🧭 Core Components核心组件
Four components in four-layer progression: epistemological foundation → ontology → epistemological standard → methodology. Each supported by a complete mathematical series and cross-disciplinary evidence.
四组件四层递进：认识论根基 → 本体论 → 认识论标准 → 方法论。每一条均有完整的数学系列与跨学科证据支持。
Layer 1 · Epistemological Foundation
第一层 · 认识论根基
📡 The Information Isomorphism Law信息同构定律
Why the world is knowable
为什么世界可知
In complex systems grounded in objective data and exhibiting regime switching, statistical structures carry information about regime structures. This law is a dual-identity meta-law: as an ontological law, it describes how the world encodes information; as an epistemological meta-law, it answers how we can know the world.
在以客观数据为基础、存在体制切换的复杂系统中，统计结构承载了体制结构的信息。该定律是双重身份元规律：作为本体论定律，它描述世界的信息编码方式；作为认识论元规律，它回答"我们如何能认识世界"。
Three progressive ontological levels: Existence (regime switching leaves quantifiable traces) → Correspondence (traces systematically correspond to regime attributes) → Precision (encoding is exact on truth-known systems).
三个递进的本体论层次：存在性（体制切换留下可量化痕迹）→ 对应性（痕迹与体制属性存在系统对应）→ 精确性（在真理已知系统上编码精确）。
Key anchor: 2D Ising exact solution — Chow F achieves global unique maximum at exact Tc (F = 118,074); bias strictly zero in analytical sense.
关键锚点：2D Ising 精确解——Chow F 在精确 Tc 处取得全局唯一最大值（F = 118,074）；偏差在解析意义上严格为零。
Layer 2 · Ontology
第二层 · 本体论
📐 The Factor Hierarchy Law因子层级定律
What the world is — regime factors vs execution factors
世界如何组织——规则因子与执行因子
In any complex system driven by multiple quantifiable factors, factors are naturally divided into two layers: regime factors (which determine which set of rules currently applies) and execution factors (which execute under the given rules). When a regime factor crosses a critical value, the entire system's factor weights are systematically reset.
在任何由多个可量化因子驱动的复杂系统中，因子天然分为两个层级：规则因子（决定当前适用哪套规则）与执行因子（在给定规则下执行）。当规则因子越过临界值时，整个系统的因子权重被系统性重置。
- Axiom 1 (Factor Bifurcation): Factors naturally divide into regime factors and execution factors.
- Axiom 2 (Regime Switch): When a regime factor crosses its critical value, the factor weights of the entire system are systematically reset.
- Axiom 3 (Interaction Effect): The function of a regime factor is not in its direct explanatory power, but in its modulation of execution factors' exposure coefficients.
- 公理1（因子二分法）：因子天然分为规则因子与执行因子两个层级。
- 公理2（体制切换）：当规则因子越过临界值时，整个系统的因子权重被系统性重置。
- 公理3（交互效应）：规则因子的功能不体现在直接解释力上，而体现在它调节执行因子暴露系数的交互效应中。
Empirical evidence: Finance (China-U.S. spread), Astronomy (proxy regime factor), Particle Physics (color charge), Chemistry (period/valence electrons), Nuclear Physics (N and Z, η > 10⁶), Statistical Physics (temperature).
实证证据：金融学（中美利差）、天文学（代理规则因子）、粒子物理（色荷）、化学（周期/价电子）、核物理（N与Z，η > 10⁶）、统计物理（温度）。
Layer 3 · Epistemological Standard
第三层 · 认识论标准
⚖️ The Testability Principle可检验性原则
What counts as reliable — beyond falsifiability
怎样才算可靠——超越可证伪性
After Popper's falsifiability, the Testability Principle establishes the second threshold for science. Falsifiability guards the entrance (science vs non-science); Testability guards the exit (reliable findings vs unverified hypotheses). Any claim about factor importance must pass complete regime-dependent tests.
