diff --git a/critical_ising_stopping_band_v2.txt b/critical_ising_stopping_band_v2.txt
index 1ba88ea..d8e5678 100644
--- a/critical_ising_stopping_band_v2.txt
+++ b/critical_ising_stopping_band_v2.txt
@@ -60,7 +60,7 @@ law mu (Edwards-Sokal). Consequences we use repeatedly:
       (because two independent replicas "-" and "+" have a common open
       path exactly when phi connects them; this is the Edwards-Sokal
       identity used in PART 2).
-  (b) FK enjoys the FKG / positive association inequalities and the
+  (b) FK enjoys the FKG / positive association ineualities and the
       domain Markov property; increasing edge sets and increasing
       boundary wiring raise connection probabilities. These are the
       Fortuin-Kasteleyn-Ginibre and Holley facts.
@@ -137,7 +137,7 @@ Add ad >= bc and eh >= fg to both sides:
    (a+e)(d+h) = ad + ah + ed + eh
              >= bc + bg + cf + fg = (b+f)(c+g).
 
-The left side is (slice_one summed)(slice_two summed); the inequality is
+The left side is (slice_one summed)(slice_two summed); the ineuality is
 exactly log-supermodularity of the summed pair. So the two-block marginal
 is log-supermodular. For more coordinates, eliminate one binary coordinate
 at a time (a nonnegative adjacent-coordinate square difference is
@@ -204,7 +204,7 @@ two-spin law with interaction K, the means vanish and the covariance is
 
    <sigma_I sigma_J>_0 = tanh K.
 
-Step 3: the Ding-Song-Sun covariance inequality. Corollary 1.3 of
+Step 3: the Ding-Song-Sun covariance ineuality. Corollary 1.3 of
 [Ding-Song-Sun 2023] (our brick C2) says that for ANY finite ferromagnetic
 Ising graph with ARBITRARY real (possibly mixed-sign) fields and two
 disjoint vertex sets I,J, the two-point covariance obeys
@@ -226,7 +226,7 @@ That ratio has mean one under the denominator law p(.|b'); a random
 variable with mean one and log-oscillation <= L is trapped in
 [e^{-L}, e^{L}] (its minimum is <= 1 <= its maximum). Exponentiating with
 L <= 4 arctanh q0 gives the displayed bounds. Averaging a pointwise
-inequality preserves it, giving the mixture statement. []
+ineuality preserves it, giving the mixture statement. []
 
 2.4 Remark fd:symmetric-terminals. The extreme rectangle L and q0 are
 symmetric under swapping I and J: the two contracted vertices are
@@ -440,7 +440,7 @@ q = |z-z'| / |z - conj(z')| in (0,1). The plus one- and two-spin formulae
    <sigma_z sigma_z'>_+ / (<sigma_z>_+ <sigma_z'>_+)
       = ( (q^{1/2} + q^{-1/2})/2 )^{1/2} > 1.
 
-Conformal covariance transfers this strict inequality to a rectangle.
+Conformal covariance transfers this strict ineuality to a rectangle.
 Continuity and compactness give a positive MINIMUM of the connected
 function on separated compact bulk sets. Uniform bulk convergence turns
 this into a discrete lower bound for large r; finite energy absorbs the
@@ -554,7 +554,7 @@ z in S in that square. The piece lies in z + B_{c s/8}, and
 z + B_{c s/2} lies in the assumed free neighbourhood (z is in S). Compare
 just this local marginal to the plus law in z + B_{c s/2}; the counting
 hypotheses persist with constants depending only on A, c. Apply the bound
-of Steps 1-2 to each piece and use the triangle inequality in L^{2p}.
+of Steps 1-2 to each piece and use the triangle ineuality in L^{2p}.
 Lattice rounding at bounded c s is absorbed in the constants. The same
 construction works in periodic charts. []
 
@@ -830,7 +830,7 @@ Cauchy-Schwarz, and the fourth line moments of Lemma 4.3,
    E X^2 <= E[ (sum_{L_1} Y_x)^2 (sum_{L_2} Y_y)^2 ] <= C_1 w^{7/2}.
 
 (The Y-moments follow from either replica's moments by the triangle
-inequality in L^4.) Paley-Zygmund gives c_2, p_2 > 0 with
+ineuality in L^4.) Paley-Zygmund gives c_2, p_2 > 0 with
 P(X >= c_2 w^{7/4}) >= p_2.
 
 Let L be the largest number of sites of L_2 lying in one auxiliary
@@ -943,7 +943,7 @@ order-positive centered density q = q(sigma_S) of its source marginal,
 The constants do not depend on the mass of the positive part of q.
 
