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COD THEORY · ONTOLOGICAL PHYSICS
Complex Quaternionic Spherical Oscillator Dynamics
InnoLab Science Inastitute · Seoul · Korea
CQSO as the fundamental unit of self-coherent existence
Complex Quaternion Spherical Oscillator
Self
i
j
k
Q = Q₀ + Q₁i + Q₂j + Q₃k ∈ S³
self-reference + three-axis quaternionic balance + spherical closure
Complex Wave Medium
superposition · resonance
diffraction · interference
entanglement · tunneling
Wave is not a secondary effect;
it is the medium of existence.
The Medium of Cosmic Management
Superposition · Entanglement · Diffraction
Tunneling · Resonance · Condensation
Scale : 10⁻⁹ m (nm) → 0⁻³⁵ m (lₚ)
Recursive Oscillation
self-organization
self-regulation
inertia preservation
Existence is maintained by
recursive self-coherence Oscillation.
· Complex Dual Energy
· Multiplication Invariant Geometry
· Complex Quonion Geometric Algebra
· Complex Spherical Oscillator Dynamics
Existence = recursive self-organized phase-equilibrium selection
© 2026 InnoLab Science Institute (ISI) CC BY-NC 4.0 https://udynamics.net/en/
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STRUCTURE SELECTION PATH
InnoLab Science Inastitute · Seoul · Korea
Structure is a phase-aligned energy path
maximum coherence · minimum action · admissible eigengeometry
Complex Wave
medium of motion
Phase-Aligned Path
energy flows coherently
Minimum Action
least energy loss
Δ(ΔΦ) → 0
recursive phase-balance condition
120° Basic Balance
self-reference + 3-axis quaternionic closure
γ_Q = √3/2
45° Unity Balance
condensation equals support
P = Q, θ = π/4
Structure selection determines which phase-equilibrium geometries can exist before mass realization.
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© 2026 InnoLab Science Institute (ISI) CC BY-NC 4.0 https://udynamics.net/en/
PHASE DYNAMICS
InnoLab Science Inastitute · Seoul · Korea
From wave phase to energy and mass
phase gradient hierarchy as a unified coordinate system
Phase Field
Ψ(r)=A(r)e^{iΦ(r)}
A(r): amplitude
Φ(r): phase structure
k = |∇Φ|
COD hierarchy
k¹
k²
k³
k⁴(BH) · 6π
phase coherence
energy support
mass condensation · 4π
E ∝ |∇Φ|² · M ∝ ∫|∇Φ|³ dV
Space is not an empty background.
Space is the oscillator manifold generated by self-coherent complex waves.
© 2026 InnoLab Science Institute (ISI) CC BY-NC 4.0 https://udynamics.net/en/
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ENGINEERING TRANSLATION
InnoLab Science Inastitute · Seoul · Korea
Engineering systems as multi-oscillator networks
COD turns phase equilibrium into a control architecture
Physical System
sensors · materials
power nodes · process nodes
{Φᵢ}
COD Control Core
8QRM · PLP · PVE
phase memory + routing
Δ[ΣKᵢⱼ(Φᵢ−Φⱼ)²]→0
Phase-Equilibrium Output
stability · efficiency
durability · adaptive control
ΔΦ → minimum
Complete individuals form a complete whole.
Engineering becomes the design of phase-aligned oscillator networks.
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© 2026 InnoLab Science Institute (ISI) CC BY-NC 4.0 https://udynamics.net/en/
COD ENGINEERING SYSTEMS
InnoLab Science Inastitute · Seoul · Korea
One phase principle across engineering domains
power · materials · computation · AGI · infrastructure
COD Phase
Engineering Core
Δ(ΔΦ)→0
Power & ESS
PMS · BMS · smart grid
Semiconductor
8QRM SoC · phase routing
Nano & Materials
graphene · perovskite · batteries
AI & AGI
NGI + human propositions
Engineering goal: reduce phase mismatch, maximize coherent flow, minimize action.
© 2026 InnoLab Science Institute (ISI) CC BY-NC 4.0 https://udynamics.net/en/
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