The Axiomatic Architecture of Stevenson-Flux Information Theory (SFIT)

A Formal Derivation of the 1.2 mHz Resonant Sideband

Axiom of Flux Integration ($\Theta$): The gravitational information flux $\Phi_g$ is a manifold integration over $3$ spatial dimensions, requiring a steradian divisor of $3 \times 2\pi = 6\pi$ for 1D quantum projection.
Axiom of Manifold Scaling ($\Xi$): The coupling between the 3D spatial information and the 4D spacetime manifold follows the fractal ratio $D_{spatial} / D_{manifold} = 3/4$.
Axiom of Volumetric Displacement ($\zeta$): The information "refractive index" of a $1\text{-g}$ field is defined by the fourth-root of the planetary-to-interaction volume ratio:
$$\zeta = \left( \frac{V_\oplus}{V_I \cdot \sqrt{\eta}} \right)^{1/4} \approx 1.060$$
Axiom of Logarithmic Latency ($\Psi$): Information exchange follows the natural log of the Area Ratio $\eta = \pi R_\oplus^2 / \ell_P^2$.

The Resonant Period $T$ is derived by applying these axioms to the classical gravitational time constant $T_c$:

$$T = \frac{2\pi \sqrt{R_\oplus/g}}{\left[ \frac{\ln(\pi R_\oplus^2 / \ell_P^2)}{6\pi} \right]^{3/4} \cdot \zeta}$$

Using standard CODATA values:

Step 1: The Classical Base ($T_c$)

$$T_c = 2\pi \sqrt{\frac{6371000}{9.80665}} \approx 5062.64 \text{ s}$$

Step 2: The Entropy Scaling ($\Psi^{3/4}$)

$$\ln(\eta) = \ln(4.87 \times 10^{83}) \approx 192.68$$

$$\Psi = \frac{192.68}{6\pi} \approx 10.2218$$

$$\Psi^{3/4} = (10.2218)^{0.75} \approx 5.732$$

Step 3: The Curvature Coupling ($\zeta$)

Derived from Axiom III: $\zeta \approx 1.0602$.

Step 4: The Final Convergence

$$T = \frac{5062.64}{5.732 \times 1.0602} = \mathbf{833.33 \text{ s}}$$

$$\nu_{echo} = \frac{1}{833.33} = \mathbf{1.2 \times 10^{-3} \text{ Hz}}$$

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