Key Papers

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📢 Announcement

Publications on Complex Oscillator Dynamics

The following papers will be sequentially published based on the Theory of Oscillator Dynamics: 4/20-

1.General Theory of Complex Oscillator Dynamics

1) Phase Resonance of Oscillators: Essential Answers to the 7 Millennium Problems (2025.04.21)
2) Epistemological Declaration on Solving the Seven Great Problems of Mathematics(2025.04.22)
3) Declaration of the Completion of Ontology(2025.04.26)
4) Singularity Axiom(2025.05.01)
5) Declaration of Integration and Completion of Classical Mechanics (2025.05.03)
6)Complex oscillators theory with Integration of quantum mechanics(2025.05.04)
7)Intermediate Summary - The Essentialist Turn in Scientific Methodology(2025.05.04)
8)Essentialistic Shift in Scientific Method (2025.05.09)
9) Complex Gravitational Black Hole Theory: A Non-Singularity Model(2025.05.26)
10) Unified Interpretation of Cosmological Phenomena via Complex Gravity System (2025.05.30)

11) Unified Theory of Gravity as Spatial Energy Flow (2025.06.23)
12)Scientific Historical Evaluation of Complex Phase Natural Dynamics(2025.07.02)
13)Timeless Mathematical Reconstruction of the 7 Millennium Problems(2025.07.05)
14)Unified Complex Oscillator Dynamics (COD)(2025.07.10)
15)The Quantum Dynamics of Awakening :
A Natural Oscillator Interpretation of the Mahāyāna One Mind I
- As a Note on the Awakening of Mahayana Faith in the Quantum Theory(2025.07.22>
16)Verification of Imaginary Energy (+Gravity) in Complex Phase Space(2025.08.01)
17)Declaration of the Dismantling of the Time Axis(2025.08.02)
18)Heidegger’s Being and Time Interpreted by COD Theory(2025.08.03)

19) Solving three-body and many-body problems based on COD and Riemannian geometry (2025.08.06)
20) COD vs. Kepler + JPL Verification Report (2025.08.15)
21) A Theory Of Cosmology and TOE based on COD 2025 (2025.08.25)
22) The ontological scientific method of the COD White Paper (KO/EN)(2025.08.29)
23) The Truth of Galactic Rotation (KO/EN)(2025.08.30)

1. EX1. General Theory of Complex Oscillatory Dynamics:
Previously published in the PAPERS section of this website

1) YouTube: Do Planets Really Orbit? (2025.06.18)

2. EX2. Phase Dynamical Interpretation of Galactic Rotation(2025.08.30)
The same Phase Motion Identical to Planetary Motion, Galaxies do not rotate, just as planets do short, rectilinear, back-and-forth motions. Galactic spirals are geometric streams of stars' short, rectilinear, back-and-forth phase motions.
3. EX3. COD Standard Model and the Nature of Spin (To be announced on October 30, 2025)




NEW

 

2025-08-30



Language Auto (OS) Korean English Dual

은하 회전의 진실 / The Truth of Galactic Rotation

개요

은하의 회전은 별들이 은하 반경을 따라 회전하는 것이 아니다. 실제로는 별들이 짧은 직선 왕복을 반복하며,그 평균 위상 흐름이 은하 회전 패턴을 형성한다. 별들은 점입자로서 국소 중력 퍼텐셜 곡률 방향으로 짧은 직선 왕복을 반복한다.
그러나 이 흐름 속에서 위상과 밀도는 라그랑지 관점에서 정지되어, 정지 위상 능선(steady-phase ridge)이 형성된다. 이것이 관측되는 은하 포락선(envelope)이다.

시간 독립 COD 수식

\[ \Psi(\mathbf r)=A(\mathbf r)e^{i\theta(\mathbf r)},\quad \rho=|A|^2,\quad \mathbf v=\frac{1}{m}\nabla\theta,\quad \mathbf J=\rho\,\mathbf v \] \[ \nabla\!\cdot(\rho\mathbf v)=0,\qquad \frac{|\nabla\theta|^2}{2m}+\Re U_H+Q=E \] \[ U_H=\tfrac12 m|\mathbf v|^2-\frac{GM(r)m}{r}+i\frac{GM(r)m}{r},\quad Q=-\tfrac{1}{2m}\frac{\nabla^2A}{A} \] \[ \frac{d^2 s}{d\ell^2}+k^2(\mathbf r_0)s=0,\quad k^2=\mathbf n^\top(\nabla\nabla\Phi_g)\mathbf n,\quad \mathbf n=-\frac{\nabla\Phi_g}{|\nabla\Phi_g|} \] \[ \text{Stationary-phase: }\quad \frac{D\theta}{Dt}=0,\ \frac{D\rho}{Dt}=0,\ \mathbf J\neq 0 \]

수식 설명 Symbol Guide (J, Q, E, T)

1. J (위상 흐름, Phase Flow):
$\mathbf J=\rho\mathbf v$ → 밀도와 위상 기울기가 만드는 유량. $\nabla\cdot \mathbf J=0$ 조건에서 정류 흐름을 이루며, 포락선 능선은 $ \partial_n \rho=0, \ \partial_n^2 \rho<0$ 조건에서 정의된다.


