Axiomatization Framework for the Riemann Hypothesis: ZFC Domain Exit and Yazhuang CBQ Inescapable Domain Governance (黎曼猜想的公理化框架:ZFC出域闭环与亚庄CBQ出不去范式统摄治理)
Abstract
论文描述
论文标题(中文):黎曼猜想的公理化框架:ZFC出域与亚庄CBQ出不去范式统摄治理
论文标题(英文):Axiomatization Framework for the Riemann Hypothesis: ZFC Domain Exit and Yazhuang CBQ Inescapable Domain Governance
卷宗编号:Yazhuang CBQ-MATH-20-RH-AX01
版本:V3 / Final / Locked
范式归属:Yazhuang CBQ Inescapable Paradigm
1. Overview
This paper provides a rigorous axiomatization framework for the Riemann Hypothesis, a cornerstone problem in analytic number theory, based on the Yazhuang CBQ Inescapable Paradigm. Proving RH establishes the optimal error term in the Prime Number Theorem and resolves one of the most profound mysteries in pure mathematics.
2. Background
ZFC classical tools are trapped by a structural break: "statistical/average constraints cannot enforce pointwise spectral rigidity."
3. Core Logic - The Necessity of ZFC Domain Exit and Bridging Closed-Loop
To achieve the closed loop, ZFC's domain exit is a strict necessity. We realize this through four completenesses:
(1) ZFC Exhaustion: Formalized dead-knot statements provided for three mainstream ZFC paths (zero-density, zero-proportion, explicit formula).
(2) Axiom Admission: Introduced the RH-A4 (Zero Distribution Global Balance Axiom) with the Critical-Line Coupling Potential Functional G(ρ), strictly verified by three CBQ admission criteria. The functional G(ρ) = |2Re(ρ)−1|² · Φ(ρ) encodes the global rigidity of zero distribution through four non-negotiable properties, including a global summation-to-zero condition.
(3) Bridging Derivation: Three intermediate lemmas (Zero-Density Constraint, Proportion Bound, Explicit Formula Constraint) interlock ZFC asymptotic bounds with G(ρ)=0 to exclude the deviation branch. Via exhaustive dichotomy, any off-critical zero would violate the global balance nullification condition (S=0), rigorously establishing ∀ρ∈D, Re(ρ)=1/2.
(4) Falsifiability: Four concrete verification tests are provided (counterexample test, numerical verification covering the first 10¹³ zeros, continuity test, weak axiom independence test).
4. Proof Type
Explicitly positioned as a Type-B Conditional Closed-Loop Proof: formal closure within the CBQ domain, with the ZFC carrier ensuring compliance.
5. Keywords
Riemann Hypothesis, ZFC Domain Exit, Yazhuang CBQ Inescapable Paradigm, Coupling Potential Functional, Universal Logic Closed-Loop, Falsifiability
Related
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BibTeX
@misc{翟2026axiomatization,
title = {{Axiomatization Framework for the Riemann Hypothesis: ZFC Domain Exit and Yazhuang CBQ Inescapable Domain Governance (黎曼猜想的公理化框架:ZFC出域闭环与亚庄CBQ出不去范式统摄治理)}},
author = {Yazhuang 翟},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23500488},
url = {https://zenodo.org/records/23500488},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Axiomatization Framework for the Riemann Hypothesis: ZFC Domain Exit and Yazhuang CBQ Inescapable Domain Governance (黎曼猜想的公理化框架:ZFC出域闭环与亚庄CBQ出不去范式统摄治理)
AU - Yazhuang 翟
PY - 2026
DA - 2026/10/20
PB - Zenodo
DO - 10.5281/zenodo.23500488
UR - https://zenodo.org/records/23500488
AB - 论文描述 论文标题(中文):黎曼猜想的公理化框架:ZFC出域与亚庄CBQ出不去范式统摄治理 论文标题(英文):Axiomatization Framework for the Riemann Hypothesis: ZFC Domain Exit and Yazhuang CBQ Inescapable Domain Governance 卷宗编号:Yazhuang CBQ-MATH-20-RH-AX01 版本:V3 / Final / Locked 范式归属:Yazhuang CBQ Inescapable Paradigm 1. Overview This paper provides a rigorous axiomatization framework for the Riemann Hypothesis, a cornerstone problem in analytic number theory, based on the Yazhuang CBQ Inescapable Paradigm. Proving RH establishes the optimal error term in the Prime Number Theorem and resolves one of the most profound mysteries in pure mathematics. 2. Background ZFC classical tools are trapped by a structural break: "statistical/average constraints cannot enforce pointwise spectral rigidity." 3. Core Logic - The Necessity of ZFC Domain Exit and Bridging Closed-Loop To achieve the closed loop, ZFC's domain exit is a strict necessity. We realize this through four completenesses: (1) ZFC Exhaustion: Formalized dead-knot statements provided for three mainstream ZFC paths (zero-density, zero-proportion, explicit formula). (2) Axiom Admission: Introduced the RH-A4 (Zero Distribution Global Balance Axiom) with the Critical-Line Coupling Potential Functional G(ρ), strictly verified by three CBQ admission criteria. The functional G(ρ) = |2Re(ρ)−1|² · Φ(ρ) encodes the global rigidity of zero distribution through four non-negotiable properties, including a global summation-to-zero condition. (3) Bridging Derivation: Three intermediate lemmas (Zero-Density Constraint, Proportion Bound, Explicit Formula Constraint) interlock ZFC asymptotic bounds with G(ρ)=0 to exclude the deviation branch. Via exhaustive dichotomy, any off-critical zero would violate the global balance nullification condition (S=0), rigorously establishing ∀ρ∈D, Re(ρ)=1/2. (4) Falsifiability: Four concrete verification tests are provided (counterexample test, numerical verification covering the first 10¹³ zeros, continuity test, weak axiom independence test). 4. Proof Type Explicitly positioned as a Type-B Conditional Closed-Loop Proof: formal closure within the CBQ domain, with the ZFC carrier ensuring compliance. 5. Keywords Riemann Hypothesis, ZFC Domain Exit, Yazhuang CBQ Inescapable Paradigm, Coupling Potential Functional, Universal Logic Closed-Loop, Falsifiability
ER -