Announcement

Over the past several years, the COD research program has evolved from an extension of classical mechanics into a unified framework encompassing ontology, mathematics, physics, engineering, and artificial intelligence.

Beginning with the formulation of the Universal Hamiltonian (UH) based on complex dual energy, the framework has expanded into a geometric-algebraic system centered on Complex Quaternionic Oscillator Dynamics (COD).

Accordingly, the original meaning of COD, Complex Oscillator Dynamics, is now extended to Complex Quaternionic Oscillator Dynamics.

This reflects the interpretation that stable existence has the fundamental structure of a Complex Quaternionic Spherical Oscillator, emerging through recursive phase equilibrium and multiplicative-invariant geometry.

COD has therefore developed beyond a single physical theory into a comprehensive geometric-algebraic physics and engineering system based on complex dual energy.

Development Timeline

2013

Septembe 2013 — Establishment of InnoLab Science Institute

• Publication of a paper on Computer Database Structure analysis of human thought forms and processes.
• Arguments regarding the structure of Kant's philosophical epistemology based on Database Structure.
• Research on universal phase equilibrium motion structures emerging in natural and social phenomena.

October 2022 - Presentation of 5GNL: 5 Natural Laws

• 5GNL: Self-organizing physical will, Efficiency, Equilibrium motion, Circulation, Global network alignment.
• Universal physical laws in space and time, and isomorphic structures of Human society and Nature.
• Inconsistent structures interpretation - Imbalance of physical structure and Phase mismatch of entities.

August 2024 — Formulation of the Universal Hamiltonian (UH)

• Establishment of the UH equations for the extended structure of classical mechanics.
• Extension of classical mechanics through complex dual energy.

November 2024 — Publication

A World Told by Ontology
InnoLab Science Institute

• Extension of classical mechanics phase space: Natural gravity theory, establishment of classical UH equations.
• Presentation of scientific methodology: Essence-based inductive ontological methodology.

December 2024 — Complex Classical Dynamics and Space-Field Theory

• Introduction of UH into complex classical equations.
• Expansion toward complex space-field theory.
• Beginning of public paper publication and sharing through the InnoLab Science Institute website.

2025

February 2025 — Complex Wave Essentialism and COD

• Establishment of Complex Wave Essentialism.
• Establishment of the original Complex Oscillator Dynamics framework.

February 2025 — Scientific Methodology

• Publication of time-independent phase equilibrium and scientific methodology.

April 2025 — Millennium Problems

• Proposal of a Solution Structure for the 7 Millennium Problems: Time-Independent + Phase Equilibrium

June 2025 — Complex Unified Gravity Theory

• Presentation of Complex Theory-Based Unified Gravity Theory

August 15, 2025 — COD vs. Kepler + JPL Validation Report

• Isomorphic Mathematical Structure Analysis of Orbital Motion and Phase-Based Linear Reciprocating Oscillations
• Structural Comparison with JPL Data

September 15, 2025 — Sovereign Artificial General Intelligence (AGI) Architecture

• Proposal of COD Phase-Based Natural Dynamics Architecture.

• Proposal of a Mathematical Architecture for Sovereign Artificial General Intelligence (AGI) Based on Cognitive Structures.

September 26, 2025 — Extension of Time-Independent Topological Ontology

January 2026 — Elucidation and Establishment of Complex Quaternion Structures

• Extension of the COD Geometric Algebra System.

June 2026 — Rediscovery of the Global Multiplication Invariant Principle

• Establishment of a geometric mass generation theory and a singularity-free mathematical model of Black Holes based on the Global Multiplication Invariant Principle

October 2025 – July 2026 — Development of Core Engineering Technologies Based on Complex Quantum Waves

• Filed 14 Core Patents Related to Complex Quantum Wave-Based Topological Engineering

Major Zenodo Publications

1. COD Phase-Equilibrium Standard Model (2025.06)
2. Supplementary Mathematics of COD Navier–Stokes Fluid Dynamics (2025.06)
3. The Geometry of Existence: Time-Independent Phase Equilibrium and the Ontology of the Riemann Critical Line (2026.06)
4. Discovery of the Multiplicative-Invariant Unified Structure (2026.06)
5. Geometry of Existence — The Geometric Process of Mass–Energy Formation Based on Multiplicative-Invariant Phase Equilibrium (2026.07)
   Macroscopic mass–radius normalization based on multiplicative invariance.
6. Eigen Structure of Complex Quaternion Spherical Condensation with Spin (2026.07)
   Microscopic geometry based on triaxial non-commutative √3 condensation with Spin.
7. Complex Quaternionic Oscillator Dynamics Based on Multiplicative Invariance
   Establishment of a general physics framework.
8. The General Structure of a Supercondensed Object Interpreted through Multiplicative-Invariant Geometry (2026.07)
   A time-independent phase-equilibrium model of Black Holes based on complex mass–energy conservation .

Current Stage

COD has now expanded from Complex Oscillator Dynamics into Complex Quaternionic Oscillator Dynamics.

• Complex Dual Energy
• Complex Quaternionic Geometry
• Time-Independent Phase Equilibrium
• Multiplicative Invariance
• Recursive Self-Organization
• Phase System Engineering Framework based on CQOD

Within this framework, stable existence is interpreted as a Complex Quaternionic Spherical Oscillator(CQSO), providing a unified geometric basis for ontology, mathematics, physics, engineering, and intelligent systems.