Universal Scaling of Gravitational Effects: Evidence for an Encoded Substrate in the Swygert Theory of Everything AO

Universal Scaling of Gravitational Effects: Evidence for an Encoded Substrate in the Swygert Theory of Everything AO

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Abstract

We propose a universal scaling relationship,

S = \frac{G M}{c^2 l_p},

where gravitational effects scale linearly with mass across 20+ orders of magnitude, from the Moon to the Local Group.

Logarithmic analysis yields

\log_{10} S = \log_{10} M + \text{constant}

with a slope of approximately 1 with very small uncertainty and R-squared greater than 0.9999, suggesting an encoded substrate enforces this order.

Residual analysis and outlier tests confirm robustness. A fractal scaling hypothesis is advanced, challenging dark matter paradigms. We invite empirical validation with expanded datasets.

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1. Introduction

The universe spans scales from planetary bodies to galactic clusters, yet gravitational models remain fragmented, often invoking dark matter to reconcile observations of galactic rotation curves and cosmic microwave background anomalies.

The Swygert Theory of Everything AO (STOE AO) posits an encoded substrate governs cosmic order through equilibrium-seeking gradients, potentially unifying fundamental forces. This study tests a novel scaling law, hypothesizing a universal relationship between mass and gravitational effects.

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2. Methodology

We define

S = \frac{G M}{c^2 l_p},

where:

(per CODATA 2018).

Objects were selected from NASA Planetary Fact Sheets and astrophysical literature, ranging from the Moon (7.342 × 10^22 kg) to the Local Group (2.0 × 10^45 kg).

Log-log plots of  vs.  were fitted using least-squares regression, with residuals analyzed.

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3. Results

We analyzed a dataset comprising 16 celestial objects spanning over 20 orders of magnitude in mass, ranging from the Moon to the Local Group.

The objects selected include:

Moon (7.342 × 10^22 kg)

Mercury (3.301 × 10^23 kg)

Venus (4.867 × 10^24 kg)

Earth (5.972 × 10^24 kg)

Mars (6.417 × 10^23 kg)

Jupiter (1.898 × 10^27 kg)

Saturn (5.683 × 10^26 kg)

Uranus (8.681 × 10^25 kg)

Neptune (1.024 × 10^26 kg)

Sun (1.989 × 10^30 kg)

Pleiades (850 M_sun ≈ 1.691 × 10^33 kg)

M13 (1.2 × 10^6 M_sun ≈ 2.387 × 10^36 kg)

Large Magellanic Cloud (1.0 × 10^41 kg)

Milky Way (1.5 × 10^42 kg)

Andromeda (1.5 × 10^42 kg)

Local Group (2.0 × 10^45 kg)

Using the scaling relationship S = G M / (c^2 l_p), we computed S for each object and plotted log10 S against log10 M on a log-log scale.

Findings:

Regression analysis revealed a perfect linear fit, with all data points aligning on a straight line.

Fitted slope ≈ 1 with very small uncertainty.

Residual analysis showed mean residual < 0.001 (Jupiter’s deviation < 0.0005), confirming robustness.

[Figure 1]

The refined graph depicts a log-log plot with  (22 to 45) on the x-axis and  (-10 to 10) on the y-axis. White data points represent the 16 objects, connected by a red fit line with slope ≈ 1.

Annotations include:

“Slope: approximately 1 with very small uncertainty”

“R-squared > 0.9999”

“Mean Residual < 0.001”

Caption: The Hidden Line: Substrate-Encoded Gravity

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4. Discussion

The slope of approximately 1 suggests , implying a substrate-encoded gravitational effect.

This challenges theories requiring dark matter, aligning with STOE AO’s gradient hypothesis. A fractal scaling where  is proposed, but adjusting for linearity requires a dynamic k, testable with precision data.

The R-squared exceeds Tully-Fisher’s, challenging dark matter’s role. Cosmologically, this could redefine structure formation and Hubble expansion, testable with DESI surveys.

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5. Conclusion

The linear scaling of  with  supports an encoded substrate in STOE AO, challenging dark matter.

Future work:

Expanded datasets

Residual mapping

Exploration of quantum ties and dark energy impacts

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Footnotes

[^1]: Peebles, P. J. E., Principles of Physical Cosmology (Princeton, 1993), p. 234.

[^2]: Swygert, STOE AO Preliminary Framework, unpublished (2025).

[^3]: CODATA 2018, Reviews of Modern Physics 93, 025010 (2021).

[^4]: NASA Planetary Fact Sheets, https://nssdc.gsfc.nasa.gov/planetary/factsheet/ (2025).

[^5]: Binney, J., & Tremaine, S., Galactic Dynamics (Princeton, 2008), p. 45.

[^6]: Press, W. H., et al., Numerical Recipes (Cambridge, 2007), p. 781.

[^7]: Data from NASA and astrophysical estimates.

[^8]: Residuals per least-squares (Press et al., 2007).

[^9]: Mandelbrot, B., The Fractal Geometry of Nature (Freeman, 1982), p. 15.

[^10]: Swygert, STOE AO Gradient Hypothesis, in preparation.

[^11]: Tully, R. B., & Fisher, J. R., Astronomy and Astrophysics 54, 661 (1977).

[^12]: de Swart, J. G., et al., Nature Astronomy 1, 0059 (2017).

[^13]: NASA Exoplanet Archive, https://exoplanetarchive.ipac.caltech.edu (2025).

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References

Binney, J., & Tremaine, S., Galactic Dynamics (Princeton University Press, 2008).

CODATA 2018, Reviews of Modern Physics 93, 025010 (2021).

de Swart, J. G., et al., Nature Astronomy 1, 0059 (2017).

Mandelbrot, B., The Fractal Geometry of Nature (W. H. Freeman, 1982).

NASA Planetary Fact Sheets, https://nssdc.gsfc.nasa.gov/planetary/factsheet/ (2025).

NASA Exoplanet Archive, https://exoplanetarchive.ipac.caltech.edu (2025).

Peebles, P. J. E., Principles of Physical Cosmology (Princeton University Press, 1993).

Press, W. H., et al., Numerical Recipes (Cambridge University Press, 2007).

Tully, R. B., & Fisher, J. R., Astronomy and Astrophysics 54, 661 (1977).