BrianMartell · December 5, 2025 18:29
diff --git a/PUH_v6_Rebound_Trigger.tex b/PUH_v6_Rebound_Trigger.tex
 \documentclass[11pt]{article}
 \usepackage{amsmath,amssymb}
 \usepackage{hyperref}
 \usepackage[a4paper,margin=1in]{geometry}

 \title{Photonic Universe Hypothesis (PUH v6):\\Big-Bang Trigger from Geometric Flaw}
 \author{Brian Martell}
 \date{4 December 2025}

 \begin{document}

 \maketitle

 \begin{abstract}
 PUH v6 rebound is triggered when geometric asymmetry $\delta \approx \ell_P / L_{\rm core}$ creates a local pressure imbalance $\Delta P \approx \delta \rho c^2$. The imbalance ruptures the tachyon shell at its weakest point, releasing stored energy as polar jets. Initial expansion rate $H_{\rm rebound} \propto c \sqrt{\delta}/\sqrt{\ell_P}$. The Big Bang is a direct consequence of Planck-scale geometric instability. No additional fields or parameters required.
 \end{abstract}

 \section{Rebound Trigger}

 Shell equilibrium: $P_{\gamma} = P_{\tau}$.

 Geometric flaw induces local containment weakness:
 $$
 P_{\tau,\rm min} = P_{\tau}(1-\delta).
 $$

 Trigger condition:
 $$
 P_{\gamma} > P_{\tau,\rm min} \quad \Rightarrow \quad \Delta P \approx \delta \rho c^2.
 $$

 Initial Hubble parameter:
 $$
 H_{\rm rebound} \propto \sqrt{\frac{\Delta P}{\rho}} \propto c \sqrt{\delta}/\sqrt{\ell_P}.
 $$

 \section{Conclusion}

 Big Bang expansion rate is set by Planck-scale geometric flaw $\delta$.

 \end{document}
	\documentclass[11pt]{article}
	\usepackage{amsmath,amssymb}
	\usepackage{hyperref}
	\usepackage[a4paper,margin=1in]{geometry}

	\title{Photonic Universe Hypothesis (PUH v6):\\Big-Bang Trigger from Geometric Flaw}
	\author{Brian Martell}
	\date{4 December 2025}

	\begin{document}

	\maketitle

	\begin{abstract}
	PUH v6 rebound is triggered when geometric asymmetry $\delta \approx \ell_P / L_{\rm core}$ creates a local pressure imbalance $\Delta P \approx \delta \rho c^2$. The imbalance ruptures the tachyon shell at its weakest point, releasing stored energy as polar jets. Initial expansion rate $H_{\rm rebound} \propto c \sqrt{\delta}/\sqrt{\ell_P}$. The Big Bang is a direct consequence of Planck-scale geometric instability. No additional fields or parameters required.
	\end{abstract}

	\section{Rebound Trigger}

	Shell equilibrium: $P_{\gamma} = P_{\tau}$.

	Geometric flaw induces local containment weakness:
	$$
	P_{\tau,\rm min} = P_{\tau}(1-\delta).
	$$

	Trigger condition:
	$$
	P_{\gamma} > P_{\tau,\rm min} \quad \Rightarrow \quad \Delta P \approx \delta \rho c^2.
	$$

	Initial Hubble parameter:
	$$
	H_{\rm rebound} \propto \sqrt{\frac{\Delta P}{\rho}} \propto c \sqrt{\delta}/\sqrt{\ell_P}.
	$$

	\section{Conclusion}

	Big Bang expansion rate is set by Planck-scale geometric flaw $\delta$.

	\end{document}
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