diff --git a/nearby_lagrangian_counterexample_v2.txt b/nearby_lagrangian_counterexample_v2.txt
index 07ad7bd..eaa8306 100644
--- a/nearby_lagrangian_counterexample_v2.txt
+++ b/nearby_lagrangian_counterexample_v2.txt
@@ -3,41 +3,6 @@ A COUNTEREXAMPLE TO THE NEARBY LAGRANGIAN CONJECTURE
 A complete, self-contained proof
 ==============================================================================
 
-What this document is.
-    In 1980s symplectic geometry, Rene Arnold asked a deceptively simple
-    question. Take a smooth closed manifold Q (closed = compact, no
-    boundary). Look at its cotangent bundle T*Q, which is the phase space
-    of a particle moving on Q. Inside it sits the zero section (the set of
-    points with zero momentum), and that zero section is a "Lagrangian"
-    submanifold. Arnold asked: if L is any closed Lagrangian submanifold of
-    T*Q that is "exact" (a technical condition meaning L has no symplectic
-    area), must L be Hamiltonian isotopic to the zero section? In plain
-    words: can every such L be slid continuously, by a physically allowed
-    motion, onto the zero section?
-
-    This is the NEARBY LAGRANGIAN CONJECTURE. For decades every known
-    example worked. This document gives one that fails. The manifold we use
-    is Q = S^9 x S^(N-1) for a sufficiently large even integer N. We build a
-    closed exact smoothly embedded Lagrangian L inside T*Q that is
-    DIFFEOMORPHIC to Q (so it looks just like the base) but that no
-    compactly supported Hamiltonian isotopy can carry onto the zero section.
-
-    The failure is not about the shape of L. Abstractly L and Q are the same
-    smooth manifold. The failure is about HOW L is knotted inside T*Q. That
-    kind of failure is exactly what symplectic topology is for.
-
-
-
-    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
-    "smooth" map is infinitely differentiable. "Closed" always means compact
-    without boundary.
-
-    
-
-
-
-==============================================================================
 SECTION 1. BACKGROUND: COTANGENT BUNDLES, LAGRANGIANS, ISOTOPY
 ==============================================================================