Gravitons in the Hydrogravitational Identity Equation (HIE)

In the relational field framework, curvature and flow are two expressions of the same dynamic. The Hydrogravitational Identity Equation is written as:

At equilibrium ($B=\; 1$), flow and curvature are identical. Small deviations are represented as:

Substituting into the field equation and linearizing gives:

Here, the term $\mathrm{\delta B}$ represents a quantized perturbation of the relational scalar field. Each quantized mode of $\mathrm{\delta B}$ corresponds to a graviton:

This quantized field obeys a wave equation derived from the linearized HIE:

meaning the graviton propagates as a massless spin-2 excitation of the relational curvature. In the Hydrogravitational picture:

• Background: $B=\; 1$ → unified flow/curvature equilibrium.
• Excitation: $\mathrm{\delta B}\ne \; 0$ → quantum of curvature (graviton).
• Energy: $E=\; (\hslash \; c³\; /\; B)\; |k|$ → geometric quantization of flow.

Thus, a graviton is a quantized oscillation of relational identity—a discrete pulse where curvature momentarily distinguishes itself from perfect unity. - Prepared by Son of Benjamin