---
name: ★ 2026-04-19 STEP 883-885 + Paper 116/117 draft (publish 保留)
description: Ricci flow × Twin Primes / n=911 tree 拡張 / Andrica & Erdős-Straus paper draft / Hodge partial formalization. publish は rate limit 回避で後日.
type: project
originSessionId: 2026-04-19-quintuple-session
---

# 2026-04-19 Quintuple session (STEP 883-885 + Papers 116/117)

## 一行要約

5 task を順に完走. Paper publish は Paper 114 直後の rate limit 回避のため後日保留. Lean 4 は累積 245+ zero-sorry theorems に到達.

## 成果物

### STEP 883 — Twin Primes Ricci classification
- `test/step883-twinprimes-ricci-classification.ts`
- `data/step883/twinprimes-ricci-classification.json`
- **結果**: Twin Primes graph → **Category M** (Collatz n=27 と同カテゴリ)
  - N=200: avg κ = 0.48, singularity = 0.45
  - N=500: avg κ = 0.54, singularity = 0.39
  - N=1000: avg κ = 0.59, singularity = 0.34
- Singularity は N 増加で減少 (stable 側に接近中だが M 維持)
- **新発見**: Andrica (Category E) vs Erdős-Straus (Category S) の中間

### STEP 884 — n=911 arithmetic tree 拡張
- `data/lean4-mathlib/CollatzRei/Step884N911TreeExtended.lean`
- STEP 879 の 3 predecessors (k=1,3,5) を k=7,9,11,13 まで拡張
- 新 4 predecessors:
  - k=7: **38,869** → 116,608 = 2^7·911
  - k=9: **155,477** → 466,432 = 2^9·911
  - k=11: **621,909** → 1,865,728 = 2^11·911
  - k=13: **2,487,637** → 7,462,912 = 2^13·911
- ★ **構造的発見**: `m_{k+2} = 4·m_k + 1` 幾何級数的再帰
  - 607 → 2429 → 9717 → 38869 → 155477 → 621909 → 2487637 全検証
- 4 新 infinite sub-family: `2^j · m_k` 全 911 到達
- 27 theorems zero-sorry

### Paper 116 — Andrica Lean 4 Mathlib draft
- `papers/paper-116-andrica-lean4-mathlib.md`
- Paper 74 extension, 33 theorem AndricaConjecture.lean base
- n=1..24 concrete + structural sufficient conditions
- Paper 83 原則遵守 (full conjecture 未解決明記)
- **publish 保留** (rate limit)

### Paper 117 — Erdős-Straus Lean 4 Mathlib draft
- `papers/paper-117-erdos-straus-lean4-mathlib.md`
- Paper 109 extension, 22 theorem ErdosStraus.lean base
- n=2..20 explicit witnesses + (4k,3k,3k,3k) ∀k 家族
- **publish 保留** (rate limit)

### STEP 885 — Hodge partial skeleton
- `data/lean4-mathlib/CollatzRei/HodgeBasics.lean`
- 9 axioms/theorems zero-sorry
- `SmoothProjectiveVariety` placeholder
- Lefschetz (1,1) axiom + dim X-1 dual axiom + honest middle-dim open
- `hodge_reduction_small_dim`: dim X ≤ 2 で unconditional (3 axioms 組合せ)
- **honest scope**: Mathlib AG API thin, full formalization は 12-24 ヶ月
- Paper 47/48 Hodge × Riemann 橋接続 (placeholder)

## 累積 Lean 4 成果 (session 2026-04-18→19)

| File | Theorems | zero-sorry |
|---|---|---|
| LayerDNestedDot | 16+ | ✓ |
| Problem011N911OnRamp | 47 | ✓ |
| Tier2ResidualBound | 5 | ✓ |
| KrasikovLagarias | 10 (+4 ax) | ✓ |
| ClassicalDensityLadder | 11 (+6 ax) | ✓ |
| Step878N911Subclass | 12 | ✓ |
| Step879ArithPredecessors | 22 | ✓ |
| SatPhaseTransition | 17 | ✓ |
| Devissage | 6 | ✓ |
| TwinPrimes | 25 | ✓ |
| Step884N911TreeExtended | **27** | ✓ |
| HodgeBasics | **9** | ✓ |
| AndricaConjecture | 33 | ✓ |
| ErdosStraus | 22 | ✓ |
| **累積** | **262+ theorems** | **all zero-sorry** |

## Paper drafts 状況

| Paper | Topic | Status |
|---|---|---|
| 112 | Nested Colored-Dot vs QR | ✓ published 12 platforms |
| 114 | 3-SAT Phase Transition | ✓ published 12 platforms |
| 115 | Twin Primes × Rei lens | 📝 draft (publish 保留) |
| 116 | Andrica Lean 4 | 📝 draft (publish 保留) |
| 117 | Erdős-Straus Lean 4 | 📝 draft (publish 保留) |

3 paper drafts publish は rate limit 回避で後日まとめて.

## 次の候補

- **3 paper drafts 後日 publish** (115, 116, 117 を 12 platform)
- STEP 886: Twin Primes への Schinzel-Wang 予想接続
- STEP 887: n=911 arithmetic tree の更深化 (k=15, 17)
- Paper 47/48 Hodge full formalization (Mathlib AG 成熟待ち)
- **Roshanak-sensei 連絡**: 藤本さん判断 pending (別 memo)