diff --git a/signed_cylinder_marked_polygons_v2.txt b/signed_cylinder_marked_polygons_v2.txt
index 1960b3c..823284c 100644
--- a/signed_cylinder_marked_polygons_v2.txt
+++ b/signed_cylinder_marked_polygons_v2.txt
@@ -145,7 +145,7 @@ Moreover,
 
     S(H) <= H^{2/3+o(1)}.
 
-Theorem (unequal marked intervals). On a physical tilted cylinder whose
+Theorem (uneual marked intervals). On a physical tilted cylinder whose
 unmarked lists have m+1 and n+1 sites, with n >= m and M = m+n+2 even, with
 unmarked logarithmic heights -f and 1-f where 0 <= f <= 0.6, and with site
 counts differing from m(1-f), mf and n(1-f), nf by at most a fixed constant,
@@ -620,7 +620,7 @@ derivative
 
 satisfies G < -b + 2/k for 0 < ell <= 1 and G >= -b with |G|/k bounded by
 2 beta^2 (ell^{-2} + ell^{-1}) for ell >= 1. Comparing G with D_0 gives the
-two stochastic inequalities on bounded intervals and tails.
+two stochastic ineualities on bounded intervals and tails.
 
 Evaluate the pure statistic on the Meixner--Pollaczek law. Normalize
 |Gamma(ell + i u)|^2 du to a probability on R; its Fourier transform is
@@ -664,7 +664,7 @@ Deficit and lower exponent. Define the positive deficit
             = M^{-1/4 + o(1)}.
 
 The coarse bound c_alpha sum_{d > 0} H(d) <= 1 from the convex balance, the
-inequality H_M(d) <= H(d), and delta_M -> 0 give saturation sum_{d > 0} H(d) =
+ineuality H_M(d) <= H(d), and delta_M -> 0 give saturation sum_{d > 0} H(d) =
 1/c_alpha. With A(n) = sum_{d >= n} H(d), this yields A(M) <= delta_M. Every
 arch contained within distance strictly less than M/2 of its source is
 disjoint from its nontrivial translates by M, so arches counted in the deficit
@@ -759,7 +759,7 @@ Proof. The common chords, confined to K and ending on a shared true boundary
 port, have the same intrinsic turning phase in both balances and cancel. The
 two remaining complex sums are equal. Every real coefficient in either convex
 domain lies between sin(alpha) and 1. Taking real parts proves both
-inequalities. The case with D_0 the saturated half-plane and K a finite convex
+ineualities. The case with D_0 the saturated half-plane and K a finite convex
 cap follows by the same convex exhaustion used in the wedge argument. QED
 
 Visit identity. Let D be a finite convex tessellation polygon and v a
@@ -900,7 +900,7 @@ expression. Its limit as the horizontal period tends to infinity recovers
 F. Concretely, write w_j for the logarithmic site coordinates and let P be
 the period; the periodic contraction kernel is the sum over horizontal
 images of a fixed odd kernel, and the Pfaffian of the resulting matrix
-equals the finite spin sum term by term. Two inequalities control the
+equals the finite spin sum term by term. Two ineualities control the
 passage to the limit: the contraction kernel decays exponentially in the
 imaginary direction, and the diagonal of the Pfaffian matrix is bounded by a
 constant multiple of the off-diagonal mass. The limit is therefore uniform
@@ -1439,7 +1439,7 @@ exponential of a fixed kernel; M and F_pair have site multiplier exactly 1.
 
 The horizontal gas.
 
-Constant modes. Write theta = vartheta + i tau, X = Y + i Z, and
+Constant modes. Write theta = theta + i tau, X = Y + i Z, and
 alpha_p = a_p + i tau 1 with a_p real. Each heat summand of the completed
 contour current has modulus
 
@@ -1453,8 +1453,8 @@ common Gaussian has covariance pi P_+/(4T) with P_+ the projector onto
 (1,1)^t, and the real completion, including e^{-pi Y^t S Y/T}, gives
 
     (sqrt(8/9) / sqrt(2T)) sum_{k_0 in Z}
-      e^{-T beta_vartheta^t L beta_vartheta/(4 pi) - beta_vartheta^t L Y},
-    beta_vartheta = (vartheta + pi k_0) 1.
+      e^{-T beta_theta^t L beta_theta/(4 pi) - beta_theta^t L Y},
+    beta_theta = (theta + pi k_0) 1.
 
