I. Difference Is Potential, Which Is EnergyAt the fundamental structure of the physical world, difference itself corresponds to a potential field, and potential field is directly equivalent to energy. This relation should not be regarded as a man-...
Relationship Between Curvature, Revolution and RotationSince real celestial bodies are not ideal rigid spheres, their mass distribution, tidal deformation, and fluid motions make the intrinsic relation between curvature and rotation difficult to v...
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...
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...
MOC Differential Geometry · Trinity of Applied Mathematics Analysis · Optimization · Learning — Three Scales of the Same Thing --- I. Traditional Perspective: Three Disciplines Separate, Each Fighting Alone In the traditional system of applied...
The Significance of Probability Theory in Multi-Origin High-Dimensional GeometryIn classical probability theory and single-origin Euclidean geometry, probability is merely a measure of the frequency of events. The sample space is attached to a sin...
Since the beginning of systematic observations of natural motions, “force” has always been the core concept used to explain all changes in the world. From the movement of celestial bodies to the falling of objects, from electromagnetic induction t...
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...
The Higgs field is a quantum field that permeates the entire universe. It is a key mechanism in the Standard Model of physics for converting energy into mass, and is regarded as the fundamental process by which elementary particles acquire mass.In...
The Core Logic of the Universe’s Eternal Motion Ultimate Minimal Axiom Force arises from potential difference.Parity is intrinsically broken.Potential difference never vanishes.Therefore, the world moves eternally. --- Layered Philosophical Ex...
Supplement I: Explicit Construction of \Omega_i (Curvature Coupling Coefficient)The coefficient \Omega_i was undefined in the original formulas; we now provide a minimal viable definition intrinsically linked to the geometry of \mathbb{M}^n_k.Let ...
The Ultimate Position of Functional Analysis in MOC Traditional Functional Analysis: Function → Infinite-dimensional vector space → Operator → Norm → Weak convergence → Hilbert space Everything is built upon: a single origin, a global linear ...
Geometry is the Mapping of the Real World, and It Ultimately Returns to Number Theory I. Proposition Statement This statement is not a theorem, but a worldview. It declares the relationship among the three major branches of mathematics at the ul...
AI Voice Agents are transforming modern sales by enabling instant, consistent, and scalable customer interactions. Platforms like Aisa-X automate lead engagement, qualification, and follow-ups through human-like conversations, ensuring no opportun...
The Intuitive Unification of Macroscopic and Microscopic Curvature Spacetime curves. Fields also curve. For a long time, physics has treated the curvature of macroscopic spacetime and the intrinsic curvature of microscopic fields as two separate...
Unified Geometric Axiom of Rectilinear and Circulating FlowAxiomatic StatementUnified Flow Axiom: For any steady or asymptotically stable flow, its trajectory satisfies the following in a local coordinate system:(i) Normal Boundedness – Displaceme...
One-Stroke Drawing Is Inevitably Valid Under the Multi-Origin High-Dimensional Framework I. Why Is One-Stroke Drawing Possible in High Dimensions? High-dimensional space provides extra degrees of freedom to bypass low-dimensional obstacles...
Mass, electric charge, and color charge are the upgraded and manifest forms of energy.Mass, electric charge, and color charge are not independent intrinsic properties of matter. Rather, they are the external expressions and upgraded forms of energ...
Gabor Transform = Projection of MOC under "Fixed Scale + Gaussian Window + Single Origin" 1. Intuitive Correspondence - Fourier Transform: Global kernel e^{-i\omega t}, no localization. - Gabor Transform: Fourier kernel with a Gaussian wi...
Gene Editing Chemistry: The Next Revolutionary Track in Industrial Manufacturing
Since the dawn of industrialization, the chemical industry has gone through two major developmental stages: fossil refining and artificial chemical synthesis. It h...
On Innovation Capacity and the Ineliminability of Process Some people imagine: using gene editing to create a child, then inputting Einstein’s consciousness into that child, and the child will become Einstein. This fantasy overlooks a most funda...
MOC: A Unified Curvature Framework with Multiple Origins as a Generalization of Hilbert Space Abstract The Hilbert space has long served as the foundational mathematical structure for harmonic analysis, functional analysis, signal processi...
For years, I’ve been curious about why root crops like sweet potatoes and potatoes are so productive and grow so large. At first, I thought it was simply because they grow underground, sheltered from wind and rain, allowing them to expand freely. ...
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...
Mellin Transform and Z-Transform: Projections in Multiplicative and Discrete Geometries
Within the MOC framework, the Fourier, Laplace, wavelet, and Gabor transforms correspond to structures on the Euclidean line, characterized by additive tran...
Geometry as Protocol: Multi-Origin High-Dimensional Geometry and Computer Networking Computer networking, for all its apparent glory, has shown clear signs of fatigue. TCP/IP has reigned for half a century. Routing protocols endlessly patch them...
The Significance of Game Theory in Multi-Origin High-Dimensional GeometryIn traditional game theory, a game refers to strategic choices made by rational agents under fixed rules, fixed payoffs, and a single global utility framework. It presupposes...
The Performance of Multiple Integrals in Multi-Origin High-Dimensional GeometryIn traditional single-origin Euclidean geometry, multiple integrals represent the measure accumulation over flat space under a unified global coordinate system. The int...
Reflections on Machism With a Discussion on Time as the Flow of Energy Preface When I was young, I had an intuition: time is the flow of energy. Later, through reading, I learned this was not considered “professional”. Physicists would say...
"All Two-Dimensional Figures Ultimately Reduce to Ellipses" — A Three‑Tier Strict Mathematical Explanation from the Perspective of Multi‑Origin Geometry / High‑Dimensional Fiber Bundles If we step outside the conventional two‑dimensional plane...