 Proof. For an ordered random pair of sources, apply (5.3) to each pair and
-integrate; magnetic differences are nonnegative, so the triangle inequality
+integrate; magnetic differences are nonnegative, so the triangle ineuality
 bounds the integral of the target difference by the integral of its
 absolute value. For the signed form, put m = E_mu q_+ = E_mu q_- (equal by
 E q = 0); if m = 0 there is nothing to prove. Otherwise
@@ -951,7 +951,7 @@ mu_+- = m^{-1} q_+- mu_S are probability laws and order positivity says
 mu_+(F) >= mu_-(F) for every increasing F, so they admit a coupling
 (s_+, s_-) with s_+ >= s_-. (Finite transport: send mass mu_-(x) from each
 lower configuration to upper ones with capacities mu_+(y); the needed
-cut inequality mu_-(B) <= mu_-(up(B)) <= mu_+(up(B)) is exactly what order
+cut ineuality mu_-(B) <= mu_-(up(B)) <= mu_+(up(B)) is exactly what order
 positivity provides.) Apply the random-source assertion to this coupling
 and multiply by m; the Gibbs continuation turns the difference of source
 integrals into E_mu[q h] and E_mu[q M_J]. []
@@ -1021,7 +1021,7 @@ depending on W/s.
 Proof. The buffered comparison (Corollary 3.4) applied to the
 NONNEGATIVE SQUARE of a line difference reduces each buffered chart to the
 whole-plane law at the cost of a fixed factor; a finite chart decomposition
-and the triangle inequality in L^2 then suffice.
+and the triangle ineuality in L^2 then suffice.
 
 In the whole-plane law the mean is zero, and by Lemma 4.1(3) normalized
 two-point sums on rescaled segments converge to the corresponding integrals
@@ -1062,7 +1062,7 @@ Unmatched ends. An unmatched end of length O(h) has second moment
 O(h^{7/4}) by the same kernel integral (integral over r in [0,h] of
 r * r^{-1/4} dr = O(h^{7/4})), hence contributes O(h^{7/8}) in norm. There
 are only boundedly many such pieces, and h^{7/8} <= h^{3/8} for h <= 1, so
-the triangle inequality gives (6.1).
+the triangle ineuality gives (6.1).
 
 Concentric squares and periodic rows. For concentric squares, trim
 corresponding sides to equal lengths, translate the matching portions in
@@ -2189,7 +2189,7 @@ separate lookup values a_i^b(delta) = E_{Q_{i,delta}^b} h_delta.
 
 Proof. The conditional target law of a stopping transcript is its Gibbs
 continuation (Lemma 8.5). On a good bin its total variation distance from
-the single law Q_{i,delta} is at most eta; the defining inequality for total
+the single law Q_{i,delta} is at most eta; the defining ineuality for total
 variation gives (10.1). On the exceptional bin both quantities are bounded by
 H in absolute value; squaring and integrating gives (10.2). All
 constructions in Theorem 10.1 preceded the choice of h_delta. The pointwise
@@ -2274,7 +2274,7 @@ laws. The bound is symmetric in the two terminal sets.
 
 Proof. This is exactly Lemma 2.3, whose full proof is in PART 2. Its inputs
 are Lemma 2.2 (extreme rectangles, L <= 4 arctanh q0) and, for the final
-inequality, the Ding-Song-Sun covariance inequality (brick C2) and the
+ineuality, the Ding-Song-Sun covariance ineuality (brick C2) and the
 Edwards-Sokal identity. []
 
 Theorem in:resolution (finite conditional resolution; = Theorem 10.1 with
@@ -2327,7 +2327,7 @@ Why the intermediate results fit together.
 
 Assumptions and imported bricks. The only unproved inputs are:
  (C1) Critical FK-Ising RSW / one-arm bounds [Duminil-Copin, Hongler, Nolin].
- (C2) The Ding-Song-Sun Ising correlation inequality with arbitrary fields.
+ (C2) The Ding-Song-Sun Ising correlation ineuality with arbitrary fields.
  (C3) Chelkak-Hongler-Izyurov bulk one- and two-spin limits.
  (C4) Benoist-Hongler convergence of Ising interfaces to nested CLE_3, with
       simultaneous common-edge approximation.
@@ -2344,7 +2344,7 @@ for the two-dimensional FK Ising model. Comm. Pure Appl. Math. 64 (2011),
 1165-1198. arXiv:0912.4253 (crossings, one-arm locators: Theorem 1 of v1;
 spatial mixing: Sec. 5.3, Prop. 5.11 of the author-hosted version).
 
-Ding, Song, Sun. Correlation inequalities for Ising models with arbitrary
+Ding, Song, Sun. Correlation ineualities for Ising models with arbitrary
 external fields. 2023. Corollary 1.3.
 
 Chelkak, Hongler, Izyurov. Conformal invariance of spin correlations in the
@@ -2361,7 +2361,7 @@ Edwards, Sokal. Generalization of the Fortuin-Kasteleyn-Swendsen-Wang
 representation and Monte Carlo algorithm. Phys. Rev. D 38 (1988), 2009.
 
 Karlin, Rinott. Classes of orderings of measures and related correlation
-inequalities. I. Multivariate totally positive distributions. J. Multivar.
+ineualities. I. Multivariate totally positive distributions. J. Multivar.
 Anal. 10 (1980), 467-498.
 
 Schaefer. Crosscuts and iterated function systems in Cantor sets. 2021.