在波普尔的可证伪性之后，可检验性原则为科学确立了第二道门槛。可证伪性守卫入口（区分科学与非科学）；可检验性守卫出口（区分可靠发现与未经验证的假说）。任何关于因子重要性的声称，必须通过完整的体制依赖检验。
Layer 4 · Methodology
第四层 · 方法论
🔬 The Testability Norms可检验性规范
How to verify — six functional dimensions
怎样操作才能实现——六个功能维度
Operationalized as six functional dimensions. Core commitment: functional dimensions are stable; implementation tools are replaceable.
操作化为六个功能维度。核心承诺：功能维度稳定，实现工具可变。
Six dimensions: Search Completeness · Modulation Relationship · Structural Break · Causal Direction · Problem Completeness · Process Closure. See detailed section below.
六个维度：搜索完整性 · 调节关系 · 结构断点 · 因果方向 · 问题完整性 · 流程闭环性。详见下方专门板块。
📚 Complete List of Preprints (48)完整预印本列表（48篇）
2026a passed external peer review on July 22, 2026; awaiting editorial board decision. The remaining 47 are preprints. All titles are shown in both Chinese and English.
2026a 于2026年7月22日通过外部同行评审，等待编委会最终决定。其余47篇为预印本。所有标题均中英双语显示。
💹 Finance & Asset Pricing (6 papers)
💹 金融与资产定价（6篇）
双锚：中美因子共同决定全球黄金与原油定价——基于VIF约束下穷举测试的系统性证据
Dual Anchors: China-U.S. Factors Jointly Determining Global Gold and Crude Oil Pricing—Systematic Evidence Based on Exhaustive Testing with VIF Constraints
利率无锚：多窗口分位、穷举测试与中美利差的定价逻辑——兼论全球资产定价的双锚体制与制度接口理论
Interest Rates Without an Anchor: Multi-Window Percentiles, Exhaustive Testing, and the Pricing Logic of the China-U.S. Yield Spread—On the Dual-Anchor Regime and Institutional Interface Theory of Global Asset Pricing
利差的统一场：中美利差作为全球资产定价的体制变量——兼论制度接口的层次结构及对利率平价、特里芬难题等理论的补充
The Unified Field of Spreads: The China-U.S. Yield Spread as a Regime Variable in Global Asset Pricing—On the Hierarchical Structure of Institutional Interfaces and Supplements to Interest Rate Parity, the Triffin Dilemma, and Related Theories
锚变：全球汇率定价体系的重构——中美利差作为体制变量的实证，兼论对利率平价、蒙代尔-弗莱明与特里芬难题的系统性替代
The Anchor Shift: Reconstructing Global Exchange Rate Determination—The China-U.S. Yield Spread as a Regime Variable, with Systematic Alternatives to Interest Rate Parity, the Mundell-Fleming Model, and the Triffin Dilemma
因子的层级：体制变量如何重置市场定价——基于全球15个权益市场穷举证据的因子定价层级理论
The Hierarchy of Factors: How Regime Variables Reset Market Pricing—Evidence from Exhaustive Testing Across 15 Global Equity Markets for a Factor Hierarchy Theory
资本流动的体制切换：中美利差如何分层驱动全球资本再配置——基于TIC面板、ETF资金流与中国跨境数据的穷举证据
The Regime Switch of Capital Flows: How the China-U.S. Yield Spread Drives Global Capital Reallocation in a Tiered Manner—Exhaustive Evidence Based on TIC Panel Data, ETF Flows, and China's Cross-Border Data
📚 Theory & Methodology (3 papers)
📚 理论与方法论（3篇）
可检验性：因子层级定律与多因子复杂系统的科学方法论——来自全球资产定价的完整实证、天文学多维验证与物理学第一性原理校准
Testability: The Factor Hierarchy Law and Scientific Methodology for Multi-Factor Complex Systems—Complete Empirical Evidence from Global Asset Pricing, Multi-Dimensional Astronomical Verification, and First-Principles Calibration in Physics
从元规律的规律到科学发现的操作系统：因子层级定律的公理化内核、哲学基础与可检验性规范——人类历史上首个程序化科学发现方法体系的确立
