Synapse
⌘+K
Synapse
PulseExploreClubsResearchersJournals
Instagram
HomeClubsExplore
August 16, 2026Open Access

Complexified 3D Numbers: An Algebraic Framework for the Riemann Hypothesis 复化三维数:研究黎曼猜想的代数框架

View Full Paper
Ask AI
Bookmark
Share

Authors

ZLZhongqiang Liu

Discussion

Loading...

Member takes

Implication

Theoretical study demonstrates geometric stability along the critical line using complexified three-dimensional numbers, suggesting a novel algebraic pathway toward the Riemann hypothesis.

Key Points

  • To establish and analyze a six-dimensional complexified 3D algebraic framework to explore geometric and analytic structures related to the Riemann hypothesis.
  • Extended the base field of a non-associative three-dimensional phase-geometric system from real to complex numbers.
  • Conducted five interlocking theoretical evaluation series (K1–K5) analyzing algebraic consistency, non-associativity phase space, isotropic geometry, critical line dynamics, and contour integration.
  • Confirmed algebraic self-consistency and identified a left-half-plane stable region with an approximately 50-fold isotropic suppression effect on non-associativity.
  • Demonstrated that the critical line Re(s) = 1/2 serves as the unique dynamic balance line between time-like and space-like regions, with Hessian oscillations connecting to GUE spacing of Riemann zeros.
  • Proved that scalar contour integration is immune to non-associativity, confirming the validity of Cauchy's theorem and the residue theorem within the framework.

Cite This Study

Zhongqiang Liu (2026) studied this question.

synapsesocial.com/papers/6a817ab4f2fb91fc834aec2ahttps://doi.org/10.5281/zenodo.21946955
View Full Paper
Ask AI
Bookmark
Share

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Complex‑Analysis and Geometric‑Structure of 3‑Dimensional Complex Numbers: From Algebraic Axioms to Conformal Field Theory 三维复数的复分析与几何结构 从代数公理到共形场论2026
  2. 2Complexified Three-Dimensional Algebra: From Isotropic Geometry to Golden Polynomial Spectra 复化三维数代数体系:从迷向几何到黄金多项式谱系2026
  3. 3Three-Dimensional Numerical Phase Geometry System: Theory of Geometric Stability for Non-Trivial Zeros — Applications and Limitations in the Study of the Riemann Hypothesis 三维数相位几何体系:非平凡零点分布的几何稳定性理论及其在黎曼假设研究中的应用与局限2026
  4. 4Three-Dimensional Number Algebra System — A Non-Associative Algebra Unifying Complex Plane and Hyperbolic Phase Space with Applications in Differential Geometry and Number Theory2026
  5. 5三维复数中的黎曼ζ函数⼏何稳定性框架 基于诱导度规流形的归谬法证明Geometric Stability Framework for the Riemann Zeta Function in 3D Complex Numbers A Proof by Contradiction via Induced-Metric Manifolds2026