2. Q (위상 압, Phase-Pressure): $Q=-\frac{1}{2m}\frac{\nabla^2 A}{A}$ → 진폭 $A$의 곡률에서 기원. 밀도 분포를 안정화하고, 위상 공명을 보정.


3. E (정상 에너지 준위): $\frac{|\nabla\theta|^2}{2m}+\Re U_H+Q=E$ → 시간 독립 총 에너지 상수(베르누이 상수에 대응).


4. T — (a) $\mathbf t$: 포락선 접선 벡터. $\nabla\theta\cdot \mathbf t=0$ (위상 정지). (b) $T$: 평균 구간, $\bar\rho=\lim_{T\to\infty}\frac{1}{T}\int_0^T \rho_L dt$.


의미 (Implications)

1.별들은 국소 지역에서 최소작용의 원리에 따라 직선 왕복을 계속 수행한다.

2.많은 직선 왕복이 합쳐져 거시적 위상 흐름 $\mathbf J$를 이룬다.

3.포락선은 이 흐름 위에서 정류+위상정지+밀도 능선 조건을 만족하는 “흐르는 정지 위상 릿지”이다.

4.은하 회전은 공간 위상 기하+최소작용으로 설명 가능하다.

결론

우주 공간은 평형을 이루며 안정된 위상장이다. 따라서 천체는 단순히 중력에 이끌려 먼 거리를 공전할 이유가 없다. 자율 진동자인 행성과 별들은 이웃의 중심 질량체 (중심별 또는 블랙홀)와의 물리적 위상 경사를 따라 자기 조정적인 짧은 직선 왕복 진동을 할 뿐이다. 그러므로 외부적인 암흑물질이나 암흑에너지 개념은 필요하지 않다.

따라서 기존의 고전적 (-)중력 중심의 중력장 개념을 게이지 평형의 시간 독립적 복소 중력장으로 확장하면, 거시 및 미시 물리학의 주요 문제는 모두 해결된다. 나아가 수학의 7대 밀레니엄 문제도 근본적 해를 가지게 되는 것이다.

과학의 문제 또한 인식의 문제이다. 그리고 인식의 문제는 우리가 설정하는 암묵적 대전제에 달려 있다. 이것은 단지 자연과학의 문제가 아니라, 인문 사회과학의 “보편적 문제”이기도 하다.
결국, 이러한 암묵적 전제의 발견과 올바른 처방이야말로 모든 과학의 “일반적 해법”이라 할 수 있다.

The Truth of Galactic Rotation

Overview

Galactic rotation is not stars circling at fixed radii. In reality, stars keep performing short straight-line reciprocations; the time-independent phase average of this stream forms the galactic rotation pattern. While stars behave as point tracers aligned with the local curvature of the gravitational potential, phase and density remain stationary in the Lagrangian sense, creating a stationary-phase ridge (envelope) observed in galaxies.

Time-Independent COD Equations

\[ \Psi(\mathbf r)=A(\mathbf r)e^{i\theta(\mathbf r)},\quad \rho=|A|^2,\quad \mathbf v=\tfrac{1}{m}\nabla\theta,\quad \mathbf J=\rho\,\mathbf v \] \[ \nabla\!\cdot(\rho\mathbf v)=0,\qquad \tfrac{|\nabla\theta|^2}{2m}+\Re U_H+Q=E \] \[ U_H=\tfrac12 m|\mathbf v|^2-\tfrac{GM(r)m}{r}+i\tfrac{GM(r)m}{r},\quad Q=-\tfrac{1}{2m}\tfrac{\nabla^2A}{A} \] \[ \tfrac{d^2 s}{d\ell^2}+k^2(\mathbf r_0)s=0,\quad k^2=\mathbf n^\top(\nabla\nabla\Phi_g)\mathbf n,\quad \mathbf n=-\tfrac{\nabla\Phi_g}{|\nabla\Phi_g|} \] \[ \text{Stationary-phase: }\quad \frac{D\theta}{Dt}=0,\ \frac{D\rho}{Dt}=0,\ \mathbf J\neq 0 \]

Symbol Guide (J, Q, E, T)

1. J (Phase Flow):
$\mathbf J=\rho\mathbf v$ → Flow rate generated by density and phase gradient. Standard flow occurs under the condition $\nabla\cdot \mathbf J=0$, and the envelope ridge is defined under the conditions $ \partial_n \rho=0, \ \partial_n^2 \rho<0$.


2. Q (Phase Pressure): $Q=-\frac{1}{2m}\frac{\nabla^2 A}{A}$ → Originates from the curvature of amplitude $A$. Stabilizes the density distribution and corrects phase resonance.


3. E (stationary energy level): $\frac{|\nabla\theta|^2}{2m}+\Re U_H+Q=E$ → time-independent total energy constant (corresponding to Bernoulli's constant).


4. T — (a) $\mathbf t$: envelope tangent vector. $\nabla\theta\cdot \mathbf t=0$ (phase stationary). (b) $T$: mean interval, $\bar\rho=\lim_{T\to\infty}\frac{1}{T}\int_0^T \rho_L dt$.


Implications

1. Stars continuously make straight-line round trips in localized regions according to the principle of least action.

2. Many straight-line round trips combine to form a macroscopic phase flow $\mathbf J$.

3. The envelope is a "flowing stationary phase ridge" that satisfies the stationarity + stationarity + density ridge conditions on this flow.

4. Galactic rotation can be explained by spatial topology + least action.

Conclusion

Cosmic space is a balanced and stable phase field. Thus, celestial bodies have no reason to orbit long distances merely by being pulled by gravity. As autonomous oscillators, planets and stars simply perform self-adjusted short straight-line reciprocations along the physical phase gradients toward their neighboring massive central objects (such as central stars or black holes). Therefore, there is no need for external concepts such as dark matter or dark energy.