From the Law of Meta-Laws to an Operating System for Scientific Discovery: The Axiomatized Core, Philosophical Foundation, and Testability Norms of the Factor Hierarchy Law—The Establishment of Humanity's First Proceduralized System for Scientific Discovery
科学发现操作系统的技术规范：数学形式化与工程架构——基于因子层级定律与可检验性规范的程序化知识发现协议
Technical Specification for the Scientific Discovery Operating System: Mathematical Formalization and Engineering Architecture—A Proceduralized Knowledge Discovery Protocol Based on the Factor Hierarchy Law and Testability Norms
🔭 Astronomy (3 papers)
🔭 天文学（3篇）
行星半径是体制依赖的关系量——系外行星半径测量存在范式缺陷的证据：基于因子层级理论与四重检验法的天文学跨学科实证
Planetary Radius as a Regime-Dependent Relational Quantity: Evidence for a Paradigm Defect in Exoplanet Radius Measurement—A Cross-Disciplinary Empirical Test in Astronomy Based on Factor Hierarchy Theory and the Four-Test Method
恒星大气模型自洽性的体制断裂：因子层级定律的第二例天文学实证——基于四重检验法的内部交叉验证证据
Self-Consistency Rupture in Stellar Atmosphere Models: The Second Astronomical Empirical Case for the Factor Hierarchy Law—Evidence from Internal Cross-Validation Based on the Four-Test Method
恒星主序的体制边界：K/G过渡带的五维度独立验证与因子层级定律的系统性确立——基于可检验性规范与物理根源追踪的跨维度整合证据
The Stellar Main-Sequence Regime Boundary: Five-Dimensional Independent Verification Across the K/G Transition Zone and the Systematic Establishment of the Factor Hierarchy Law—Cross-Dimensional Integrated Evidence Based on the Testability Norms and Physical Root Tracing
📊 Statistical Physics (3 papers)
📊 统计物理（3篇）
回归拓扑与统计力学的信息理论对偶——因子层级定律对Ehrenfest相变分类的数据驱动等价性证明及其在2D Ising模型上的系统性验证
Information-Theoretic Duality Between Regression Topology and Statistical Mechanics: A Data-Driven Equivalence of the Ehrenfest Classification Validated on the 2D Ising Model as the Physics Cornerstone for the Factor Hierarchy Law
双峰裂变：3D Ising模型有限晶格相变的隐藏结构——因子层级定律在NP完全系统上的验证：双峰裂变、过渡体制、分段控制函数与多体制状态解耦算法
Double-Peak Splitting: The Hidden Structure of Finite-Lattice Phase Transitions in the 3D Ising Model—Verification of the Factor Hierarchy Law on an NP-Complete System: Double-Peak Splitting, Transition Regime, Piecewise Control Function, and Multi-Regime State Decoupling Algorithm
普适性的降维：有限系统相变的体制边界理论——双峰裂变、前导体边界与工具依赖性定理的跨模型证据
The Reduction of Universality: A Regime Boundary Theory for Finite-System Phase Transitions—Cross-Model Evidence for Bimodal Splitting, the Precursor Regime Boundary, and the Tool-Dependence Theorem
🧲 Particle Physics (4 papers)
🧲 粒子物理（4篇）
因子层级定律对粒子物理标准模型的体制审计——激活算子、双中心体制与粲/底夸克阈值的精确锁定 (I)
Regime Audit of the Standard Model of Particle Physics by the Factor Hierarchy Law: Activation Operators, Dual-Center Regimes, and Precision Locking of Charm/Bottom Quark Thresholds (I)
奇异区发现、前导体级联与过渡带宽度定理——四工具交叉验证、级联不对称性确认与切换类型二分法的数学证明 (II)
Strange Region Discovery, Precursor Cascade, and the Transition Zone Width Theorem: Four-Tool Cross-Validation, Cascade Asymmetry Confirmation, and Mathematical Proof of the Switching Type Dichotomy (II)
规范群结构定理、直积定理与三代命题——从体制边界到SU(3)×SU(2)×U(1)的必然涌现与重夸克数量的拓扑约束 (III)
