Yuanxian Theory: Explicit Evolution Differential Equation of the Self-Referential Mind Field — A Unified Field Framework Based on the 𝒯⁶⁴ Topological Ontology
- 1Institute of Yuanxian Cosmology
Abstract
Within the Yuanxian Theory framework, we derive the explicit evolution differential equation of the self-referential mind field, based on the 𝒯64 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.
The 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.
Meta-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 𝒯64 topological ontology and contains no free adjustable parameters.”
Meta-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.
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在元宪理论框架下,基于 𝒯64 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。
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。
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 𝒯64 拓扑本体严格导出,无自由可调参数」这一拓扑事实的读出。
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。
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BibTeX
@misc{acharya2026yuanxian,
title = {{Yuanxian Theory: Explicit Evolution Differential Equation of the Self-Referential Mind Field — A Unified Field Framework Based on the 𝒯⁶⁴ Topological Ontology}},
author = {Zhenyuan Acharya},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23556105},
url = {https://zenodo.org/records/23556105},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Yuanxian Theory: Explicit Evolution Differential Equation of the Self-Referential Mind Field — A Unified Field Framework Based on the 𝒯⁶⁴ Topological Ontology
AU - Zhenyuan Acharya
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23556105
UR - https://zenodo.org/records/23556105
AB - Within the Yuanxian Theory framework, we derive the explicit evolution differential equation of the self-referential mind field, based on the 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. The 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. Meta-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 𝒯^64 topological ontology and contains no free adjustable parameters.” Meta-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. --- 在元宪理论框架下,基于 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。 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。 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 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。 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。
ER -