diff --git a/nearby_lagrangian_counterexample_v2.txt b/nearby_lagrangian_counterexample_v2.txt
index d48bc2e..2f84327 100644
--- a/nearby_lagrangian_counterexample_v2.txt
+++ b/nearby_lagrangian_counterexample_v2.txt
@@ -26,12 +26,7 @@ What this document is.
     smooth manifold. The failure is about HOW L is knotted inside T*Q. That
     kind of failure is exactly what symplectic topology is for.
 
-How to read this document.
-    Section 1 sets up the basic objects and the two key tools (generating
-    families and stable tube data). Section 2 states the main theorem.
-    Sections 3-7 prove the ingredients in the order you need them. Section 8
-    assembles everything into the final proof. You can read 1, 2, then 8 for
-    the shape of the argument, then come back for the details.
+
 
     We use only plain ASCII. R^n is real n-space. S^k is the unit sphere in
     R^(k+1). <v,w> is the dot product. |x| is the length of a vector. A
@@ -42,15 +37,7 @@ How to read this document.
     intuition paragraphs and the boxed ideas; the technical lemmas can be
     taken as read on a first pass. Nothing is hidden: every step is proved.
 
-TABLE OF CONTENTS
-    1.  Background: cotangent bundles, Lagrangians, isotopy
-    2.  The main theorem
-    3.  Stable tube data and a nonzero class
-    4.  A family with one critical point has zero tube class
-    5.  The zero-level cobordism argument
-    6.  Building the exact embedded Lagrangian
-    7.  Hamiltonian transport: the final contradiction
-    8.  Putting it together: proof of the main theorem
+
 
 ==============================================================================
 SECTION 1. BACKGROUND: COTANGENT BUNDLES, LAGRANGIANS, ISOTOPY