Gauge Group Structure Theorem, Direct Product Theorem, and the Three-Generation Proposition: The Inevitable Emergence of SU(3)×SU(2)×U(1) from Regime Boundaries and the Topological Constraint on the Number of Heavy Quarks (III)
规范场论的降维、标准模型的理论重构与五层公理化结构——前导体级联不对称性、希格斯机制的体制功能、虚态统计对应与因子层级定律的最终形式化 (IV)
The Demotion of Gauge Field Theory, the Theoretical Reconstruction of the Standard Model, and the Five-Layer Axiomatization Structure: Precursor Cascade Asymmetry, the Regime Function of the Higgs Mechanism, the Statistical Correspondence of Virtual States, and the Final Formalization of the Factor Hierarchy Law (IV)
🧪 Chemistry (3 papers)
🧪 化学（3篇）
钙-镧奇异性定理：元素周期表d区与f区体制切换中心的穷举发现与多工具交叉验证——因子层级定律在化学中的首次部署、规则因子统计签名的验证与化学版χ失明的确证 (I)
The Calcium-Lanthanum Singularity Theorem: Exhaustive Discovery and Multi-Tool Cross-Validation of the d-Block and f-Block Regime Switching Centers in the Periodic Table—First Deployment of the Factor Hierarchy Law in Chemistry, Verification of the Statistical Signature of Regime Factors, and Confirmation of the Chemical χ-Blindness (I)
体制周期表：118个元素的体制身份证与元素周期律的普适性降维——例外概念的消灭、119/120号元素的数值预言与全样本横向收敛审计 (II)
The Regime Periodic Table: Regime Identity Cards for 118 Elements and the Reduction of Universality of the Periodic Law—Elimination of Exceptions, Numerical Predictions for Elements 119/120, and Cross-Sample Convergence Audit (II)
从体制边界到化学规范群：元素周期律的必然涌现与因子层级定律的跨学科统一——化学规范群定理的推导、希格斯机制的化学对应与五层公理化结构的确立 (III)
From Regime Boundaries to Chemical Gauge Group: The Inevitable Emergence of the Periodic Law and the Cross-Disciplinary Unification of the Factor Hierarchy Law—Derivation of the Chemical Gauge Group Theorem, the Chemical Counterpart of the Higgs Mechanism, and the Establishment of the Five-Layer Axiomatic Structure (III)
⚛️ Nuclear Physics (6 papers)
⚛️ 核物理（6篇）
核壳层体制审计：幻数偏移定理与N=14统计断裂的发现——零预设穷举的η层级结构、Bai-Perron盲测最优10断点及六条定量定理
Nuclear Shell Regime Audit: The Magic-Number Shift Theorem and the Discovery of the N=14 Statistical Rupture—The η Hierarchy Structure, Bai-Perron Optimal 10 Breakpoints from Zero-Preset Exhaustive Search, and Six Quantitative Theorems
体制切换网络与核壳层的真实结构——确认断点网络的内部自洽性、壳模型完备性审计与十五项新发现：基于多工具汇总的过渡带宽度定理、级联骨架、液滴遮蔽效应与壳修正补偿痕迹
Regime-Switch Network and the True Structure of the Nuclear Shell: Internal Self-Consistency of the Confirmed-Breakpoint Network, Completeness Audit of the Shell Model, and Fifteen New Discoveries—Transition-Zone Width Theorem, Cascade Skeleton, Liquid-Drop Masking Effect, and Shell-Correction Compensation Traces Based on Multi-Tool Aggregation
核壳层的三重降维——壳模型、液滴模型与独立粒子运动公理：基于2D Ising精确解校准、连续球形度权重恢复与QCTI指数的推导型降维论证
The Triple Demotion of the Nuclear Shell: The Shell Model, the Liquid Drop Model, and the Independent-Particle-Motion Axiom—Derivational Demotion Based on 2D Ising Exact Solution Calibration, Continuous Sphericity Weight Recovery, and the QCTI Index
量子-经典混合体的理论延伸与方法论输出——规则因子纯度谱、确认断点网络二元结构与跨学科预测：基于三重降维的范式深化、可检验预言与操作系统完整部署