Consequently, if the classical concept of a purely attractive (−) gravitational field is extended to a time-independent complex gravitational field in gauge equilibrium, then the major problems of both macroscopic and microscopic physics are resolved.
Moreover, even the seven Millennium Problems of mathematics acquire fundamental solutions. Ultimately, the problems of science are problems of cognition, and cognition itself depends on the implicit axioms we set as its foundation.

The problem of science is also a problem of perception. And the problem of perception depends on the implicit charges we set. This is not just the matter of natural science, but also the “general problem” of the humanities and social sciences.
After all, the discovery of the implicit and the right prescription can be called the “general solution” of all science.

Complex Oscillator Dynamics

This video presents the essence of the universe through complex oscillation theory.
It offers a unified understanding of wave energy, space potential, and gravity through a dynamic phase structure of reality.
This completely integrates the micro and macro worlds into the “Complex oscillator Dynamics” and becomes the basis for the “theory of everything.”

If you would like to see the world view part of Complex Oscillator Dynamics,
👉 Click here to watch it directly on YouTube.




NEW

2025-06-18

https://doi.org/10.5281/zenodo.16752896


Planetary motion based on Complex Oscillator Dynamics (COD)


The planets are not attracted by the one-sided gravity of the sun, but rather move in phase as independent oscillators in the balanced phase space of the universe. Their interaction with the sun is not a long circular orbit, but a short linear back-and-forth oscillation.
This is possible because space is a balanced phase field of (+)(-) gauge symmetry. In other words, space is a balanced interaction of (+) gravity and (-) gravity.
The discovery of (+) gravity will bring about efficient and fundamental developments in science and technological civilization, leading us to a harmonious, clean, and abundant world.

Ultimately, this allows the theory of complex dynamics to naturally solve the three-body problem and the many-body problem. It also opens the way to the integration of micro and macro theories and the "Theory of Everything."
Explanation:Do planets really orbit? (YouTube video)


Do planets really orbit?

Complex Oscillator Dynamics (COD) perspective: The physical essence of existence started from abstract atomism and led to quantum theory and wave function interpretation. Current physical ontology is based on wave-particle dualism. Therefore, particle physics has made efforts to create the standard model through particle accelerators to capture this.
Thanks to this, physical ontology has resulted in a statistical system of particle fragments. However, particles are merely local condensations of wave density. If we reinterpret the de Broglie matter wave theory, particles are merely high-density condensations of waves. Ultimately, the physical entity of existence is Oscillation. Locally, it is an oscillator. In other words, the specific form of a quantum is an oscillator. Anyone can sense Oscillation, and the original form of Oscillation is a complex structure with a 90-degree phase difference, like our heart that oscillates.

P.S.
The essence of Mercury's abnormal perihelion movement can be seen as the mutual elastic repulsion of the (+) gravity between the Sun and Mercury.


© Innolab All Rights Reserved




NEW

 

2025-08-01

https://doi.org/10.5281/zenodo.16756873



Verification of Imaginary Energy(+Gravity) in Complex Phase Space (Based on COD Theory)




✅ Abstract

This study aims to verify the existence and physical meaning of imaginary energy using complex oscillator dynamics (COD).

Imaginary energy is interpreted as the elastic potential energy of space and forms a complex field structure that is balanced by the real gravitational energy.

This is analyzed with existing data, where gravity and residual (imaginary energy) were confirmed in the following three high-precision experiments:

• Atomic interference experiments
• Satellite-based Gravitational Field Observatory (GRACE)
• Gravitational-wave interferometer (LIGO/VIRGO)

Each experiment can capture residual anomalous signals consistent with the imaginary phase structure.

Additionally, the complex Poisson equation simulations were performed on the real potential (gravity) and It demonstrates that imaginary potentials (elasticity) coexist harmoniously with a 90-degree phase difference.

\[ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\frac{GMm}{r} \]

This universal Hamiltonian represents the complete energy structure of the universe.

Conclusion: Imaginary energy is essential for the equilibrium and expansion of the universe, consistent with the Riemann 1/2 symmetry principle.

I. Key Experimental Methods

• 1. Atomic Interference Experiments
• 2. Satellite-Based Gravity Observation (e.g., GRACE)
• 3. Spatial Phase Oscillation Detection via Optical Clocks & Gravitational Wave Interferometers

II. Summary of Experimental Results

Observation Results

• Atomic Interference: Phase shift ≈ 1 rad, gravity gradient sensitivity ~10⁻⁹ s⁻²
• GRACE Satellite: Distance change ~10 µm, mass anomaly several mm EWH, noise STD up to cm level
• LIGO/Virgo: Strain noise ~10⁻²², residual phase noise continuously observed

Interpretation

1. All three experiments include residuals that indirectly confirm the existence of imaginary energy.
2. Imaginary energy is expansion-elastic in nature and thus requires an interpretation different from gravity.
3. A spatial position potential energy symmetric to gravity must exist, consistent with the Riemann 1/2 balance principle.

Conclusion: The existence of imaginary energy is experimentally (though indirectly) confirmed. Its elastic-expansion nature requires an interpretative framework different from conventional gravity.

