The relationship between mass and frequency, as presented in this framework, can be a source of confusion due to the interplay of different physical concepts and unit systems. To clarify, let's delve into the nuances of mass and frequency notation and their implications. In physics, mass can be described in two primary ways: **rest mass ($m_0$)** and **relativistic mass ($m$)**. Rest mass is an intrinsic, invariant property of a particle, representing its mass when it is not in motion. It is the mass that contributes to the particle's rest energy ($E_0 = m_0c^2$). Relativistic mass, on the other hand, is a concept where the mass of a particle is considered to increase with its velocity, given by $m = \gamma m_0$, where $\gamma$ is the Lorentz factor. The equation $E = mc^2$ then represents the total relativistic energy of a particle, encompassing both its rest energy and its kinetic energy. While the concept of relativistic mass is still encountered, modern particle physics often prefers to use "mass" to refer exclusively to rest mass ($m_0$) and to discuss "total energy" ($E$) and "momentum" ($p$) for particles in motion, related by the equation $E^2 = (m_0c^2)^2 + (pc)^2$. In this paper, when $m$ is used in $E=mc^2$ without a subscript, it generally refers to the relativistic mass, representing the total energy. However, the core identity linking mass and frequency is most fundamentally tied to the *intrinsic* frequency of a particle, which is derived from its *rest mass*. Similarly, frequency can be expressed as **linear frequency ($f$)** in Hertz (cycles per second) or **angular frequency ($\omega$)** in radians per second, where $\omega = 2\pi f$. The fundamental quantum mechanical energy-frequency relation is $E = hf$, using linear frequency. However, in theoretical physics, the angular frequency is often preferred, leading to the expression $E = \hbar\omega$, where $\hbar = h/2\pi$ is the reduced Planck constant. For a particle at rest, its intrinsic energy ($E_0 = m_0c^2$) corresponds to a specific intrinsic angular frequency known as the **Compton frequency ($\omega_C$)**. This relationship is expressed as $m_0c^2 = \hbar\omega_C$, which means $\omega_C = m_0c^2/\hbar$. This Compton frequency is considered the characteristic oscillation frequency of a particle at rest, supported by theoretical phenomena like Zitterbewegung. The apparent "discrepancies" in the relationship between mass and frequency (e.g., $m=\omega$, $m=\omega_C$, or $m \propto \omega_C$) arise from the choice of unit systems and the specific context of the discussion, rather than representing contradictions in the underlying physics. When working with **standard units** (such as kilograms, meters, and seconds), the fundamental constants $\hbar$ and $c$ must be explicitly included to ensure dimensional consistency. In this system, the "Bridge Equation" $mc^2 = \hbar\omega$ (or $m_0c^2 = \hbar\omega_C$ for rest mass) demonstrates a direct proportionality between mass and frequency. Rearranging this equation, we get $m = (\hbar/c^2)\omega$, which clearly shows that **mass is proportional to frequency ($m \propto \omega$)**, with $\hbar/c^2$ serving as the constant of proportionality. When specifically referring to the intrinsic frequency of a particle at rest, this becomes $m_0 \propto \omega_C$. However, to reveal the most fundamental and elegant relationship, theoretical physicists often employ **natural units**, where fundamental constants like the reduced Planck constant ($\hbar$) and the speed of light ($c$) are set to unity (1). This mathematical convenience simplifies equations and highlights underlying symmetries, without altering the physics itself. In this system: * The quantum mechanical energy relation $E = \hbar\omega$ simplifies to $E = \omega$. * The relativistic energy-mass equivalence $E = mc^2$ simplifies to $E = m$. * By equating these simplified expressions for energy, we arrive at the profound identity **$\omega = m$**. When this identity $\omega = m$ is stated, it implicitly refers to the **Compton angular frequency ($\omega_C$)** of a particle at rest and its **rest mass ($m_0$)**, within the context of natural units. The subscript 'c' is often omitted for brevity when the context clearly indicates that the intrinsic frequency of a massive particle is being discussed. Therefore, the statements $m = \omega_C$ or $m = \omega$ are specific instances of this proportionality when natural units are employed, making the proportionality constant equal to 1. In essence, the fundamental constants $\hbar$ and $c$ act as universal conversion factors that translate between our arbitrarily defined human units and the natural units where the intrinsic identity between a particle's mass and its characteristic oscillation frequency becomes numerically identical. The "reappropriation" of variables is not a change in the physics, but rather a deliberate simplification of the mathematical framework to unveil a deeper, simpler ontological connection between mass and frequency, suggesting that mass is an intrinsic frequency of a stable relational pattern within the Universal Relational Graph.