Theoretical Extensions and Methodological Output of the Quantum-Classical Hybrid: The Regime-Factor Purity Spectrum, the Binary Structure of the Confirmed-Breakpoint Network, and Cross-Disciplinary Predictions—Paradigm Deepening, Testable Predictions, and Complete Deployment of the Operating System Based on the Triple Demotion
核素体制地图（I）：确认断点网络的跨性质验证、二维结构与网络更新——基于核壳层体制切换理论的预测检验与新发现
The Regime Nuclide Map (I): Cross-Property Verification, Two-Dimensional Structure, and Network Update of the Confirmed Breakpoint Network—Predictive Test and New Discoveries Based on the Nuclear Shell Regime-Switching Theory
核素体制地图（II）：壳修正能的统计定位、多维响应定理与方法论贡献——基于核壳层体制切换理论的实证检验与.ssr陷阱修正
The Regime Nuclide Map (II): Statistical Localization of Shell Correction Energy, Multidimensional Response Theorem, and Methodological Contributions—Empirical Test Based on the Nuclear Shell Regime-Switching Theory and the .ssr Trap Correction
📚 Philosophy of Science & Epistemology (4 papers)
📚 科学哲学与认识论（4篇）
信息同构定律：一个横跨本体论与认识论的元规律——从科学发现操作系统的跨学科成功追问其必然前提
The Information Isomorphism Law: A Meta-Law Spanning Ontology and Epistemology—Tracing the Necessary Premise from the Cross-Disciplinary Success of the Scientific Discovery Operating System
信息同构认识论：从因子层级定律到可知论的重建——论一套原创认识论操作系统的建立如何使康德的"物自身"不再必要
Information Isomorphism Epistemology: From the Factor Hierarchy Law to the Reconstruction of Knowability—How the Establishment of an Original Epistemological Operating System Renders Kant's "Thing-in-Itself" Unnecessary
第三人称认识论：信息同构认识论与可检验性的客观根基——从"我思"到"任何人运行代码"
Third-Person Epistemology: Information Isomorphism Epistemology and the Objective Foundation of Testability—From "I Think" to "Anyone Running the Code"
同构读取：客观数据系统认识通道的唯一性——从因子层级定律与信息同构定律到条件化唯一性定理
Isomorphic Reading: The Uniqueness of the Epistemic Channel for Objective Data Systems: From the Factor Hierarchy Law and the Information Isomorphism Law to the Conditional Uniqueness Theorem
📐 Mathematical Statistics & Statistical Theory (15 papers)
📐 数理统计与统计理论（15篇）
Switch Measure Theory (7) · Survey: 2026al
切换度量论（7篇）· 综述：2026al
全局最大值点不变量定理：结构断点检测的统计不变量理论——统一形状函数、标准化极限与多体制推广
The Global Maximum Point Invariance Theorem: A Statistical Invariant Theory of Structural Break Detection—Unified Shape Function, Standardized Limits, and Multi-Regime Generalization
切换度：结构断点检测的公理化效应量——公理化基础、推断理论、功效分析与切换耦合度分解
Switching Degree: An Axiomatic Effect Size for Structural Break Detection—Axiomatic Foundation, Inference Theory, Power Analysis, and Switching Coupling Decomposition of Regime-Switch Metrics
非线性体制切换的切换度：级数估计框架下的L²影响函数、谱加权家族与有限样本推断
The Switching Degree for Nonlinear Regime Switching: L² Influence Functions in a Series Estimation Framework, the Spectral Weighting Family, and Finite-Sample Inference
边界未知时切换度的渐近等价性：固定断点模型下√n推断的自适应性、有限样本修正方向与后选择推断框架
Asymptotic Equivalence of the Switching Degree with Unknown Boundary: √n-Inference Adaptivity in the Fixed-Breakpoint Model, Finite-Sample Correction Directions, and a Post-Selection Inference Framework
