Vector Cosmology III: The Natural Generator

Subtitle: 矢量宇宙论 III：自然的生成元

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Version: 1.0

Status: Initial Release

Preface

• Preface: The Natural Generation (前言：自然的生成)

Prologue

• 0.1 Euler’s God Formula (欧拉的上帝公式)
• 0.2 The Nature of Change (变化的本质)

Book Structure

Chapter 1: The Rotating Exponential

• 1.1 Schrödinger’s $e$ (薛定谔的 $e$)
• 1.2 Imaginary is Orthogonal (虚数即正交)

Chapter 2: The Sum of Paths

• 2.1 Feynman’s Exponential (费曼的指数)
• 2.2 The Compound Interest Interpretation of Least Action (最小作用量的复利解释)

Chapter 3: The Derivative is the Ontology

• 3.1 The Power of the Instant (瞬时的力量)
• 3.2 The Generation of Lie Algebra (李代数的生成)

Chapter 4: Continuous Compounding

• 4.1 Planck’s Interest (普朗克的利息)
• 4.2 The Bridge Between Discrete and Continuous (离散与连续的桥梁)

Chapter 5: Imaginary Time

• 5.1 Wick Rotation (威克转动)
• 5.2 Geometric and Thermal Unity (几何与热的统一)

Chapter 6: The Modular Flow Hypothesis

• 6.1 Who is Ticking? (谁在滴答？)
• 6.2 Tomita’s Alchemy (托米塔的炼金术)

Chapter 7: The Measure of Information

• 7.1 Boltzmann’s Logarithm (玻尔兹曼的对数)
• 7.2 $\ln$ as Decoder ($\ln$ 作为解码器)

Chapter 8: The Logarithmic Law of Sensation

• 8.1 The Weber-Fechner Law (韦伯-费希纳定律)
• 8.2 The Geometry of Cognition (认知的几何)

Chapter 9: The Self-Caused

• 9.1 The Trinitarian Closed Loop (三位一体的闭环)
• 9.2 The Final Formula (最后的公式)
• 9.3 The Ultimate State (终极状态)

Bonus Chapter

• The Final Bonus: The Seal of Dimension Four — The Conspiracy of Riemann and Poincaré (终极番外：四维的封印：黎曼与庞加莱的共谋)

Appendices

• Appendix A: The Mathematics of Modular Time (模时间的数学原理)
• Appendix B: Information Geometry and Logarithmic Metric (信息几何与对数度量)
• Appendix C: Lie Algebras and the Exponential Map (李代数与指数映射)
• Appendix D: The Evolution Equation and Cosmic Coordinates (演化方程与宇宙坐标)

Acknowledgements

• Acknowledgements: The Grace of the Exponential (致谢：指数的恩典)

Glossary

• Glossary: The Lexicon of Nature (术语表：自然的词典)

Afterword

• Afterword: The Silence of Nature (后记：自然的静默)

Documentation Version: 1.0

Last Updated: Initial Release