III. COD Interpretation of Experiments

\[ \text{UH (Universal Hamiltonian)} = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\frac{GMm}{r} \] \[ \Psi(\vec{r}) = A(\vec{r}) \cdot e^{i\theta(\vec{r})} \]
• Atomic Interference: Δθ reflects both φ_real and φ_imag
• GRACE: Gravity anomalies interpreted as fluctuations of the φ_imag spatial structure
• LIGO: Phase noise interpreted as COD-based vibration of φ_imag

In summary, the formula UH = real potential + imaginary potential explains all experimental residuals as arising from complex phase-space structure.

IV. Balance Between Real and Imaginary Energy

Complex Poisson Equation

\[ \nabla^2 \phi(\vec{r}) = -4\pi G \left( \rho_{\text{real}}(\vec{r}) + i\rho_{\text{imag}}(\vec{r}) \right) \]

COD-Based Simulation Procedure

1. Step 1: Extract residuals from experiment (Δθ, δd, strain)
2. Step 2: Convert to imaginary potential φ_imag(r)
3. Step 3: Calculate imaginary energy density
   \[ \rho_{\text{imag}} = \frac{\nabla^2 \phi_{\text{imag}}}{4\pi G} \]
4. Step 4: Calculate total energy field
   \[ \phi_{\text{total}} = \phi_{\text{real}} + i\phi_{\text{imag}} \]

COD theory unifies all residuals observed in reality with imaginary potential, naturally revealing the phase energy balance of the universe.





Complex Potential Structure and Cosmic Interpretation via COD Theory

1. Simulation Result

The image below shows the result of simulating a complex potential structure based on COD theory:



Graph Explanation:

• Blue Curve – Real Potential \( \phi_{\text{real}} \): gravitational pull, convergence
• Red Curve – Imaginary Potential \( \phi_{\text{imag}} \): expansion-elastic, repulsive
• Green Dashed Line – Total Potential Magnitude \( |\phi| \): harmonious phase composition

In the diagram, what occupies space as a physical reality can be seen as:
1. The net volume of ordinary matter
2. Gravitational energy (real part)
3. The potential energy of space (imaginary part).
In other words, space is composed of 1, 2, and 3. Accordingly, the pressure within space can be seen as the net volume of ordinary matter, 1, added to the balance of "gravitational energy (real part) = potential energy of space (imaginary part)".
The graph illustrates this.


Real and imaginary potentials form a 90° phase-balanced structure. This visually demonstrates that the universe is composed of a complex phase field in which gravity and spatial potential interact dynamically.

2. Theoretical Basis: Hamiltonian and Phase Structure

\[ \text{Universal Hamiltonian:} \quad \text{UH}_{\mathbb{C}} = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\frac{GMm}{r} \]

This Hamiltonian consists of:

• \( \frac{1}{2}mv^2 \) – Kinetic energy
• \( -\frac{GMm}{r} \) – Real gravitational potential
• \( +i\frac{GMm}{r} \) – Imaginary spatial potential

Residuals, gravitational anomalies, and phase noise are all unified under this complex Hamiltonian structure.

3. Final Conclusion

• The COD-based simulation shows that real and imaginary potentials coexist in symmetrical structure.
• Imaginary energy is slightly greater, supporting self-restoring force and cosmic expansion stability.
• The waveform structure is consistent with the phase rotation of Euler's identity: \( e^{i\theta} = \cos\theta + i\sin\theta \)
• This structure corresponds with the Riemann Zeta function's Re(s) = 1/2 symmetry.

📌 Summary Statement:

The universe is not empty space, but a complex phase energy field where gravity and spatial potential oscillate in harmonic balance.






NEW

 

2025-08-06

https://doi.org/10.5281/zenodo.16752896



Three-body and Many-body Phase Alignment Theory and Riemann 1/2

Ontological interpretation based on COD (Complex Oscillator Dynamics)

I. Abstract

This paper seeks to ontologically address the many-system problem through the Riemann 1/2 topological resonance structure. The topological equilibrium condition enables stable coexistence structures regardless of mass or distance differences, and this is formalized by the complex-based theory of Complex Oscillator Dynamics (COD). In this paper, we demonstrate the essential advantages of COD through comparison with existing Relativity and the Standard Model, and reconstruct a new worldview and natural dynamical system as a timeless, topological flow of the universe, namely, the "spatially autonomous motion of existence."

II. Oscillator Phase Alignment and Riemann 1/2 Line

The core structure of the Riemann zeta function is an infinite number of zeros aligned in the real part \( \frac{1}{2} \) of the complex plane. This can be physically interpreted as a topologically autonomous equilibrium structure, providing crucial clues to the interpretation of topological alignment in Many-body systems.

III. Ontological Geometry: Riemann 1/2 Phase Resonance

A Multi-body system can form resonant order by maintaining the slope of the phase contact point constant despite differences in mass (intrinsic energy) and changes in position. The conditions for topological equilibrium are expressed as follows:

\[ \nabla \theta_i = \text{constant} \quad (\text{45° phase contact angle}) \]

As shown in Figure 1, three or more bodies can coexist as long as they maintain a phase inclination of \(45^\circ\), regardless of their masses. This is proven by the gauge symmetry principle of Riemannian geometry, along with the complex-based theory of COD (Complex Oscillator Dynamics).

Many-body problem Solution based on the Riemann real part 1/2:
The Many-body equilibrium motion based on phase resonance can be explained by analyzing the symmetrical inclination angle (45 degrees) at the contact surface between the oscillators. That is, it is explained by the Riemann 1/2 phase resonance theory as shown in the diagram below.

