Axiomatization Framework for the Yang-Mills Existence and Mass Gap: Dual-Premise ZFC Domain Exit Closed-Loop…

Abstract

论文描述

论文标题(中文):杨-米尔斯存在性与质量缺口的公理化框架:双前提ZFC出域闭环与亚庄CBQ出不去范式统摄治理

论文标题(英文):Axiomatization Framework for the Yang-Mills Existence and Mass Gap: Dual-Premise ZFC Domain Exit Closed-Loop and Yazhuang CBQ Inescapable Domain Governance

卷宗编号:Yazhuang CBQ-MATH-24-YM01-SUPP

版本:V3

范式归属:Yazhuang CBQ Inescapable Paradigm

1. Overview

This paper provides a rigorous axiomatization framework for the Yang-Mills existence and mass gap problem based on the Yazhuang CBQ Inescapable Paradigm. ZFC perturbative and local gauge-theoretic tools are insufficient to control the non-perturbative infrared behavior and enforce a strictly positive mass gap. ZFC is forced to execute a Domain Exit. We introduce the "Gauge Field Spectral Gap Coupling Functional" Γ[A] and establish dual legislative axioms: T-YM’ (Continuum Limit Existence) and T-YM” (Strictly Positive Mass Gap).

2. Background

ZFC classical tools in Yang-Mills theory are trapped by structural breaks: Osterwalder-Schrader reconstruction requires proving five axioms simultaneously in the continuum limit, Wilson’s renormalization group cannot bridge UV asymptotic freedom to IR confinement, perturbative asymptotic freedom is a UV property while mass gap is an IR phenomenon, and ’t Hooft instanton calculus provides semi-classical insights but cannot rigorously prove spectral gap generation. Five distinct ZFC paths have been rigorously diagnosed (OS reconstruction, lattice gauge renormalization group, asymptotic freedom/infrared confinement, ’t Hooft instanton topology, and spectral gap), each equipped with a Formal Dead Knot Statement proving that ZFC cannot establish existence and mass gap without circular reasoning.

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: We rigorously diagnose five ZFC paths (OS reconstruction, lattice RG, asymptotic freedom, ’t Hooft instantons, spectral gap), each providing a Formal Dead Knot Statement proving ZFC structural unreachability in the Yang-Mills context.

(2) Axiom Admission: Introduced the Gauge Field Spectral Gap Coupling Functional Γ[A] with four dynamical properties (non-negativity, minimal value condition, global balance nullification, and spectral gap control), establishing dual legislative axioms T-YM’ (Continuum Limit Existence) and T-YM” (Strictly Positive Mass Gap), strictly verified by three Yazhuang CBQ admission criteria.

(3) Bridging Derivation: Three intermediate lemmas (OS reconstruction constraint, asymptotic freedom infrared bottleneck, ’t Hooft instanton topological constraint) interlock ZFC tools with Γ[A]=0 to exclude the failure branch. Via exhaustive dichotomy, any failure branch would violate the global balance nullification condition (Γ[A]=0), rigorously establishing both continuum limit existence and a strictly positive mass gap.

(4) Falsifiability: Four concrete verification tests are provided (counterexample test, lattice Monte Carlo numerical test, renormalization group flow continuity test, weak axiom independence test), ensuring the dual axioms T-YM’ and T-YM” make empirically testable predictions.

4. Proof Type

Explicitly positioned as a Dual-Premise Type-B Conditional Closed-Loop Proof: formal closure within the Yazhuang CBQ domain, with the ZFC carrier ensuring academic compliance. The framework includes 17 classical references (from Yang-Mills 1954 to ’t Hooft 1976 and beyond), four concrete Falsifiability Tests, and the Yazhuang CBQ Axiom Admission Criteria Verification with minimality argument.

