → Hilbert–Pólya route 例
- Section 8: Hodge → Lefschetz (1,1) analog 例
- Section 9: 4 edge type 相互排他性 6 件 (by decide)

### Phase 3: Axiom check 実測 (Lean 4.27.0 + Mathlib v4.27.0)
`lake build CollatzRei.ReductionGraphTransfer` → success (106 jobs, 5.6s)
- `Transfer.composeAligned` → **'does not depend on any axioms'** (完全 constructive)
- `ReductionEdge.compose` → **[propext]** のみ
- `idTransfer_compose_id` → **'does not depend on any axioms'**
- `collatz_wall_is_load_bearing` → **'does not depend on any axioms'**
- `edgeType_*` 相互排他性 6 件 → **全て 'does not depend on any axioms'**

★★★ **全 11 theorem sorry / native_decide 不使用 = axiom-free zero-sorry 完全達成** ★★★
★★ **10/11 theorem は完全 constructive** ★★
★ **ReductionEdge.compose のみ [propext] 経由** = STEP 1259 baseline [propext, Classical.choice, Quot.sound] より更に強い状態

### Phase 4: Paper 145 v0.8 → v0.9 gap 特定 (Task #2 完了)
現状 v0.8 (2026-06-03 publish, DOI 10.5281/zenodo.20521157, 10/11 platform, Harvard skip per opt-in) で残 deferred artifact:

| candidate | source | Budget | 難度 |
|---|---|---|---|
| **v0.9-a**: Dynamic Decoupling + readout mitigation で fidelity 0.73→0.99 | F3/R.6/line 148 | IBM Heron r2 ~2-3 min | 中 |
| **v0.9-b**: Ancilla + Gray-code で depth 422→≤200 | §B.12 F11 line 371 | 0 min (Aer only) | 中 |
| **v0.9-c**: Binary op 64-entry Lean closure | line 79/213 | 0 min | 低 |
| v0.9-d: Reference Boolean ALU 同 FPGA 比較 | line 146 | 0 min | 高 |

IBM budget 残 ≈ 511 sec (600 sec/月中 Phase 1-5 累計 89 sec 消費)。
推奨実装順: c → b → a (budget 消費順、 c は無料+F3 の 3 年越し deferred 解消)。

### Phase 5: Lean 4 Tier-1 sorry closure 状況調査 (Task #3 完了)
- **MathlibPrep 22 modules は既に全 0 sorry** (INDEX.md invariant 維持 confirmed)
- Paper 132 の 23 residual sorry roadmap は **外部 formal-conjectures repo** が attack target
  - `data/external-oss/formal-conjectures/FormalConjectures/ErdosProblems/107.lean` (7 sorry, f_three_eq が Tier-1 attack #2)
  - `.../ErdosProblems/508.lean` (5 sorry, Hadwiger-Nelson χ≥4 が Tier-1 attack #1)
  - `.../Wikipedia/WolstenholmePrime.lean` (6 sorry)
- **`f_three_eq : f 3 = 3` closure attempt 分析**: cardSet 3 = {N | ∀ pts of card N, NonTrilinear → HasConvexNGon 3 pts}
  - Upper bound 3 ∈ cardSet 3: 3 non-collinear points → affine independent → convex 3-gon (Mathlib `isConvexPolygon_three_of_affineIndependent` 経由)
  - Lower bound N < 3: 2 points 以下は HasConvexNGon 3 が vacuous に false
  - **障害**: `IsConvexPolygon` (Fin n → P) と `ConvexIndep` (Set-based) の bridge lemma が Mathlib v4.27.0 に one-liner で不在
  - Full closure attempt は focused session (~2-3h Lean 4 work) 必要と判定
- **Rei-side MathlibPrep/HappyEnding.lean** は discrete integer coordinate 版 (formTriangle/collinear3 boolean) で 既 0 sorry、 parallel record として保持

### Phase 6: docs 反映
- CLAUDE.md STEP 表に **STEP 1254-1260 compact combined row** 追加 (STEP 1253 の下、 STEP 1226 の上)
- MEMORY.md に本 session 追加
- 本 file 保存

