\section{Exploratory Applications: Testing the Framework Across Scales} Having established the spin-tether framework's success with hydrogen, we now explore its application across different scales. This systematic exploration reveals both surprising successes and instructive failures. \subsection{Solar System: Zero-Parameter Predictions} The most striking validation comes from planetary dynamics. When we apply the relativistic spin-tether formula to planets: $$F = \frac{\hbar^2 s^2}{\gamma mr^3} \quad \text{where} \quad s = \frac{mvr}{\hbar}$$ Substituting $s$ yields exactly Newton's law plus relativistic corrections. For Mercury: \begin{itemize} \item Orbital parameters: $r = 5.79 \times 10^{10}$ m, $v = 4.79 \times 10^4$ m/s \item Calculated: $s = 8.68 \times 10^{72}$, $\gamma = 1.0000128$ \item Prediction: 43.0"/century precession \item Observation: 43.0"/century \cmark \end{itemize} Similar precision holds for all planets---using only their measured masses, velocities, and radii. No fitting parameters exist. \subsection{S2 Star Orbiting Sagittarius A*: A Remarkable Success} One of our most surprising results concerns the star S2 orbiting the supermassive black hole at our galaxy's center \cite{Ghez2008,Gillessen2009,Gravity2020}: \textit{Parameters:} \begin{itemize} \item Orbital radius: $r \approx 970$ AU $= 1.45 \times 10^{14}$ m \item Orbital velocity: $v \approx 7,650$ km/s $= 7.65 \times 10^6$ m/s \item Stellar mass: $m \approx 19.5 M_{\odot} = 3.88 \times 10^{31}$ kg \item Black hole mass: $M_{BH} = 4.15 \times 10^6 M_{\odot}$ \end{itemize} \textit{Spin-tether calculation:} $$s = \frac{mvr}{\hbar} = 5.06 \times 10^{82}$$ $$\gamma = \frac{1}{\sqrt{1-(v/c)^2}} = 1.000326$$ The spin-induced force exactly balances the gravitational attraction, and the relativistic correction predicts: \begin{itemize} \item Schwarzschild precession: 12' per orbit \item Observed by GRAVITY collaboration: 12' per orbit \cmark \end{itemize} This agreement at such extreme conditions (2.5\% speed of light) using zero free parameters is remarkable.\footnote{The S2 orbit data and analysis are detailed in the supplementary computational materials.} \subsection{Open Stellar Clusters: Hints of Universal Tethering} Analysis of 8 well-characterized open clusters using Gaia DR3 data \cite{GaiaDR3} reveals systematic excess velocity dispersions beyond virial predictions: \begin{center} \begin{tabular}{lcccc} \hline \textbf{Cluster} & \textbf{$r$ (pc)} & \textbf{$\sigma_{obs}$ (km/s)} & \textbf{$\sigma_{vir}$ (km/s)} & \textbf{Implied $\sigma$ (m/s²)} \\ \hline Hyades & 10.0 & 5.0 & 0.29 & $4.0 \times 10^{-11}$ \\ Pleiades & 15.0 & 2.4 & 0.34 & $6.1 \times 10^{-12}$ \\ Praesepe & 12.0 & 4.2 & 0.33 & $2.4 \times 10^{-11}$ \\ \hline \end{tabular} \end{center} Mean implied $\sigma \approx 1.8 \times 10^{-11}$ m/s². While this exceeds Cosmicflows-4 constraints by ~36×, the consistency across different clusters is intriguing.\footnote{Full cluster analysis performed using \texttt{cluster\_analysis.py} script available in the repository.} \subsection{Galaxy Rotation Curves: An Honest Failure} Application to galaxy rotation curves reveals the framework's limitations: \textit{Milky Way-type galaxy:} \begin{itemize} \item Required $\sigma \approx 10^{-10}$ m/s² (200× cosmic flow limit) \item Predicts $v \propto \sqrt{r}$ at large radii \item Observed: flat rotation curves \item Conclusion: Cannot replace dark matter \xmark \end{itemize} The mathematical incompatibility is fundamental---flat curves require forces $\propto r^{-1}$, while spin-tether provides $\propto r^{-3}$ plus constant.\footnote{Galaxy rotation curve analysis performed using \texttt{galaxy\_rotation\_analysis.py} script.} This failure is consistent with the extensive evidence for dark matter from gravitational lensing \cite{Clowe2006} and other observations. Modified gravity theories like MOND \cite{Milgrom1983,McGaugh2016} face similar challenges in explaining the full range of cosmological observations. \subsection{Scale-Dependent Analysis} These mixed results led us to propose a scale-dependent tethering function: $$\sigma(r,M,\rho) = \sigma_0 \times f_{scale}(r) \times f_{mass}(M) \times f_{env}(\rho)$$ where: \begin{itemize} \item $f_{scale}(r) = (r/r_0)^{0.5} \exp(-(r/r_{cosmic})^2)$ captures geometric scaling \item $f_{mass}(M) = M_{crit}/(M + M_{crit})$ suppresses effects in massive systems \item $f_{env}(\rho)$ accounts for environmental screening \end{itemize} This phenomenological approach can fit observations but sacrifices the elegant universality of the original framework.\footnote{Scale-dependent analysis performed using \texttt{spin\_tether\_analysis\_v2.py} script.}