diff --git a/switch_chain_polynomial_mixing_v2.txt b/switch_chain_polynomial_mixing_v2.txt
index ba70a81..9339724 100644
--- a/switch_chain_polynomial_mixing_v2.txt
+++ b/switch_chain_polynomial_mixing_v2.txt
@@ -3,7 +3,6 @@
                  for every graphical degree sequence
 ==========================================================================
 
-An accessible exposition for a curious high school reader.
 September 2026.
 
 --------------------------------------------------------------------------
@@ -491,7 +490,7 @@ the pair (U_i, W_i), we claim
 Note that g_i is a function of row i only; "block sizes fixed" means
 |U_i| and |W_i| are constants, not random.
 
-Proof sketch for the curious.  The idea is to find a self-adjoint
+Proof sketch.  The idea is to find a self-adjoint
 operator J on functions of (U_1,U_2,U_3;W_1,W_2,W_3) whose kernel is
 the constants, and whose quadratic form is the sum of squared
 "differences" over all transpositions of labels.  Specifically,