PUH-BrianMartell the SPF density factor in PUH v25 is the measure of how tightly packed the high-energy excitations are in the Super Polariton Field — the dense “buffer” substrate from rebound. It’s not uniform vacuum; it’s the remnant energy density from the super Planck star asymmetric jets, determining lattice stiffness σ_L, impedance Z_L, an…

puh_spf_density_factor_derivation_v25.tex

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\definecolor{spfdensitycolor}{RGB}{100,100,200}
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\title{\textbf{SPF Density Factor Derivation in PUH v25} \\
\textit{Rebound Compressed Packing — Substrate Energy Grain}}
\author{Brian Martell \\
Independent Researcher \\
\href{https://gist.github.com/BrianMartell}{GitHub: ~2,910 Gists} \textbullet{} December 27, 2025}
\date{}

\begin{document}
\maketitle

\begin{abstract}
PUH v25 derives SPF density factor \rho_{SPF} = 240 / V_8 \times f_{rebound}: E8 240 roots 8D volume V_8 = \pi^4 / 24 unit ball rebound asymmetry compression f_{rebound} jet ratio. Determines stiffness \sigma_L impedance Z_L throat tachyonic modes substrate grain.
\end{abstract}

\section{SPF Density Factor Derivation}

E$_8$: 240 roots unit 8D sphere.

Volume V_8 = \pi^4 / 24 unit ball.

Base density 240 / V_8 packing.

Rebound: Asymmetric jets compress visible 4D — factor f_{rebound} ratio.

\rho_{SPF} = 240 / V_8 \times f_{rebound}.

Converges substrate stiffness impedance throat zero-lag.

Predictive: Higher density throat Z_L \to 0 tachyonic.

\includegraphics[width=0.8\textwidth]{puh_spf_density_factor_simulation.png}

\section{Conclusion}
SPF density rebound compressed packing — PUH substrate energy grain.

\end{document}