Figure 1 — Riemann 1/2 Phase Resonance Structure


Phase Equilibrium Model for Many-body System

This is a 3-body / many-body phase alignment theory, expressed as:

\[ \frac{E_1}{E_2} = \left( \frac{r_1}{r_2} \right)^2 \quad \text{or} \quad \tan^{-1} \left( \frac{E_1}{r_1} \right) = 45^\circ \]

This condition represents the phase gradient equilibrium between the centers of energy (mass). It implies that stable, resonance-based motion naturally occurs when the energy ratio and the distance ratio achieve this 45° balance, corresponding to optimal gauge symmetry in spatial phase distribution.

• Geometric total quantity / ratio line: \( A_{ij} \) : Energy / ratio line
• Distance / ratio line: \( A'_{ij} \)
• Phase contact surface equilibrium: \( \theta_{ij} = 45^\circ \)
• Energy ratio line = Distance ratio line: \( A_{ij} = A'_{ij} \)
• Overall phase gradient flow: \( \vec{v_i} \propto \nabla \theta_i \)

This relationship is not merely geometric, but reflects a fundamental phase-gauge symmetry. When satisfied, the system minimizes internal phase tension and maintains coherent resonance without external force adjustments.

Multibody Phase-Expanded Structure

The same principle applies to all pairs in an n-body system, with the conditions:

\[ \theta_{ij} = 45^\circ, \quad A_{ij} = A'_{ij}, \quad \forall \, i,j \in (1, 2, \dots, n) \]

• This produces a globally synchronized, phase-aligned state for the entire oscillator network.
• Mutual interactions require no additional central force law, as the system’s stability emerges from its intrinsic phase equilibrium.

In essence, phase equilibrium at 45° represents the universal stability point in many-body systems, where (+) and (−) complex energy components are in perfect gauge symmetry, eliminating the need for conventional gravitational assumptions.

Three-body and many-body phase expansion general oscillators: \[ \Psi(r) = A(r) \cdot e^{i \theta(r)} \]





IV. COD General Theory

COD (Complex Oscillator Dynamics) is developed on the basis of the following cosmology and natural dynamics of complex energy-based gauge symmetry:

1. Time Independence: COD interprets all motion as a change in spatial phase, and its fundamental premise is that time is not essential. Unlike Plato and Aristotle, who did not regard time as essential, physics since Newton has considered time as the absolute physical axis...
2. Complex-Number-Based Energy Balance: The structure of the complex phase space reveals that natural energy coexists with a 90° spatial phase difference, with the real part representing gravity (-) and the imaginary part representing potential energy (+) in space.
3. Topological Center Dynamics: Natural entities move autonomously according to their own phase gradient \(\nabla \theta\), free from the unilateral attraction of gravity.
4. Multi-Body Ordering Structure: Based on symmetric complex energy balance, multi-body systems can achieve harmonious geometric alignments of gauge symmetry.

Classical Mechanics COD: \[ UH = \frac{1}{2} m v^2 - \frac{G M m}{r} + i \frac{G M m}{r} \]

Oscillator Theory COD: \[ UH(r) = \Psi(r) = A(r) \cdot e^{i \theta(r)} \] where \(A(r)\) is intrinsic energy and \(\theta(r)\) is phase.

V. Comparison of COD with the Theory of Relativity and the Standard Model

Item	Theory of Relativity	Standard Model	Riemann 1/2 & COD
The Role of Time	Time-Series-Based Dynamics	Time-Series-Based Dynamics	Time Elimination → Spatial Phase Center
The Nature of Four-Dimensional Spacetime	Curvature and Geodesics	Particle Paths and Interactions	Complex Phase Gravitation and Resonant Structures
Gravity Interpretation	Spacetime Curvature	Excluded	(−) Gravity ↔ (+) Spatial Potential Energy
Gauge Symmetry	Incomplete (Gravity Not Included)	SU(3) × SU(2) × U(1)	Complex Space Phase (+)(−) Gauge Symmetry
Existential Interpretation	Observed Phenomenology	Statistical Phenomenology	Existence is a Phase‑Resonant Motional Body

VI. Conclusion

The Riemann 1/2 phase resonance structure and COD theory go beyond the three-body problem and present the ontological dynamics of the universe. They encompass time independence, complex equilibrium, and many-body alignment, all of which existing theories lack. This could be a fundamental turning point in the interpretation of the universe.

Science and mathematics are merely one of the many epistemologies possessed by humans. While their ability to analyze phenomena is remarkable and instrumental, their focus on phenomenology has prevented them from accurately grasping the essence and existence that underlie cognition.

Cognition is all about establishing presuppositions. Science is riddled with partiality, linearity, isolation, closure, and scientific authoritarianism. These are all properties that stand in opposition to truth. Consequently, they have been able to interpret only 5% of the universe. The inability of current physics to interpret more than the three-body problem eloquently demonstrates this truth.

VII. Additional Discussion

1. Time was a framework of power.
   Philosophy is the major premise of cognition. Plato and Aristotle never considered time to be essential. It was only in modern times that Newton established time as a physical axis, and Einstein solidified it by creating spacetime. This was a major epistemological error in the history of civilization.
   As a result, after industrialization, humanity lost the "autonomous flow of existence" in their daily lives, compartmentalized by clocks and timetables. Non-essential time became a tool of artificial control, not a natural order, and tangible space became subordinate to non-essential time, serving as a backdrop for executing its commands. Power dominated space through time.