 Here L is the fixed real symmetric two-by-two symbol of the common channel:
 L kills the difference vector (1,-1) and is positive on the diagonal, so the
@@ -1678,7 +1678,7 @@ cancelling its short measure forces equal P and M coefficients and a zero F
 coefficient, and the remaining outer measure then forces both coefficients to
 vanish.
 
-Coercivity inequality. Let u = e^{-k/2} and set
+Coercivity ineuality. Let u = e^{-k/2} and set
 
     x = X^t M_0^{-1} X,   y = X^t M_0^{-1} V,   v = V^t M_0^{-1} V.
 
@@ -1717,11 +1717,11 @@ with coefficients in ascending order
 
 All coefficients of N_+, D_+, N_-, D_- are positive for z >= 0, so the
 right side is finite and positive, which prevents w_sigma from vanishing. In
-the plus channel M_0 - h_+ X X^t > 0, so w_+ > 0 and the displayed inequality
+the plus channel M_0 - h_+ X X^t > 0, so w_+ > 0 and the displayed ineuality
 is 1 - lambda w_+ > 0; both negative rank-one updates then preserve
 positivity. In the minus channel the first update has exactly one negative
 direction, and since w_- -> -3 as u -> 0 it is negative throughout, so the
-inequality gives 1 + lambda w_- < 0. The determinant lemma makes the
+ineuality gives 1 + lambda w_- < 0. The determinant lemma makes the
 determinant positive after adding lambda V V^t, and a positive rank-one
 update cannot add negative directions, so it removes the unique negative
 direction. Hence A_sigma > 0 for every k > 0.
@@ -1838,7 +1838,7 @@ with c_2, C_2 depending only on d and Theta. The local constants have
 logarithmic cost O_d(N), and the Berry factors carrying real state charges
 are phases whose theta-dependent parts cost O_Theta(N). For the
 pre-collision product the same identity holds with the real angle
-vartheta = Re theta; the symmetrised local constants are finite for fixed
+theta = Re theta; the symmetrised local constants are finite for fixed
 d < 0 and cost O_d(N), and the same bound holds with
 -log W^{pre}_{d, Re theta} on the left.
 
@@ -1852,7 +1852,7 @@ same unit box. Each jump of p_c has magnitude at most sqrt 2. For x in box j
 write p_c(x) - (g_T * p_c)(x) by integrating its increments against the
 Gaussian; a jump in a box r boxes away is multiplied by a Gaussian tail
 bounded by C e^{-c (r-2)_+^2}, and the resulting sequence of bounds is
-summable uniformly after periodisation. Discrete Young's inequality therefore
+summable uniformly after periodisation. Discrete Young's ineuality therefore
 gives
 
     ||p_c - g_T * p_c||_2^2 <= C_1 sum_j n_j^2.
@@ -1879,7 +1879,7 @@ state path p with jumps -q_i and closure in Z^2/8Z(1,-1), satisfies
 in the post-collision case, with n_j the number of physical particles in
 [j, j+1) and p_{c,j} = (p_1(j+) + p_2(j+))/sqrt 2. The same bound holds for
 W^{pre}_{d, Re theta}(Y,p) in the pre-collision case. Zero weights already
-satisfy the inequality.
+satisfy the ineuality.
 
 Summability. For a fixed common integer p_1 + p_2 there are eight classes in
 Z^2/8Z(1,-1), and the Gaussian bound on the common charge sums over that
@@ -1914,7 +1914,7 @@ modified cost. Let Phi(S) be the infimum of modified costs of paths from a
 reference state to S. Every state can be reached and returned from: insert P
 and M charges as needed at distinct positions, then insert the required final
 block. A fixed return path bounds the infimum below by the negative of its
-cost, so the infimum is finite, and the directed triangle inequality gives the
+cost, so the infimum is finite, and the directed triangle ineuality gives the
 displayed bound. For measurability, restrict the intermediate positions in
 the infimum to rational translated coordinates and use continuity on the open
 simplices; the terminal state stays arbitrary and fixed. The discrete