5. Keywords

Yang-Mills Existence, Mass Gap, ZFC Unreachability, Yazhuang CBQ Inescapable Paradigm, Gauge Field Spectral Gap Coupling Functional, Universal Logic Closed-Loop, Falsifiability

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BibTeX RIS

BibTeX

@misc{翟2026axiomatization,
  title = {{Axiomatization Framework for the Yang-Mills Existence and Mass Gap: Dual-Premise ZFC Domain Exit Closed-Loop and Yazhuang CBQ Inescapable Domain Governance (杨-米尔斯存在性与质量缺口的公理化框架:双前提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.23503020},
  url = {https://zenodo.org/records/23503020},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Axiomatization Framework for the Yang-Mills Existence and Mass Gap: Dual-Premise ZFC Domain Exit Closed-Loop and Yazhuang CBQ Inescapable Domain Governance (杨-米尔斯存在性与质量缺口的公理化框架:双前提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.23503020
UR  - https://zenodo.org/records/23503020
AB  - 论文描述  论文标题(中文):杨-米尔斯存在性与质量缺口的公理化框架:双前提ZFC出域闭环与亚庄CBQ出不去范式统摄治理  论文标题(英文):Axiomatization Framework for the Yang-Mills Existence and Mass Gap: Dual-Premise ZFC Domain Exit Closed-Loop and Yazhuang CBQ Inescapable Domain Governance  卷宗编号:Yazhuang CBQ-MATH-24-YM01-SUPP  版本:V3  范式归属:Yazhuang CBQ Inescapable Paradigm  1. Overview  This paper provides a rigorous axiomatization framework for the Yang-Mills existence and mass gap problem based on the Yazhuang CBQ Inescapable Paradigm. ZFC perturbative and local gauge-theoretic tools are insufficient to control the non-perturbative infrared behavior and enforce a strictly positive mass gap. ZFC is forced to execute a Domain Exit. We introduce the "Gauge Field Spectral Gap Coupling Functional" &Gamma;[A] and establish dual legislative axioms: T-YM’ (Continuum Limit Existence) and T-YM” (Strictly Positive Mass Gap).  2. Background  ZFC classical tools in Yang-Mills theory are trapped by structural breaks: Osterwalder-Schrader reconstruction requires proving five axioms simultaneously in the continuum limit, Wilson’s renormalization group cannot bridge UV asymptotic freedom to IR confinement, perturbative asymptotic freedom is a UV property while mass gap is an IR phenomenon, and ’t Hooft instanton calculus provides semi-classical insights but cannot rigorously prove spectral gap generation. Five distinct ZFC paths have been rigorously diagnosed (OS reconstruction, lattice gauge renormalization group, asymptotic freedom/infrared confinement, ’t Hooft instanton topology, and spectral gap), each equipped with a Formal Dead Knot Statement proving that ZFC cannot establish existence and mass gap without circular reasoning.  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: We rigorously diagnose five ZFC paths (OS reconstruction, lattice RG, asymptotic freedom, ’t Hooft instantons, spectral gap), each providing a Formal Dead Knot Statement proving ZFC structural unreachability in the Yang-Mills context.  (2) Axiom Admission: Introduced the Gauge Field Spectral Gap Coupling Functional &Gamma;[A] with four dynamical properties (non-negativity, minimal value condition, global balance nullification, and spectral gap control), establishing dual legislative axioms T-YM’ (Continuum Limit Existence) and T-YM” (Strictly Positive Mass Gap), strictly verified by three Yazhuang CBQ admission criteria.  (3) Bridging Derivation: Three intermediate lemmas (OS reconstruction constraint, asymptotic freedom infrared bottleneck, ’t Hooft instanton topological constraint) interlock ZFC tools with &Gamma;[A]=0 to exclude the failure branch. Via exhaustive dichotomy, any failure branch would violate the global balance nullification condition (&Gamma;[A]=0), rigorously establishing both continuum limit existence and a strictly positive mass gap.  (4) Falsifiability: Four concrete verification tests are provided (counterexample test, lattice Monte Carlo numerical test, renormalization group flow continuity test, weak axiom independence test), ensuring the dual axioms T-YM’ and T-YM” make empirically testable predictions.  4. Proof Type  Explicitly positioned as a Dual-Premise Type-B Conditional Closed-Loop Proof: formal closure within the Yazhuang CBQ domain, with the ZFC carrier ensuring academic compliance. The framework includes 17 classical references (from Yang-Mills 1954 to ’t Hooft 1976 and beyond), four concrete Falsifiability Tests, and the Yazhuang CBQ Axiom Admission Criteria Verification with minimality argument.  5. Keywords  Yang-Mills Existence, Mass Gap, ZFC Unreachability, Yazhuang CBQ Inescapable Paradigm, Gauge Field Spectral Gap Coupling Functional, Universal Logic Closed-Loop, Falsifiability
ER  -

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