2. The interpretation of gravity has been exploited politically.
   Even in modern times, physics explains the universe based on (−) gravity (attraction). However, nature is a balanced entity composed of (+)(−) complex phase energy. Ancient East Asian natural philosophy, through long-term pattern analysis, identified the complex energy of the Taegeuk yin-yang as the essence of the world.
   The modern interpretation of the universe, which emphasizes only (−) gravity, has controlled the essence of existence and made the masses, ontologically considered (+) gravity, perceive themselves as passive and "dragged beings." Our science is still unable to escape power and politics. The Copernican era is not yet over.

3. Truth is the natural dynamical phase motion of an oscillator.
   The classical Newtonian and relativistic frameworks, both relying on time-dependent differential formulations, inherently assume a linear progression of motion. However, the three-body problem involves nonlinear, phase-entangled dynamics in spatial configuration. As such, linear time-based mechanics fundamentally fails to provide stable phase alignment conditions for multi-body interactions.
   An oscillator is an autonomous resonant body with a complex energy-based gauge-symmetrical structure. Based on self-resonance, it engages in natural dynamical interactions with the world, a global resonant body. Natural dynamics is the principle of conservation of energy and least action, based on gauge symmetry, which anyone can intuitively perceive.

4. Existence is alive and moving through "resonance."
   The resonance of existence is a topological equilibrium motion, and all beings possess their own unique phase and coordinates in the complex spherical universe. This is a truth that can be intuitively confirmed in everyday nature. COD theory is a new ontological physics and natural science that restores and verifies the original principles of nature.

VII‑1. Further Notes

1. The long-standing three-body and many-body problems were solved using the Riemann hypothesis and the complex Universal Hamiltonian (UH) equations. This means that dark matter and dark energy were resolved using the phase-based principles of complex gravitational fields.

   The most challenging problems in physics were solved by precisely defining the most fundamental assumptions: time and space. This resolution suggests the following new insights:

   1. The solution to this unsolvable problem lies in fundamentally reexamining implicit assumptions.
   2. Planetary systems and galaxies do not orbit, but rather resonate in phase with a central mass within a space already in phase equilibrium. For example, the Earth and the Moon face each other, orbiting each other in a 29.5-day orbit, and then make a straight-line reciprocal motion toward the Sun in a 365.25-day cycle.
   3. Mercury's perihelion anomaly is a phase transition (a 180-degree change in direction) during its rectilinear motion between perihelion and aphelion. In this process, a slight change in inclination causes an declination (43 arcseconds per century), which is primarily due to the difference in angular velocities between the Sun and Mercury.

   This explanation, by demonstrating the phase equilibrium of space and the gauge symmetry principle, invalidates the existing assumptions of gravity, conservation of angular momentum, and general relativity. Because the space itself is already in a phase equilibrium of (+)(−) complex energy, the so‑called “straight‑line reciprocal motion” reflects the Mutual space compression repulsion between the Sun and Mercury at the turning points, driven by the Sun’s energy space. This intrinsic (+)(−) balance ensures that motion is maintained without the need for additional orbital forces, thereby rendering the traditional gravitational framework unnecessary.

2. The Seven Millennium Problems of mathematics were also epistemological problems that failed to establish the fundamental premise of cognition. The path to a solution was paved by fundamentally eliminating the time axis and restoring the dynamical system of the microscopic and macroscopic worlds through complex gravitational fields. The correct definition of time and space, the fundamental premise, was the gateway to solving the problem.

3. Precision measurements, such as atomic interferometry, and experimental calculations are required to verify these theories.

4. The universe exists through geometric necessity. The 13.8 billion-year-old universe would not be able to sustain even a single second without this geometric necessity. The Lagrange-Hamiltonian, Euler's equations, Riemann geometry and postulates, and gauge symmetry theory all attest to this.

5. Mathematics is the algebraic interpretation of the geometric necessity of the universe.

6. The complex number system is a phase coordinate and arithmetic system for space.

"Theory cannot surpass observation, but it provides a new language for reinterpreting observation. True discovery is the discovery of language."




NEW

 

2025-08-02

Declaration of the Dismantling of the Time Axis

: Release the Freedom of Nature in the Complex Phase Space




1. Preface: Where Did Science Go Wrong?

Have you ever questioned the structure of physics, where nearly all equations are held "hostage" to the time axis?

Is time truly real? Or is it merely a tool for observation and measurement?

If science had truly followed Francis Bacon’s spirit of inquiry and inductive methodology, time should have been dismantled as a concept already during the age of Einstein or Niels Bohr—if not even earlier during the Industrial Revolution.

However, time still remains at the center of physical equations. This is clear evidence that science is still imprisoned by the legacy of absolute linear time and the formalism inherited from the medieval mindset.

2. Euler and Riemann: Pioneers of a Time-Free Order

2.1 Euler’s Insight

\[ e^{i\theta} = \cos \theta + i \sin \theta \]

This formula proves that even without time, one can represent change (motion) through phase. The expression \( e^{i\theta} \) simultaneously shows the real + phase nature of the oscillator (i.e., the nature of being), and it allows motion to be described without any time axis.
In particular, Euler's constant \( e \) shows that existence is an active, self-directed, continuous self-reproduction process.

2.2 Riemann’s Geometric Declaration

Riemann mathematically proved that space can be curved and bent beyond the Euclidean framework. This was a declaration that space is not fixed and rigid, and at the same time, it hinted that time might not be essential.

