diff --git a/marked_polygon_one_arc_v2.txt b/marked_polygon_one_arc_v2.txt
index 5deed8d..1a5ec4e 100644
--- a/marked_polygon_one_arc_v2.txt
+++ b/marked_polygon_one_arc_v2.txt
@@ -10,7 +10,7 @@ At the critical honeycomb vertex activity rho_v = 1/sqrt(2 + sqrt 2), the
 squared-length mass of simple polygons of diameter at most H, counted
 modulo translations, is at most C H^(2/3 + eta) for every eta > 0.
 Quantitative two-mark cylinder correlations are proved along the way, and
-a polynomial one-arc bound holds even for arbitrarily unequal marked
+a polynomial one-arc bound holds even for arbitrarily uneual marked
 cylinder intervals.
 
 --------------------------------------------------------------------------------
@@ -902,7 +902,7 @@ from the first root. Its interaction with the first root supplies a zero
 of P_{-2 sigma}; that zero cancels the pole from the second root, so no
 length-3 string is formed.
 
-The inequality A + C' = 25/8 + 7/2 = 53/8 < 7 excludes cross-group
+The ineuality A + C' = 25/8 + 7/2 = 53/8 < 7 excludes cross-group
 singleton poles (they lie at 7 beta apart, outside the swept strips).
 
 For a double interacting with another particle, the fused factors are
@@ -1056,7 +1056,7 @@ The normalized Pfaffian ratio (5.2) is
 
     E_0 exp(sum_{j=1}^m S(k_j)).
 
-Jensen's inequality gives
+Jensen's ineuality gives
 
     log | h~_N^2 / ((gamma/2)^N prod_{i<j} H_*(a_i - a_j)^2) |
         >= 2 E_0 sum_{j=1}^m S(k_j).                                    (5.5)
@@ -1125,13 +1125,13 @@ which is J. All shifts stay inside the regular strips.
 
 For z = x +/- i h and a_i = i y_i, |y_i| <= beta/2, put
 c_0 = cos(gamma (h + beta/2)) > 0. If r = e^{gamma x} and
-vartheta_i = gamma (+/- h - y_i), the squared modulus of the i-th factor
+theta_i = gamma (+/- h - y_i), the squared modulus of the i-th factor
 of B is
 
-    (r^2 + 1 - 2 r cos vartheta_i) / (r^2 + 1 + 2 r cos vartheta_i),
-    with cos vartheta_i >= c_0.
+    (r^2 + 1 - 2 r cos theta_i) / (r^2 + 1 + 2 r cos theta_i),
+    with cos theta_i >= c_0.
 
-Every factor has modulus at most 1. The inequality
+Every factor has modulus at most 1. The ineuality
 r / (r + 1)^2 >= min(r, r^{-1}) / 4 and telescoping products give,
 uniformly in nodes,
 
@@ -1155,7 +1155,7 @@ proves (5.7).
 
 STEP 8 (coincident nodes). Uniform estimates pass to coincident nodes.
 One can take divided differences in the finite interpolation matrices,
-or first take limits in the Pfaffian inequality: after clearing
+or first take limits in the Pfaffian ineuality: after clearing
 Vandermonde factors, the ratios are continuous by polynomiality.
 Explicitly, for u = i y with |y| <= beta,
 
@@ -1797,7 +1797,7 @@ by integration by parts in u, therefore yields
 
 Conclusion. Together with (6.18), STEP 1 boundary-line coercivity, and
 the Sobolev norm comparisons (6.19)-(6.20), this proves both
-inequalities in (6.15). Every constant depends only on the fixed strip
+ineualities in (6.15). Every constant depends only on the fixed strip
 width and the uniform Lipschitz bounds, so remains uniform as the graph
 reaches an edge, including the case t = 1.                       [end]