diff --git a/symplectic_ball_packings_v2.txt b/symplectic_ball_packings_v2.txt
index d74dd1c..eee0378 100644
--- a/symplectic_ball_packings_v2.txt
+++ b/symplectic_ball_packings_v2.txt
@@ -1,30 +1,10 @@
 ================================================================
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         SYMPLECTIC BALL PACKINGS IN HIGHER DIMENSIONS
-              a complete proof, for a curious beginner
+              a complete proof
 ================================================================
 ================================================================
 
-NOTE TO THE READER
-----------------------------------------------------------------
-This file is the full proof of one theorem, written out step by
-step. It is meant to be read by a strong high-school student who
-knows calculus and complex numbers but has never seen symplectic
-geometry. Everything we use is either proved here or is a named
-standard fact (Bertini's theorem, the implicit function theorem,
-Moser's trick, the classification of line bundles on a surface).
-Nothing is waved away as "obvious". When a step is genuinely deep
-we say so and say exactly what the deep fact is.
-
-We use a few ASCII conventions:
-    A ^ B        the wedge (exterior) product of forms;
-    sum_j        means sum over j = 1,...,m (or 1,...,n), as named;
-    (x)_+        means max(x, 0);
-    <=, >=       ordinary inequalities;
-    x.y          the dot product b_1 p_1 + ... + b_m p_m.
-No other notation is special. Figures are described in words.
-
-
 1. THE ANSWER
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 Fix an integer n >= 3 (the "complex dimension"; the real dimension