This document presents the full integrated structure of the Talek Harmonic Oscillation Model, organized across five primary modules and one appendix.

Each section builds a distinct analytical layer within the Talek architecture — from the core mathematical formulation to system-level modulation and applied simulation frameworks.

1. Core Formalism: Talek Harmonic Oscillation Model

$E(t) = A \cdot \sin(Ft) \cdot e^{-t/D}$

Where:

• A (Amplitude) — Governs initial signal magnitude or displacement from baseline.
• F (Frequency) — Describes the rate of internal oscillatory recurrence.
• D (Damping Constant / Duration) — Controls the decay rate and retention profile of the oscillatory system.

This formalism is equivalent to a damped harmonic oscillator, a foundational model used in:

• wave mechanics
• vibrational systems
• resonance circuits
• dissipative dynamical analysis
• signal attenuation frameworks

The Talek Harmonic Oscillation Model applies this classical structure to endogenous information processes—allowing the underlying oscillatory dynamics of internal states to be quantified, simulated, and compared across computational, biological, and hybrid systems.