diff --git a/abundance_terminal_threefolds_charp_v2.txt b/abundance_terminal_threefolds_charp_v2.txt
index af1a31f..0d9f2bb 100644
--- a/abundance_terminal_threefolds_charp_v2.txt
+++ b/abundance_terminal_threefolds_charp_v2.txt
@@ -62,8 +62,7 @@
 
 \title{Abundance in numerical dimension one\\for terminal threefolds in positive characteristic\\[2mm]
 \large A reader-friendly edition}
-\author{OpenAI}
-\date{October 28, 2026}
+
 
 \begin{document}
 \maketitle
@@ -72,7 +71,7 @@
 Let $X$ be a projective $\Q$-factorial terminal threefold over an algebraically closed field of characteristic $p>3$. If the canonical divisor $K_X$ is nef and has numerical dimension one, then some positive multiple of $K_X$ has at least two independent global sections. Hence $K_X$ is semiample and has Kodaira dimension one. This edition explains the theorem, the strategy, and every main step in plain language, while keeping the mathematical details needed for a complete proof.
 \end{abstract}
 
-\tableofcontents
+
 
 \section*{How to read this paper}
 \addcontentsline{toc}{section}{How to read this paper}