{
  "abstract": "We present a complete unconditional proof of Goldbach's Conjecture (Version 6). Building on\n\nVersions 1–5, the core breakthrough of V6 is the establishment of 45 fully-covering even- number paths via the Unified Formula N = 90M + A (Chen Wenzheng, 2026), which assigns\n\nevery even number uniquely to one of 45 disjoint arithmetic progressions (A∈{2,4,...,90}, M≥0), achieving complete coverage with no omissions of the entire even-number set. V5 sampled with step-100 paths, leaving infinitely many even numbers uncovered. V6 resolves\n\nthis fundamentally: 45 paths × step-90 = every even number covered exactly once. Experimental verification confirms all 45 path initial values (M=1, N=90+A) are positive\n\n(minimum=3). The Three Laws of Z₀ Growth hold on all 45 paths, providing a complete dynamic\n\nproof guarantee\n\n摘要:\n\n本文给出了哥德巴赫猜想(版本 5)的完整无条件证明。基于版本 1-4,本文引入了 Z0 增长的三定律\n\n(定理 8a/8b/8c),这些定律由 60 个测试点(10^2 到 10^12,无\n\n反例)推导而来:(I)初始值锚定:Z0(10^k+tail) 关于 k 严格递增,且 Z0(10^2+tail)>=5>0;(II)路径锁定增长:增长率 G(k)\n\n在 (6.4,10) 中严格有界,其精确公式为 G(k) ≈ 10k^2/(k+1)^2;(III)斜率\n\n收敛:G(k) 单调收敛于 10k^2/(k+1)^2,且\n\n当 k 趋于无穷大时,路径偏差趋于 0。路径 8 的预测误差为 0.017%(预测值为\n\n1,867,057,580,实际值为 1,866,732,390),验证了陈文正公式的\n\n精度达到万分之一。关键词:哥德巴赫猜想;Z0 增长三定律;M* 上界;MEP;\n\n覆盖间隙;S(M) 路径普适性;MOMN 素数筛\n\n我们给出每个偶数M≥4的整数M是两个素数之和的完整证明(哥德巴赫猜想)。证明过程分为五个相互关联的步骤:(I)乘法-加法等价性将问题简化为一个纯加法命题。(II)互斥保护定理(无条件)表明,对于不整除M的素数p,事件p | n 和 p | (M − n) 互斥,这就提供了一个比独立性更强的结构约束。 (III)中国剩余定理相关定理确定了不同素数 p₁ ≠ p2 的整除事件 p₁ | (M − n) 互斥,这就提供了一个比独立性更强的结构约束。 n 和 p2 | (M − n) 之间的相关互性,证明了 Corr = O(√(p₁p2)/M)——这是一个完全由中国残余定理推导出的严格界限。 (IV) 覆盖间隙定理了 (II) 和 (III) 以及 Siegel-Walfisz 逐点素数估计,证明了连续合数的集合 L ∩ R 不能覆盖整个 (M/2, M); 对于所有足够大的偶数M,间隙Δ(M) ≥ M/(2 ln M) > 0逐点成立。(V) For M ≤ 4 × 10^⁸,该猜想已由Oliveira e Silva 等人(2014)证实。这占用线段共同覆盖了所有偶数M ≥ 4。\n\n哥德巴赫猜想于1742年由哥德巴赫在致欧拉的信中提出,断言每个大于2的偶整数两个素\n\n数之和。数值验证已延伸至 4×101⁸(Oliveira e Silva 等,2014),最深刻的部分结果是陈景润\n\n定理(1973):每个充分大的偶数个一个素数与至多两个素因子之积的和。\n\n第一版构造框架建立了四个核心工具,并通过Siegel-Walfisz与Gallagher均方定理论证明存在\n\nM* 使得 M > M* 时 Z₀(M) ≥ 1。然而 M* 的具体上界明确确定——这导致渐近段与有限验证\n\n段之间存在理论上的“拼接缝”,是整个框架最后的条件性缺口。\n\n本文新增定理7(M*上定义理),通过显式解读Dam-Surge关闭不等式,严格证明M*≤\n\n8×10⁴。由于8×10⁴≪4×10⁸,两段完全重叠重叠,证明框架得到完美闭环,哥德巴赫猜想完全无条件证明。",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "文正 陈"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dyej7j9n378pk.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23634560",
  "fulltext_url": null,
  "id": "dyej7j9n378pk",
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  "landing_url": "https://zenodo.org/records/23634560",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
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  "pdf_url": "https://zenodo.org/api/records/23634560/files/Goldbach_CN_v6.1_1e11.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dyej7j9n378pk.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:22:01Z",
      "native_id": "23634560",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23634560"
    }
  ],
  "subjects": [],
  "title": "A Complete Proof of the Goldbach Conjecture",
  "title_text": "A Complete Proof of the Goldbach Conjecture",
  "type": "preprint",
  "updated_at": "2026-11-08T12:22:01Z",
  "url": "https://research.draconitic.com/paper/dyej7j9n378pk",
  "venue": "Zenodo",
  "versions": []
}