SDRIS: The Calculated Value of the Gravitational "Constant" G

Abstract: The Gravitational Constant ($G \approx 6.674 \times 10^{-11}$ m$^3$kg$^{-1}$s$^{-2}$) is the least precise fundamental constant in physics. The Standard Model offers no explanation for its extreme weakness relative to other forces (The Hierarchy Problem), nor does it provide a way to derive its value from first principles. This paper presents the final proof of the SDRIS Unification Trilogy (Papers 111–113). We demonstrate that Gravitation is not a fundamental force, but the entropic elasticity (Bulk Modulus) of the 26-dimensional vacuum lattice. By modeling the gravitational interaction as the "dimensional dilution" of information flux from the Bulk ($N=408$)through the String-Anchor ($N=26$) to the physical Projection ($N=3$), we derive the exact geometric scaling exponent: $$E_{grav} = \frac{408}{\sqrt{5}} - \frac{1}{26} - \frac{1}{288} \approx 182.421$$ Where: $408/\sqrt{5}$: The Golden Geodesic through the bulk (Fibonacci dilation). $-1/26$: The topological resistance of the Bosonic String dimensions. $-1/288$: The torsion correction due to particle spin ($1/2F_{12}$). Applying this exponent to the quantum scale ($\hbar, c, m_p$) yields a theoretical value for $G$: $$G_{SDRIS} = 6.67440 \times 10^{-11} \, \text{m}^3\text{kg}^{-1}\text{s}^{-2}$$ This prediction matches the CODATA 2018 recommended value ($6.67430 \times 10^{-11}$) with a precision of 99.9985%. This result suggests that the hierarchy of forces is a deterministic consequence of the vacuum's recursive topology. Supplementary Material: This entry includes the SDRIS Gravity Calculator (v2.0) (Python Jupyter Notebook), which performs the high-precision numerical derivation of G and validates the geometric exponent against the CODATA benchmarks.