The Primal Source of the Three Noether SymmetriesUnder the MOC (Multi-Origin Curvature) Framework...

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 ...

Matrix and Multi-Origin High-Dimensional Geometry
—— MOC System Axiom V: The Matrix is the Low-Dimensional Projection, the High-Dimensional Noumenon
Traditional linear algebra has committed a categorical error that has persisted for three centur...

Here is the English translation of the MOC Five Axioms, rendered in a style suitable for a formal manifesto or a Meditations on Science equivalent.
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MOC: Multi-Origin High-Dimensional Geometry · Five Axioms
Axiom I: Set Defines Domain
The f...

The Impact of Multi-Origin High-Dimensional Geometry on Radar DesignIn modern national defense and detection systems, radar has long been more than a device for detecting targets. It serves as a core strategic equipment supporting battlefield situ...

Multi-Origin High-Dimensional Geometry and TopologyIn the landscape of classical mathematics, topology is devoted to the study of properties preserved under continuous deformations of space. It concerns connectivity, compactness, genus, parity, an...

Multi-Origin High-Dimensional Geometry and the Chip Revolution: From the Two-Dimensional Dead End to One-Stroke High-Dimensional ConnectivityAll core bottlenecks of modern chips—routing congestion, signal interference, heat concentration, timing d...

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...

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...

Multiple Integrals in Multi-Origin Curvature (MOC) Geometry

(Including the Mathematical Definition of “Integrate First, Then Couple”)

Core Thesis:
The classical multiple integral in a single‑origin Euclidean space is a degenerate special ca...

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...

The Essential Meaning of Sets in the Multi-Origin High-Dimensional SystemIn traditional Euclidean geometry and classical set theory, a set is merely a container for points and elements, attached to a single global origin. All coordinates, metrics,...

The Riemann Hypothesis and the Goldbach Conjecture: Continuous Global Symmetry and Discrete Local Completeness on the Same Multi-Origin Recursive Tree

Under the framework of Multi-Origin High-Dimensional Geometry, the Riemann Hypothesis and the...

All Functions Return to Elliptic Functions
I. Proposition
Within the unifying worldview that "geometry is the mapping of reality, ultimately culminating in number theory," the world of functions also has its ultimate destination:
All functions ...

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...

Why Primes Are Bound to Elliptic Geometry: A Geometrical Ontology Based on Multi-Origin High-Dimensional Projection and Elliptic Convergence
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Abstract
The distribution of primes exhibits a dual character: apparent randomness and deep regular...

Projective Generation Theory of Multi-Origin High-Dimensional Geometry and the Ultimate Convergence Principle of Two-Dimensional Figures
This chapter establishes the ontological foundation and the ultimate closed-loop structure of the entire theo...

"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...

A Physical Proof of the Isoperimetric Problem —— On the Isomorphism with the Method for the Poincaré Conjecture
 
Abstract
 
This paper presents a complete proof strategy for the isoperimetric problem: by introducing the potential energy E = ...

In contemporary biological breeding, species propagation, and ecological germplasm cultivation, a one-sided and deeply entrenched consensus has long been solidified: hybridization equals advantage, crossbreeding equals improvement, and inter-varie...

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...

The Decisive Influence of Gravity on the Evolution of Animal Body Size and Physiology
In the natural world, the evolution of animal body size and species distribution is often attributed to climate, food availability, and competition. But the hid...

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. ...

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...

Liu E’zi always went to the town market only on the fifth and tenth days of each lunar month. On...

Quantum Entanglement: Several Misconceptions
I. Entanglement has no infinite range — it all depends on whether you can withstand environmental interference
In theoretical equations, the correlation of quantum entanglement indeed does not decay n...

A Physical Intuition Framework: Geometric Fundamentals Governing Quantum Phenomena
 
This text does not seek to replace or negate the computational systems and experimental findings of established quantum mechanics, nor does it claim to have ach...

The Planckian Homunculus – A Different Kind of Observation
If we could shrink ourselves down to the Planck scale – that extreme microscopic world where space is as small as 10^{-35} meters and time as short as 10^{-43} seconds – and become, so to...

The Time Perspective of the Planck Tiny ManThe Planck Tiny Man is tiny not only in spatial scale but also in temporal scale, operating at 10⁻⁴³ seconds. At this scale, “quantum superposition” vanishes from its view: an electron does not pass throu...

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...