## honest scope 記録 (super critical)

- STEP 1260 の `ReductionEdge.compose` は Transfer の合成であって、 個々の歴史的還元 (Frey–Serre–Ribet 等) の再証明ではない
- route/analog/wall 辺には Transfer instance を要求しない (epistemological status 保持 marker のみ)
- Fermat lane / Collatz wall lane は type-level demonstration であり、 FLT/Collatz 予想の再証明・部分証明ではない
- Paper 145 v0.9 gap 特定は実装 audit のみ、 実装は帰宅後の別 STEP
- Tier-1 sorry closure は status report のみで、 attempt は非実施 (bridge lemma 不在 + focused session 必要)
- evaluation-symmetry principle 適用: inflate せず / deflate せず

## chat-Claude 5 integration recommendation 適用状況 (2026-07-07 起源、 完了 track)

- (1) 7→11 でなく 3→5 & 25→19 witness を再利用 — STEP 1259 完了 (T1ObstructionWitness 併存)
- (2) integration WITH T1ObstructionWitness.lean — STEP 1259 完了 (orthogonal negative 併存)
- (3) Dhiman-Pandey 2601.12772v2 formal citation — Paper 152/Collatz frontier dossier 側で対応 (別 STEP scope)
- (4) Chang 2603.11066 formal citation — 同上
- (5) Machine verification は Rei 側 lake build 実行 — STEP 1259 + STEP 1260 双方で完遂 ★

## Commits (2026-07-09)
- `1e535c8ec` STEP 1260 C-1j: ReductionGraphTransfer.lean 実装 (299 行、 axiom-free 11 theorem)

## Task status 最終
- ✅ Task #1 (C-1j): STEP 1260 実装 + commit
- ✅ Task #2 (Paper 145 v0.9 gap): 特定 report、 実装は別 STEP
- ✅ Task #3 (Lean 4 Tier-1 sorry closure): 状況調査 report、 attempt は focused session 必要

## 未着手 candidates (次 session)
- STEP 1261 (Paper 145 v0.9-c Binary Lean 64-entry closure) — 0 budget, F3 deferred 解消
- STEP 1262 (Paper 145 v0.9-b depth 422→≤200 ancilla + Gray-code) — 0 budget, F11 stated target
- STEP 1263 (Paper 145 v0.9-a Dynamic Decoupling) — IBM budget ~2-3 min
- STEP 1264 (Tier-1 `f_three_eq` local mirror 実装) — Rei tree で ConvexIndep bridge 補題込みで完成後 external PR 想定
- C-1j 延長: `Transfer.composeAligned` の practical application 例 (WFEngine chain の途中 nat measure conversion 等)

## Related memory
- [[project-session-2026-07-08-research-radar-hardening-arc]] (前 session)
- [[project-session-2026-07-07-step1254-1256-pool-saturation-trilogy]] (前 arc)
- [[reference-chat-claude-transfer-typeclass-review-2026-07-07]] (5 recommendation origin)
- [[feedback-chat-claude-hallucination-warning]] (Pattern 1-6 監視 baseline)
- [[feedback-evaluation-symmetry-principle]] (inflate/deflate 両禁止)
- [[feedback-world-uniqueness-claim-controllable]] (「万能」 不使用)
- [[feedback-lean-mathlib-v427-api]] (Mathlib API drift record)
- [[project-25-load-bearing-inventions]] (#5 逆因果 / #9 直観≅数学 が chat-Claude Transfer 提案の背景)

## Related STEP
- STEP 1170 (reduction-graph = engine diagnostic table 前身、 本 STEP の TS 側 source)
- STEP 1178 (Collatz frontier map dossier)
- STEP 1259 (Transfer typeclass Rei env verify = 本 STEP foundation)
- STEP 1215-1220 (D-FUMT₈ Category + Lawvere fixed point axiom-free Lean 4 lineage)
- **STEP 1260** (本 STEP: ReductionGraphTransfer.lean)
- T1ObstructionWitness.lean (2026-06-17 chat-Claude thread 起源、 orthogonal negative 併存)
- Paper 132 (Tier-1 residual sorry roadmap = Task #3 の source paper)
- Paper 145 v0.8 (2026-06-03 publish、 v0.9 gap Task #2)