MOC Differential Geometry · Trinity of Applied Mathematics
Analysis · Optimization · Learning — Three Scales of the Same Thing
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I. Traditional Perspective: Three Disciplines Separate, Each Fighting Alone
In the traditional system of applied...

MOC Differential Geometry (Multiple Origins with Higher Dimensions)
Axiom 1 — Hierarchical Multiple Origins Axiom
Space contains hierarchically nested origins, such as the Galactic origin, the Solar origin, and the Earth origin. Each origin is i...

Multi-Origin High-Dimensional GeometryA Unified Framework: Dynamics · Information Theory · Neural Networks I. FoundationMulti-Origin + Curvature Space + High-Dimensional Projection- Each node (particle, information source, neuron) acts as an indep...

Multi-Origin High-Dimensional Geometric Unified Framework
 Dynamics · Information Theory · Neural Networks
 
I. Foundation: Multi-Origin + Curvature Space + High-Dimensional Projection
 
- Each node (particle, information source, neuron) is a...

Multi-Origin High-Dimensional Geometric Neural Networks
All current neural networks are fundamentally locked into two-dimensional planes, a single origin, and matrix tiling operations. No matter how large or deep the models become, they merely st...

Winter is here, and while some of us are bundled up indoors, others are craving the rush of a snowy mountain. If the slopes are calling your name, but you're stuck at your desk, then Snow Rider 3D offers a surprisingly satisfying alternative. This...

Dynamics and Multi-Origin High-Dimensional Geometry
Classical dynamics, based on a single-origin flat coordinate system, describes motion with all forces, displacements, and rotations normalized to a single coordinate reference. Motion evolution ...

Textbooks state: conservation of energy, conservation of momentum, and conservation of angular momentum are equal in status.They arise from Noether’s theorem, corresponding respectively to the symmetries of time translation, space translation, and...

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...

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...

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...

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...