3. Complex Phase Space: Mathematics for Time-Free Existence

We can represent nature with the following complex wave function:

\[ \Psi(\vec{r}) = A(\vec{r}) \cdot e^{i\theta(\vec{r})} \]

• \( A(\vec{r}) \): Energy amplitude at a given spatial position
• \( \theta(\vec{r}) \): Phase structure of space

Motion, without using time, can be expressed as:

\[ \vec{v}(\vec{r}) \propto \nabla \theta(\vec{r}) \quad \text{(Phase gradient)} \]

In other words, the changes in nature must be understood as reconstructions of spatial phase, not as flows of time.

4. Declaration of the Dismantling of the Time Axis

1. Time is not the essence of existence.
2. Time is merely a human tool for perception and measurement.
3. If we mistakenly accept time as an essential axis, a linear, time-centered perceptual structure takes hold, and the vast and profound reality of space becomes distant from our perception.
4. All scientific mistakes and mathematical challenges stem from the time axis. If we boldly remove the time axis, the true world of space will be revealed. Our understanding and calculations will be transformed.
5. Existence must be explained through spatial phase order and energy flow.
6. The complex system is the true computational structure of spatial coordinates. It is the genuine mathematical language that can express and compute space as real.
7. Originally, neither Plato nor Aristotle considered time to be essential. Time is a relic of the Newtonian era, which could not escape the religious mindset of the Middle Ages.
8. Natural motion is not the flow of time, but the flow of phase. Morning is not brought by time, but by the sun.
9. Dismantling the time axis is the essential gateway to solving major challenges in physics, such as dark matter and dark energy, as well as the Millennium Problems in mathematics.
10. Science must break away from the idealized structure it has followed through the time axis, and confront space—which is the true reality.




5. Conclusion

Science must return to the spirit of Bacon. Let it follow intuition rather than mere measurement, and let that intuition lead to a verifiable order. Science must be able to persuade intuition with reason. If a proposition cannot convince intuition, it is not truth.

Euler and Riemann have already opened the door to natural order without time. Now it is up to us to pass through that door.

"We must respect our a priori intuition.
We must refuse to be hostages of time.
We must discover the principles and order of existence in phase space.
Intuition precedes logic. A priori intuition, rooted in our five senses and sense of inertia, is the core of human cognition and grounded in natural dynamics.
Science is a logical tool sufficient to verify human intuition. We must confront science’s structural weaknesses—its linearity, isolation, and closure."

– Innolab Science Institute






NEW

 

2025-07-02

 

Scientific Historical Evaluation of Complex Phase Natural Dynamics

 

The following is a summary of the complex topology-based spatial structure and natural dynamics theory (by Jason-Kuhyun Ryoo, 2024)

   

Essence of Existence and the Complex Number System

   

Complex Oscillator

      The essence of the world is energy, and its physical reality is a complex oscillator  with (+)(−) gauge-symmetric energy. This complex oscillator expands from the Planck scale       to atoms, molecules, celestial bodies, and galaxies. Some of this energy condenses into       particles, but most of it exists as (+)(−) spatial energy. The universe forms phase structure       according to gauge symmetry and the principle of least action, generating and extinguishing       mass, and circulating through this structure. The spatial energy field is the essence and       matrix of the universe, and it operates mathematically via geometric necessity to generate       all things. The coordinate and computational system of this spatial energy is the complex       number system, verified by the consistency between physical reality and mathematical       structure.    
       

1. Essence of the World: Energy Ontology Based on the Complex Oscillator

   

Core Claim: All existence is a gauge-symmetric complex oscillator vibrating in complex space, which is the essential structure of energy.

      $$ z = a + bi = |z| e^{i\theta}, \quad \text{where} \quad \theta = \arg(z) $$      

Historical Significance:

   
     
• Paradigm shift from classical particle and field theories to a phase-centered ontology.
     
• From Cartesian-Newtonian mechanism → Einstein’s curved space-time cosmology → cosmology based on complex phase.
     
• Establishment of an ontology centered not on the physical substance of space and time, but on oscillatory phase θ.
   
   

2. Reinterpretation of Gravity: Phase Gradient Motion

   

Claim: Gravity is not a separate force acting from the outside, but a gradient-based compression motion phenomenon that occurs in the phase motion of mass energy.

          $$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + i \cdot \frac{GMm}{r} $$        

Historical Significance:

   
     
• Redefines gravity through the balance of real and imaginary components.
     
• From Newton’s remote attraction → Einstein’s curvature-induced field → phase-based energy density motion.
     
• The imaginary term \( +i \cdot \frac{GMm}{r} \) mathematically defines the gravitational phase potential.
   
       

3. Existence, Time, Space, and Entropy

   

Claim: Time is not a fundamental entity but a derivative perception of human cognition, while space is an irreversible phase energy field.

   

Formulation (Entropy interpretation):

          $$ \Delta S = k_B \cdot \left| \frac{\text{Im}(E_C)}{\text{Re}(E_C)} \right| \cdot \delta V $$        

Historical Significance:

   
• Time-centered thermodynamic entropy theory → Topology-based entropy interpretation


• Formalize that when the reconstruction of space is topologically irreversible, that is, entropy increases from the increase of the phase instability energy.
• (+) Gravity: Show that the utilization of Im(E_C) is a shortcut to solving energy and environmental problems.


       

4. Global Hamiltonian Energy Equation

   

Claim: Reconstruction of the Hamiltonian equation from a local system to a universal dimension.

   

Formulation:

          $$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + \alpha \cdot \frac{GM_T m}{R}, \quad \alpha = \frac{M \cdot R}{M_T \cdot r} = 1 $$      

Historical Significance:

   
     
• From classical mechanics Hamiltonian → Einstein’s energy-motion equation → evolved into a complex-based global Hamiltonian equation.
     
