---
name: Paper 83 — Yang-Mills Mass Gap (toy model, honest position paper)
description: STEP 807. Phase 2.5 attack #5 FINAL. 27-dim Fock toy model, 9 configs 全 positive gap. 3 structures → D-FUMT₈ (ZERO/INFINITY/SELF). 7 missing capabilities 明示 out-of-scope. Millennium 解答 NOT claim.
type: project
originSessionId: a08149e8-f1de-4fbc-b4eb-fb2cec8fad21
---
# Paper 83 — Yang-Mills Mass Gap (honest toy map) (2026-04-16)

**Why:** Phase 2.5 attack target #5 最終. Clay Millennium Yang-Mills. **honest scope**: NOT a solution, just Rei framework map.

## STEP 807 結果 (9 configurations)

| Label | dim | E0 | E1 | gap Δ | >0? |
|---|---:|---:|---:|---:|---|
| 1 site free | 8 | 0.0000 | 1.0000 | 1.0000 | ✓ |
| 1 site anharm g=2 | 8 | 0.1492 | 1.6389 | 1.4897 | ✓ |
| 2 sites anharm+J | 16 | 0.0325 | 0.8690 | 0.8365 | ✓ |
| 3 sites free | 27 | 0.0000 | 1.0000 | 1.0000 | ✓ |
| 3 sites strong coupling | 27 | −1.3358 | −1.3210 | **0.0148** | ✓ |

**9/9 positive gap**. Strong coupling で 0.0148 まで縮むが positive 維持 (phase transition 接近示唆).

## D-FUMT₈ framework map

| Yang-Mills 要素 | D-FUMT₈ | 根拠 |
|---|---|---|
| vacuum (E₀) | **ZERO** | Paper 76 STEP 800 bosonic vacuum ⟨n̂⟩=0 |
| mass gap Δ | **INFINITY** | Paper 76 harmonic tower gap invariance |
| vacuum projector P₀ | **SELF** | Paper 76 P²=P idempotent |
| non-abelian color (未実装) | BOTH | Paper 75 \|+⟩ analogue (placeholder) |
| confinement (r→∞, out of scope) | NEITHER | Infinite distance, toy reach 外 |

## 公開

| サイト | URL |
|---|---|
| Zenodo | https://doi.org/10.5281/zenodo.19599986 |
| IA | https://archive.org/details/rei-aios-paper-83-1776290119131 |
| Qiita | https://qiita.com/fc0web/items/a5ae53aaef11d318f5cd |
| Harvard | https://doi.org/10.7910/DVN/KC56RY |

## ★ Honest Disclaimer ★

NOT claiming:
1. 非摂動 Yang-Mills ℝ⁴ 存在 proof
2. 連続極限 (a → 0)
3. 無限体積極限 (N → ∞)
4. Confinement
5. Asymptotic freedom
6. Clay Millennium Prize 解決

DOES claim:
1. 9/9 toy configs で positive gap
2. 3 structural 要素 (vacuum/gap/projector) の Rei D-FUMT₈ consistent 対応
3. Framework consistency check (解答時に Rei が破綻しないことの確認)

## Phase 2.5 全 5 attack targets 完了

| 順 | ターゲット | Paper | 結果 |
|---|---|---|---|
| 1 | Tao 2019/2022 Collatz | Paper 79 | Tao log-density 0 実証, n=27 extremal 再確認 |
| 2 | Generalized Collatz Cycles | Paper 80 | a=3/a∈{5,7} multiplier dichotomy |
| 3 | Tree Chains | Paper 81 | K=bit+2 exact identity, fast/slow families |
| 4 | Erdős Discrepancy | Paper 82 | 全 ±1 列 unbounded, Liouville canonical anchor |
| **5** | **Yang-Mills Mass Gap** | **Paper 83** | **Toy positive gap, honest framework map** |

★★ Phase 2.5 RDE→Paper pipeline 100% 完遂 ★★

## 累計

- 論文 **82 本** (Papers 1-83, 56/59 欠番), 全 4/4 サイト完全投稿
- Phase 2.5: **5/5 完了** (完璧な closed loop)
- Papers 79-83 = Phase 2.5 Discovery Engine の empirical validation