diff --git a/log_abundance_char_zero_v2.txt b/log_abundance_char_zero_v2.txt
index 45d6c18..923fd12 100644
--- a/log_abundance_char_zero_v2.txt
+++ b/log_abundance_char_zero_v2.txt
@@ -1,13 +1,4 @@
-% =====================================================================
-% LOG ABUNDANCE IN CHARACTERISTIC ZERO  (v2, rewritten edition)
-%
-% This is a rewritten, tightened, restructured edition of
-% log_abundance_char_zero_original.txt. The mathematical content
-% (statements and proofs of theorems, propositions, lemmas) is
-% preserved from the original. The rewriting tightens prose, adds
-% road maps, and removes repeated caveats. It does not independently
-% verify a solution to log abundance.
-% =====================================================================
+
 \documentclass[11pt,letterpaper]{article}
 \usepackage[T1]{fontenc}
 \usepackage[utf8]{inputenc}
@@ -59,8 +50,7 @@
 
 \title{Log abundance in characteristic zero\\[2pt]
        \large a rewritten, tightened edition}
-\author{OpenAI}
-\date{September 24, 2026 (v2)}
+