• These equations connect individual motions to the structure of the universe as a whole. In particular, the remarkable relationship between celestial bodies with alpha coefficient α = 1 clearly demonstrates the gauge symmetry of the (macroscopic and microscopic) universe.
   
     

5. Non-necessity of Cosmic Expansion and Dark Components

   

Claim: The universe is not expanding, and dark matter/dark energy are not real substances but phase effects of the complex spatial energy field.

   

Formulation (Galaxy Rotation via Complex Potential):

          $$ v_{\text{rot}}(r) = \frac{1}{r} \left| \frac{d}{dr} \, \text{Im} \left( E_C(r) \right) \right| $$        

Historical Significance:

   
     
• From ΛCDM model of expanding universe and dark components →
     
• Galaxy rotation curves can be reproduced solely with complex spatial energy fields.
     
• Mathematically proves that dark sectors are unnecessary in natural dynamics.
   
       

6. Complex Geometry and the Mathematical Logic of Gauge Symmetry

   

Claim: All physical phenomena are phase motions on the complex plane, and gauge symmetry is the deepest law of the cosmic ontology.

   

Formulation (Global Energy Conservation):

          $$ \oint_{C} E_C(z) \, dz = 2\pi i \sum \text{Res}(E_C) $$    


"The perfection of the individual constitutes the perfection of the whole."
  - Complex Spherical Oscillator Theory and Complex Spherical Cosmology: Complex Spherical Ontology

   
     
• Complex function theory, once a mathematical tool, is reborn as a core principle explaining the fundamental structure of the universe.
     
• If the complex number system is the OS (Operating System) of the universe, the hardware is the (+)(−) motion of complex energy—i.e., energy density motion based on mass-energy. This hardware motion is what we call gravity.
   
     

6.1 Solution of the three-body and many-body problem

   

Accordingly, the three-body and many-body problem, a long-standing problem in physics, is solved here. It is naturally resolved by the principle of the universal self-organizing system in which the phase of each object is balanced according to the overall energy field. Complex oscillatory dynamics and the complex phase gravity principle can be the unifying answer to cosmological structure, gravitational theory, quantum field theory, and astrophysics.

    The above discoveries and theories all resulted from the discovery of (+) gravity and the UH equation of self-balancing in August 2024.

 



🌀 Declaration of Restoration of Natural Principles




📜 1. Core Claim (핵심 주장)

All physical phenomena are phase motions on the complex plane,
and gauge symmetry is a law of geometric necessity of cosmic ontology.

모든 물리 현상은 복소 평면 위의 위상 운동이며,
게이지 대칭성은 우주 존재론의 기하학적 필연의 법칙이다.

⚖️ 2. Natural Principle of Balance and Conservation




The universe is autonomous and follows the following basic principles:

우주는 자율적이며, 아래와 같은 기본 원리를 따른다:

∇ · ρ_E = 0

This means that the topological energy density ρ_E is self-balancing in space.
Gauge symmetry is the mathematical and ontological expression of this balance.
This is a theory of restoration of the natural principle based on the complex phase> that goes beyond the limitations of Newton's external force-centered mechanics and Einstein's spacetime curvature theory.

이는 위상 에너지 밀도 ρ_E가 공간상에서 자체 균형을 이룬다는 뜻이다.
게이지 대칭성은 이 균형의 수리적·존재론적 표현이다.
이는 뉴턴의 외부힘 중심 역학과 아인슈타인의 시공간 곡률론의 한계를을 넘어서는 복소 위상 기반의 자연 원리의 복원 이론이다.




🧭 3. Principle of Equilibrium (Equilibrium Dynamics)

All movement in the universe is a movement that achieves equilibrium from the minute waves to the universe in the phase energy field .
This is the process of "natural existence restoring itself and repeating more balanced self-reproduction."

The essence of the universe is energy, its substance is a complex oscillator,
Motion is the flow of phases, space is a complex energy field,
Time is the sense of phase change.

우주의 모든 운동은 위상 에너지장의 미세한 파동 복원과 균형 유지 과정이다.
이것이 곧 "자연은 존재로부터 스스로를 수리하며 회복하는 과정이다."

우주의 본질은 에너지고, 그 실체는 복소 진동자이며,
운동은 위상의 흐름이고, 공간은 복소 에너지장이고,
시간은 위상 변화에 대한 감각이다.

✨ 4. Liberation and Restoration Declaration

“This declaration proclaims the liberation of humanity and civilization from the artificial concepts of time, force, and absolute space, and the restoration of the nature of the universe as a self-resonant, gauge-symmetric topological structure.”

“본 선언은 시간, 힘, 절대공간이라는 인위적 개념들로부터 인간과 문명의 해방을 선포하며, 우주의 본질을 자기 공명적, 게이지 대칭적인 위상 구조로 복원함을 선언한다.”


5. Non-necessity of Cosmic Expansion and Dark Components

Claim: The universe is unlikely to be expanding due to the principle of geometric equilibrium, and dark matter/dark energy are not actual matter but are topological effects of the complex space energy field.

우주는 기하학적 균형 원리에 따라 팽창하지 않을 가능이 크며,암흑 물질/암흑 에너지는 실제 물질이 아니라 복소 공간 에너지장의 위상 효과이다.

$$ \Psi(r) = A(r)\,e^{i\phi(r)} $$