体制边界估计的信息下界：固定断点模型下n²尺度的最优精度极限与普适常数c=1/8
Information Lower Bound for Regime Boundary Estimation: Optimal Precision Limit at the n² Scale and Universal Constant c=1/8 in the Fixed-Breakpoint Model
弱依赖切换度推断的一般渐近正态性定理：长期方差的方向依赖性修正、移动分块Bootstrap一致性与结构不变性保持
A General Asymptotic Normality Theorem for Switching Degree Inference under Weak Dependence: Direction-Dependent Long-Run Variance Correction, Moving Block Bootstrap Consistency, and Preservation of Structural Invariance
切换度量论：定义、定理体系与数学根基评估——统一形状函数、切换度、谱加权家族与信息下界综述
Switch Measure Theory: Definitions, Theorem System, and Assessment of Mathematical Foundations—A Survey of the Unified Shape Function, Switching Degree, Spectral Weighting Family, and Information Lower Bound
Factor Hierarchy Law Mathematization (4) · Survey: 2026ap
因子层级定律数学化（4篇）· 综述：2026ap
切换类型与调节结构的数学分类：k体制线性切换模型中的三类切换、六类层级结构、变异系数下界与离散化平台效应
Mathematical Classification of Switching Types and Hierarchical Structures: Three Switching Types, Six Hierarchical Structures, Coefficient of Variation Lower Bound, and Discretization Plateau Effect in the k-Regime Linear Switching Model
结构断裂的几何必然性：统一形状函数的尖点、斜率跳跃、级联传递效率与检测功率
Geometric Necessity of Structural Breaks: Cusps, Slope Jumps, Cascade Transmission Efficiency, and Detection Power of the Unified Shape Function
交互效应与η发散定理：切换形态的η极限、过程性变量η轨迹与η的几何解释
Interaction Effects and the η Divergence Theorem: The η Limits of Switching Morphologies, η Trajectories of Processual Variables, and the Geometric Interpretation of η
因子层级定律数学化综述：三条公理的形式化、跨学科验证矩阵与初步建立声明
A Survey of the Mathematization of the Factor Hierarchy Law: Formalization of the Three Axioms, the Cross-Disciplinary Verification Matrix, and a Preliminary Establishment Statement
Information Isomorphism Law Mathematization (4) · Survey: 2026at
信息同构定律数学化（4篇）· 综述：2026at
L²函数体制切换下的充分性定理：X-依赖凸组合、检测信息损失、谱加权充分性与检测分辨率-信息下界对偶
L² Sufficiency Theorem under Functional Regime Switching: X-Dependent Convex Combination, Detection Information Loss, Spectral Weighted Sufficiency, and Detection Resolution–Information Lower Bound Duality
体制切换零假设下的无假峰定理与极值极限：必要方向、置换检验精确控制与函数空间推广
No-False-Peak Theorem and Extreme Value Limit under the Null Hypothesis of Regime Switching: Necessity Direction, Exact Control of Permutation Tests, and Function-Space Generalization
局部加权统一形状函数与体制边界的一一对应：多体制局部峰值对应、总体极限几何与全局分割的伪峰现象
Locally Weighted Unified Shape Function and the One-to-One Correspondence with Regime Boundaries: Multi-Regime Local Peak Correspondence, Population Limit Geometry, and the Pseudo-Peak Phenomenon of Global Splitting
信息同构定律的数学根基：三个本体论层次、检测充分性与置换精确控制的完整形式化
Mathematical Foundations of the Information Isomorphism Law: A Complete Formalization of the Three Ontological Levels, Detection Sufficiency, and Exact Permutation Control
🏛️ Master Framework (1 paper)
🏛️ 体系总纲（1篇）
因子层级体系：跨学科复杂系统研究的统一理论框架
The Factor Hierarchy System: A Unified Theoretical Framework for Cross-Disciplinary Complex Systems Research