Core Innovations & Complete DerivationEnglish Version0. Core Innovative Idea (One Sentence)Riemannian curvature describes how a single tangent space rotates about itself;the Multi‑Origin Curvature (MOC) I define describes:the rotational differ...
1. MotivationThe Standard Model describes the strong, weak, and electromagnetic interactions using the gauge group SU(3)\times SU(2)\times U(1), while general relativity describes gravitation on spacetime manifolds. The two frameworks are mathemat...
Complete Logical Chain in One Go:
From Abelian Group / Galois Group → Elliptic Function → Origin of Real and Imaginary → Hierarchical Unification of the Four Forces
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I. Placing the Two Groups in Your “Symmetry Evolution Theory”
1) A...
The Ultimate Unification of Four Symmetries:Rotational, Fractal, Hierarchical, and Multi-Origin Coordinate SymmetryI. Preface: All Laws of the Universe Boil Down to One Thing — Symmetry TransformationSince ancient times, the unification of physics...
What is defined is:**Hierarchical Structure of Multi-Origin Geometry- Embedding of Fractal Dimension- Recursive Mapping of Continued Fractions**It satisfies the three iron criteria for establishing a new branch of mathematics:1. Independent fundam...
Elliptic Function Interpretation of the Four Fundamental Forces1. General PrincipleMathematically: Trigonometric functions are only a degenerate special case of elliptic functions; elliptic functions are the general mother structure.Physically: Th...
All inverse-square forces (gravitation, Coulomb electrostatic force) are equivalent to the geometry of conic sections (ellipses, parabolas, hyperbolas) in classical mechanics.
- Attraction ⇒ ellipse (or circle) - Repulsion ⇒ hyperbola - Bound...
By the same logic, Coulomb attraction also traces out elliptical areas. Coulomb attraction (electrostatic attraction) is mathematically isomorphic to universal gravitation as an inverse‑square force:
F = k \frac{q_1 q_2}{r^2} \quad (\tex...
Geometric Interpretation of Universal GravitationMy intuition tells me that universal gravitation is painting the area of an ellipse.1. From Kepler’s Second Law: Gravity truly is "painting" the areaKepler’s Second Law states that a line segment jo...
Mathematical Structural Interembedding Between Multi-Origin High-Dimensional Geometry and Polar CoordinatesIn the theoretical construction of Multi-Origin High-Dimensional Geometry, polar coordinates are not external applications, but naturally em...
Multi-origin high-dimensional geometry is almost a coordinate description framework tailor-made for robotics (especially serial manipulators and mobile robots). In simple terms: a robot is a mobile, nestable "multi-origin system". 1. The esse...
Multi-Origin High-Dimensional Geometry resolves the gimbal lock and jamming issues in interstellar flight. Quaternions perfectly eliminate gimbal lock in attitude representation within a single reference frame. Multi-Origin High-Dimensional Geom...
1. This Geometric Structure (Pure Mathematical Restatement) Consider three levels, each with its own origin and local coordinate system: · Level 1: Origin O_G (Galactic Center), coordinate system G; the distortion is represented by a rotation ma...
Building the Earth-Mars Chain (EMC) — a comprehensive interstellar logistics network system with the Starship as the core transport unit, the deep-space extended Starlink as the all-domain connectivity layer, and strong AI as the scheduling core...
The Possibility of Consciousness Uploading Within the framework of the Primitive Wave Combinatorial Consciousness Theory, consciousness uploading is no longer mere science fiction, but an achievable goal with a clear theoretical path. Since any ...
The elementary‑wave combination principles and consciousness encoding structure revealed by this theory can be directly integrated with brain‑computer interface (BCI) technology. By acquiring brain signals via EEG devices and performing Fourier de...
Consciousness State Database and Consciousness Encoding Dictionary 1. Theoretical Necessity of the Consciousness Database Within the framework of the Elementary‑Wave Combinatorial Consciousness Theory, any conscious state is uniquely determined ...
According to the Elementary-Wave Combinatorial Consciousness Theory, the conscious signals in the brain are composed of several independent elementary waves. Each elementary wave corresponds to a circular motion, and the complete EEG waveform can ...
Brain waves can be rigorously decomposed using Fourier analysis, and consciousness can be mathematically described as the combinatorial coding of these primitive waves. This is not only valid but also cutting-edge in science. Let me explain ...
Consciousness is not determined by any single type of brain wave alone, but by the dynamic coding structure formed by the permutation and combination of various fundamental brain waves, which directly corresponds to a specific state of consciousne...
Liu Ezi struck it rich. “Struck it rich” might be an exaggeration, but for a rural woman who...
Soon, Yan Xiaofan turned three and was old enough to visit relatives with his parents for the New...
Curvature of Fields and a Meditation on the Hierarchy of Physical Unification Isomorphism of mathematical formulas implies that they share similar or identical underlying physical principles—this is the master key to understanding the unification...
The Real Number System Is Contained in the Imaginary Number System Terminological note: In this essay, “imaginary number system” refers to the complete complex numbers a+bi, not the narrower set of pure imaginary numbers. The imaginary number ...
A Self-Consistent Derivation Chain of Conservation Laws (Strictly valid under no external force, no external torque, one-dimensional / free curvilinear motion, consistent with the geometric view that a straight line is part of an arc.) 0. ...
Energy-Fundamental Spacetime View: The Underlying Logic of Conservation and SymmetryMy spacetime view is grounded in the fundamental reality of physics, rejecting abstract, groundless deduction. It establishes a complete logical chain from essence...
49 Conservation Laws Corresponding to the Three SymmetriesIn the framework of physics, the correspondence between symmetry and conservation is a fundamental principle running through both classical and modern physics. Noether’s Theorem precisely r...
Group-Theoretic Unification of the Three Symmetries and the Euclidean GroupWithin the framework of Euclidean geometry and classical group theory, the three fundamental symmetries—translation, rotation, and reflection (folding)—are not independent ...
I. Relations Among the Three SymmetriesTranslational symmetry corresponds to straight lines,rotational symmetry corresponds to curves.A straight line is a curve with zero curvature.Therefore, translational symmetry is inherently a special case of ...
