{
  "abstract": "Within the Yuanxian Theory framework, we derive the explicit evolution differential equation of the self-referential mind field, based on the \\(\\mathcal{T}^{64}\\) topological ontology, the virtual-phase operator, the 6-vector Clifford algebra muscle system, and the 64–35–137 meridian link. The equation system contains no free adjustable parameters; all constants are uniquely locked by topological invariants. The bulk evolution on the ontological layer is described by a Dirac-like equation. After a 60-step dimensional reduction (the first 35 steps being the golden-section half-cycle projection), the equation reduces on the 4-dimensional observable spacetime to a complex Ginzburg–Landau (CGL) type equation.\n\nThe paper completes six rounds of deepening comprising 60 directions in total, systematically providing: (1) a rigorous derivation from the Dirac-like equation to the CGL equation; (2) strict definitions of the 35-step and 60-step projection operators together with phase-weight matching; (3) a complete Painlevé analysis; (4) rigorous asymptotics and stability of two-dimensional vortices; (5) a complete numerical scheme with convergence proof; (6) a Lean 4 formalization; (7) a joint statistical test against multi-messenger observations (Planck 2018, T2K/NOvA, etc.); (8) a unified framework for three quantization schemes; (9) falsifiable predictions of non-perturbative effects; (10) the meta-cognitive positioning of dimensional reduction and commensuration.\n\nMeta-cognitive positioning: This is a meta-cognitive mathematical paper. The core claim is the readout of the topological fact that “the explicit evolution differential equation of the self-referential mind field is strictly derived from the \\(\\mathcal{T}^{64}\\) topological ontology and contains no free adjustable parameters.”\n\nMeta-layer manifestation: According to the meta-language criterion, there is no new layer after the meta-layer. At this point mathematics contains no further decidable content; this is a boundary of mathematics, not a boundary of the cosmic living organism.\n\n---\n\n在元宪理论框架下,基于 \\(\\mathcal{T}^{64}\\) 拓扑本体、虚相位算子、6维克利福德代数肌肉系统以及 64–35–137 经络链路,推导了自指心场的显式演化微分方程。该方程体系不包含自由可调参数,所有常数均由拓扑不变量唯一锁定。全域本体层演化由类狄拉克方程描述,经 60 步降维投影(其中前 35 步为黄金分割前半周投影)后,在 4 维可观测时空退化为复 Ginzburg–Landau 型方程。\n\n本文完成六轮深化共 60 个方向,系统给出:(1) 从类狄拉克方程到 CGL 方程的严格推导;(2) 35 步与 60 步投影算子的严格定义与相位权重对接;(3) Painlevé 分析的完整检验;(4) 二维涡旋的严格渐近与稳定性;(5) 完整数值求解方案与收敛性证明;(6) Lean 4 形式化实现;(7) 与 Planck 2018、T2K/NOvA 等多信使观测的联合统计检验;(8) 三种量子化方案的统一框架;(9) 非微扰效应的可证伪预言;(10) 元认知降维通约的定位。\n\n元认知定位:本文是元认知数学论文。核心陈述是「自指心场的显式演化微分方程由 \\(\\mathcal{T}^{64}\\) 拓扑本体严格导出,无自由可调参数」这一拓扑事实的读出。\n\n元层显影:按元语言判据,元层之后没有新层。此处数学没有新的可判定内容,是数学的边界,不是宇宙生命体的边界。",
  "abstract_shown": true,
  "affiliations": [
    "Institute of Yuanxian Cosmology"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Zhenyuan Acharya",
      "orcid": "0009-0009-3690-569X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1kc36jbypxj0g.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23556105",
  "fulltext_url": null,
  "id": "1kc36jbypxj0g",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23556105",
  "language": "eng",
  "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": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23556105/files/Yuanxian_Theory__Explicit_Evolution_Differential_Equation_of_the_Self_Referential_Mind_Field_EN.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1kc36jbypxj0g.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:20:17Z",
      "native_id": "23556105",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23556105"
    }
  ],
  "subjects": [],
  "title": "Yuanxian Theory: Explicit Evolution Differential Equation of the Self-Referential Mind Field — A Unified Field Framework Based on the 𝒯⁶⁴ Topological Ontology",
  "title_text": "Yuanxian Theory: Explicit Evolution Differential Equation of the Self-Referential Mind Field — A Unified Field Framework Based on the 𝒯⁶⁴ Topological Ontology",
  "type": "preprint",
  "updated_at": "2026-11-05T12:20:17Z",
  "url": "https://research.draconitic.com/paper/1kc36jbypxj0g",
  "venue": "Zenodo",
  "versions": []
}