diff --git a/three_manifold_no_conjugate_v2.txt b/three_manifold_no_conjugate_v2.txt
index 3dd383c..6ec7d4f 100644
--- a/three_manifold_no_conjugate_v2.txt
+++ b/three_manifold_no_conjugate_v2.txt
@@ -2,7 +2,6 @@ A THREE-MANIFOLD WITHOUT CONJUGATE POINTS
 AND WITHOUT A NONPOSITIVELY CURVED METRIC
 
 A complete and self-contained proof.
-Written so that a determined high-school student can follow it.
 
 NOTATION CONVENTION
   R^n      : n-dimensional Euclidean space
@@ -20,59 +19,6 @@ NOTATION CONVENTION
   Inline math uses $...$ like LaTeX.  The file is plain text.
 
 
-================================================================
-PART 0.  WHAT THIS PAPER PROVES
-================================================================
-
-Punchline, then idea, then proof.
-
-  THEOREM.  There is a closed, connected, orientable smooth 3-manifold
-  M that carries a smooth Riemannian metric with NO conjugate points,
-  but that admits NO smooth Riemannian metric whose sectional
-  curvature is everywhere <= 0.
-
-Where the words come from.  On a flat plane, two geodesics starting
-parallel stay parallel forever.  On a sphere, two geodesics starting
-parallel in the northern hemisphere converge and meet at the south
-pole; that meeting is called a CONJUGATE POINT.  On a saddle surface
-(sec <= 0), parallel geodesics always drift apart and never meet.  A
-classical fact:
-
-    sec <= 0 everywhere   ==>   no conjugate points.
-
-The converse, for a SINGLE metric, is false: Gulliver (1975) deformed
-negatively curved metrics to create tiny regions of positive
-curvature while preserving absence of conjugate points.  But those
-examples always live on manifolds that ALREADY admit some negatively
-curved metric.  A sharper, deeper question remains:
-
-    If a closed manifold hosts SOME metric without conjugate points,
-    must it also host SOME (possibly different) metric with sec <= 0?
-
-The answer, in dimension 3, is NO.  This paper constructs an explicit
-counterexample M.
-
-Three details worth noticing.
-
-  (1) The obstruction is topological.  It comes from the fundamental
-      group pi_1(M).  If pi_1(M) admits no proper cocompact isometric
-      action on any CAT(0) space, then NO metric with sec <= 0 can
-      exist on M, whatever it might attempt to be.
-
-  (2) We do NOT merely exhibit a metric with some positive curvature.
-      That would be trivial: perturb anything a little and you get
-      some positive curvature.  We show that NO nonpositively curved
-      metric on M exists at all.
-
-  (3) The same M also rules out three weaker conditions:
-      (i)   no locally CAT(0) length metric inducing the topology;
-      (ii)  no Riemannian metric without focal points;
-      (iii) no Riemannian metric of nonpositive sectional curvature.
-      Fact (ii) uses a theorem of Ivanov and Kapovitch for closed
-      3-manifolds: a metric without focal points exists iff a metric
-      of nonpositive sectional curvature exists.
-
-
 ================================================================
 PART 1.  TERMINOLOGY
 ================================================================
@@ -193,15 +139,6 @@ HALF B (geometric).  A metric without conjugate points exists.
 Part 11 is an appendix: an explicit hyperbolic punctured torus, used
 as the "core" of each product piece in Part 6.
 
-READING GUIDE.
-  * Part 4 identifies the manifold.
-  * Part 5 is pure group theory, no differential geometry; skip it
-    if you only care about the metric construction.
-  * Parts 6-10 are the analytic heart of the paper.
-  * The final assembly of the theorem is the last proof of Part 10.
-
-
-================================================================
 PART 4.  THE MANIFOLD M
 ================================================================