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Proof of the Hodge Conjecture within the Unified Metabolic Causal Field

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1. Verfasser:	Zhu, Jianbing
Format:	Recurso digital
Sprache:	Englisch
Veröffentlicht:	Zenodo 2026
Schlagworte:	Hodge Conjecture; unified metabolic causal field; metabolic element; holism; category theory; Hodge structure; algebraic cycle
Online-Zugang:	Acceder al recurso
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_version_	1866901898003480576
author	Zhu, Jianbing
author_facet	Zhu, Jianbing
contents	<p><span>本文利用整体数学中的代谢元素构造和逆极限定理论,严格证明了统一代谢因果场框架下的霍奇猜想:对于任意非奇异的复射影代数簇</span><span><span><span>X</span><span><span><span>X</span></span></span></span></span><span>,每个霍奇类(即中的元素)</span><span><span><span>H2p(X,Q)∩Hp,p(X)</span><span><span><span><span>H</span><span><span><span><span><span><span><span>2</span><span>p</span></span></span></span></span></span></span></span><span>(</span><span>X,Q</span><span>)</span><span>∩</span></span><span><span><span>H</span><span><span><span><span><span><span><span>p</span><span>,</span><span>p</span></span></span></span></span></span></span></span><span>(</span><span>X</span><span>)</span></span></span></span></span><span>)是上代数环的有理线性组合</span><span><span><span>X</span><span><span><span>X</span></span></span></span></span><span>.该证明完全依赖于《从数学基础到系统哲学的完整理论链》\cite{zhu2026a}中确立的核心概念和定理,并将代数几何中的概念如霍奇结构、代数环和周群纳入统一代谢因果场的范畴论框架中。该证明展示了整体数学在解决代数几何核心问题中的强大解释能力。</span></p>
format	Recurso digital
id	zenodo_https___doi_org_10_5281_zenodo_19507975
institution	Zenodo
language	eng
publishDate	2026
publisher	Zenodo
record_format	zenodo
spellingShingle	Proof of the Hodge Conjecture within the Unified Metabolic Causal Field Zhu, Jianbing Hodge Conjecture; unified metabolic causal field; metabolic element; holism; category theory; Hodge structure; algebraic cycle <p><span>本文利用整体数学中的代谢元素构造和逆极限定理论,严格证明了统一代谢因果场框架下的霍奇猜想:对于任意非奇异的复射影代数簇</span><span><span><span>X</span><span><span><span>X</span></span></span></span></span><span>,每个霍奇类(即中的元素)</span><span><span><span>H2p(X,Q)∩Hp,p(X)</span><span><span><span><span>H</span><span><span><span><span><span><span><span>2</span><span>p</span></span></span></span></span></span></span></span><span>(</span><span>X,Q</span><span>)</span><span>∩</span></span><span><span><span>H</span><span><span><span><span><span><span><span>p</span><span>,</span><span>p</span></span></span></span></span></span></span></span><span>(</span><span>X</span><span>)</span></span></span></span></span><span>)是上代数环的有理线性组合</span><span><span><span>X</span><span><span><span>X</span></span></span></span></span><span>.该证明完全依赖于《从数学基础到系统哲学的完整理论链》\cite{zhu2026a}中确立的核心概念和定理,并将代数几何中的概念如霍奇结构、代数环和周群纳入统一代谢因果场的范畴论框架中。该证明展示了整体数学在解决代数几何核心问题中的强大解释能力。</span></p>
title	Proof of the Hodge Conjecture within the Unified Metabolic Causal Field
topic	Hodge Conjecture; unified metabolic causal field; metabolic element; holism; category theory; Hodge structure; algebraic cycle
url	https://doi.org/10.5281/zenodo.19507975