diff --git a/kadison_kaplansky_projection_counter_v2.txt b/kadison_kaplansky_projection_counter_v2.txt
index 0a1c914..f37fecf 100644
--- a/kadison_kaplansky_projection_counter_v2.txt
+++ b/kadison_kaplansky_projection_counter_v2.txt
@@ -1442,9 +1442,9 @@ MASK DECAY.  Each f_{ik,nu,omega} is smooth with compact support
 and derivatives of size at most C_j w_i^{-j} in the L^1 norm.
 Consequently its Fourier coefficients decay:
 
-   |hat{f}(n)|  <=  C_j w_i (1 + |n| w_i)^(-j)  for every j >= 1,
+   |f(n)|  <=  C_j w_i (1 + |n| w_i)^(-j)  for every j >= 1,
 
-so summing over n gives sum |hat{f}(n)| <= C, and truncating at
+so summing over n gives sum |f(n)| <= C, and truncating at
 K_i = ceil(L / w_i) for a small fixed L adds error C_j (1+L)^(1-j).
 Replacing the mask by its truncated Fourier series costs a
 DETERMINED amount, uniformly in layer.
@@ -1605,7 +1605,7 @@ in the layers.
 
 MOMENTS.  Expand
 
-   E[ Tr( hat{X}_{ik}^{2 l} ) ]
+   E[ Tr( X_{ik}^{2 l} ) ]
 
 where l = ceil(C_2 H_i / log_2 d) is a FIXED even power.
 Summands whose walk uses a single undirected edge exactly once
@@ -1615,7 +1615,7 @@ counting lemma gives at most C_b^l Delta^l walks, with
 Delta <= 6D.  Because each factor is bounded by 2 C_epsilon and
 each compressed test matrix has at most 2^{C_1 H_i} dimensions,
 
-   E[Tr(hat{X}_{ik}^{2 l})]  <=  2^{C_1 H_i} (C_4 D)^l.
+   E[Tr(X_{ik}^{2 l})]  <=  2^{C_1 H_i} (C_4 D)^l.
 
 MARKOV AT THRESHOLD epsilon sqrt(d D_{ik}).  The finite test in
 8.4 contributes a fixed absolute error, which is smaller than