Level 10 Math Upgrade for JMP Draft

papers/project_paper_1_relativity/master_key/paper_1_master_key.bbl

@@ -74,11 +74,6 @@ Raphael Bousso.
 \newblock A covariant entropy conjecture.
 \newblock {\em Journal of High Energy Physics}, 1999(07):004, 1999.
 
-\bibitem{Hayden2007}
-Patrick Hayden and John Preskill.
-\newblock Black holes as mirrors: quantum information in random subsystems.
-\newblock {\em Journal of High Energy Physics}, 2007(09):120, 2007.
-
 \bibitem{Sekino2008}
 Yasuhiro Sekino and Leonard Susskind.
 \newblock Fast scramblers.
@@ -90,28 +85,10 @@ Nima Lashkari, Douglas Stanford, Matthew Hastings, Tobias Osborne, and Patrick
 \newblock Towards the fast scrambling conjecture.
 \newblock {\em Journal of High Energy Physics}, 2013(4):22, 2013.
 
-\bibitem{Hoory2006}
-Shlomo Hoory, Nathan Linial, and Avi Wigderson.
-\newblock Expander graphs and their applications.
-\newblock {\em Bulletin of the American Mathematical Society}, 43(4):439--561,
-  2006.
-
-\bibitem{Chung1997}
-Fan R~K Chung.
-\newblock {\em Spectral Graph Theory}, volume~92 of {\em CBMS Regional
-  Conference Series in Mathematics}.
-\newblock American Mathematical Society, 1997.
-
-\bibitem{Cheeger1970}
-Jeff Cheeger.
-\newblock A lower bound for the smallest eigenvalue of the laplacian.
-\newblock {\em Problems in Analysis}, pages 195--199, 1970.
-
-\bibitem{Alon1985}
-Noga Alon and Vitali~D Milman.
-\newblock $\lambda_1$, isoperimetric inequalities for graphs, and
-  superconcentrators.
-\newblock {\em Journal of Combinatorial Theory, Series B}, 38(1):73--88, 1985.
+\bibitem{Hayden2007}
+Patrick Hayden and John Preskill.
+\newblock Black holes as mirrors: quantum information in random subsystems.
+\newblock {\em Journal of High Energy Physics}, 2007(09):120, 2007.
 
 \bibitem{Winkler1985}
 Peter~M Winkler.
@@ -123,33 +100,6 @@ B{\'e}la Bollob{\'a}s.
 \newblock {\em Random Graphs}.
 \newblock Cambridge University Press, 2nd edition, 2001.
 
-\bibitem{Mohar1991}
-Bojan Mohar.
-\newblock The laplacian spectrum of graphs.
-\newblock {\em Graph Theory, Combinatorics, and Applications}, 2:871--898,
-  1991.
-
-\bibitem{Polya1921}
-George P{\'o}lya.
-\newblock {\"U}ber eine aufgabe der wahrscheinlichkeitsrechnung betreffend die
-  irrfahrt im stra{\ss}ennetz.
-\newblock {\em Mathematische Annalen}, 84:149--160, 1921.
-
-\bibitem{Lawler2010}
-Gregory~F Lawler and Vlada Limic.
-\newblock {\em Random Walk: A Modern Introduction}.
-\newblock Cambridge University Press, 2010.
-
-\bibitem{Barlow2004}
-Martin~T Barlow.
-\newblock Random walks and heat kernels on graphs.
-\newblock {\em London Mathematical Society Lecture Note Series}, 438, 2017.
-
-\bibitem{Coulhon2003}
-Thierry Coulhon and Alexander Grigor'yan.
-\newblock Heat kernel estimates and the green function on infinite graphs.
-\newblock {\em Annals of Probability}, pages 763--788, 2003.
-
 \bibitem{Bousso2006}
 Raphael Bousso.
 \newblock Holographic probabilities in eternal inflation.
@@ -185,6 +135,18 @@ Daniel~A Roberts, Douglas Stanford, and Leonard Susskind.
 \newblock Localized shocks.
 \newblock {\em Journal of High Energy Physics}, 2015(3):51, 2015.
 
+\bibitem{Hoory2006}
+Shlomo Hoory, Nathan Linial, and Avi Wigderson.
+\newblock Expander graphs and their applications.
+\newblock {\em Bulletin of the American Mathematical Society}, 43(4):439--561,
+  2006.
+
+\bibitem{Alon1985}
+Noga Alon and Vitali~D Milman.
+\newblock $\lambda_1$, isoperimetric inequalities for graphs, and
+  superconcentrators.
+\newblock {\em Journal of Combinatorial Theory, Series B}, 38(1):73--88, 1985.
+
 \bibitem{tHooft1993}
 Gerard 't~Hooft.
 \newblock Dimensional reduction in quantum gravity.

papers/project_paper_1_relativity/master_key/paper_1_master_key.blg

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+            697 strings with 7908 characters,
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papers/project_paper_1_relativity/master_key/paper_1_master_key.tex

@@ -295,7 +295,7 @@ is a pair $\Obs = (V_{\Obs}, \gamma)$ where:
 The imposition of an internal temporal Fieldprint of
 macroscopic length $T_{\mathrm{coh}}$ enforces Sovereign continuity, analogous
 to demanding a coherent proper-time worldline.
-Rather than imposing an ad hoc integer parameter, the persistence scale $T_{\mathrm{coh}} \gg 1$ is dynamically selected by the causal set itself. Specifically, $T_{\mathrm{coh}}$ is defined as the decoherence length dictated by the fluctuations of the Benincasa-Dowker action along the worldline, $\Delta S_{\mathrm{BD}}(\gamma) \sim \pi$. This ensures that the observer persists through sufficient Coherence intervals to process local Lattice information before natural quantum action fluctuations induce Agentic Drift.
+Rather than imposing an ad hoc integer parameter, the persistence scale $T_{\mathrm{coh}} \gg 1$ is dynamically selected by the causal set itself. For the purposes of this foundational framework, we explicitly postulate that macroscopic coherence requires the fluctuations of the Benincasa-Dowker action along the worldline to satisfy $\Delta S_{\mathrm{BD}}(\gamma) \sim \pi$, which dynamically limits the decoherence length $T_{\mathrm{coh}}$. The rigorous saddle-point derivation of this phase boundary is deferred to a subsequent paper. This ensures that the observer persists through sufficient Coherence intervals to process local Lattice information before natural quantum action fluctuations induce Agentic Drift.
 
 \begin{definition}[Global causal connectedness]\label{def:connected}
 A causal set $\Cset = (V, \preccurlyeq)$ is
@@ -580,9 +580,9 @@ Instead of falling into the classical-quantum bifurcation of evaluating classica
 
 \begin{proposition}[Dimensional selection via Quantum Recurrence]
 \label{prop:dimension}
-Let $\Cset$ be a causal set whose causal structure is quasi-isometric
-to a $d$-dimensional Lorentzian manifold with $d \geq 3$.
-Then for any macroscopic $T_{\mathrm{coh}} \gg \ln N$, the quantum information dynamics
+Let $\Cset$ be a causal set. Assuming its causal structure is quasi-isometric
+to a $d$-dimensional Lorentzian manifold with $d \geq 3$,
+then for any macroscopic $T_{\mathrm{coh}} \gg \ln N$, the quantum information dynamics
 on $\Cset$ fail to satisfy the memory-persistence condition.
 \end{proposition}