diff --git a/o3_model_massive_continuum_v2.txt b/o3_model_massive_continuum_v2.txt
index 342cb91..f3104a5 100644
--- a/o3_model_massive_continuum_v2.txt
+++ b/o3_model_massive_continuum_v2.txt
@@ -1485,7 +1485,7 @@ The retained mean vector at Y is
 
 The retained spin V_Y is m_Y / |m_Y| (normalized-mean branch),
 provided |m_Y| >= 1/2. If |m_Y| < 1/2 (fallback branch), one uses a
-measurable selection \hat m_Y with |\hat m_Y| = 1; the choice does
+measurable selection m_Y^hat with |m_Y^hat| = 1; the choice does
 not affect any estimate.
 
 The chord process. For a bond e = {x, y}, set r_e = |q_x - q_y| in
@@ -1500,14 +1500,14 @@ LEMMA 2.2 (Mean error). Uniformly in the cell Y (ordinary or
 inclined), the pin configuration, the strengths beta_e in [0, b],
 and the spin configuration q,
 
-  | m_Y - \hat m_Y | <= (C/L) sum_{e in B_Y} r_e,          (2.6)
-  | m_Y - \hat m_Y | <= (C/L_*) sum_{e in B_Y^{O+}} r_e,   (2.7)
+  | m_Y - m_Y^hat | <= (C/L) sum_{e in B_Y} r_e,          (2.6)
+  | m_Y - m_Y^hat | <= (C/L_*) sum_{e in B_Y^{O+}} r_e,   (2.7)
 
 with an absolute constant C > 0. If every nearest-neighbour chord
 in the cell satisfies r_e <= T for some T with C L_*^2 T^2 <= 3/4,
 then the fallback branch is not taken and
 
-  | m_Y - \hat m_Y | <= 1 - |m_Y|^2 <= C_L T^2.            (2.8)
+  | m_Y - m_Y^hat | <= 1 - |m_Y|^2 <= C_L T^2.            (2.8)
 
 Proof. For (2.6): join any pair x, y in the cell by a coordinate-
 aligned lattice path inside the cell (length O(L) ordinary, O(L_*)
@@ -1524,7 +1524,7 @@ Combining with (2.5) gives
 
   1 - |m_Y|^2 <= (C/L) sum_{e in B_Y} r_e.                (2.9)
 
-On the normalized-mean branch, |m_Y - \hat m_Y| = 1 - |m_Y| <=
+On the normalized-mean branch, |m_Y - m_Y^hat| = 1 - |m_Y| <=
 1 - |m_Y|^2, giving (2.6). On the fallback branch |m_Y| < 1/2,
 every projection of m_Y onto S^2 satisfies |m_Y - q_x| <= 1 + |m_Y|
 <= 2(1 - |m_Y|^2), giving (2.6) again after possibly enlarging C.
@@ -1536,14 +1536,14 @@ For (2.8): if r_e <= T everywhere, then by (2.5),
               <= C L_*^2 T^2.
 
 Choosing T with C L_*^2 T^2 <= 3/4 yields |m_Y| >= 1/2 so the
-fallback branch is not taken, and |m_Y - \hat m_Y| = 1 - |m_Y| <=
+fallback branch is not taken, and |m_Y - m_Y^hat| = 1 - |m_Y| <=
 1 - |m_Y|^2 <= C_L T^2.  []
 
 COROLLARY 2.3 (Small-chord mean). At the terminal scale of a layer
 j, with r_e <= T_j = H_j^{-1/2} p_j throughout the cell, the mean
 error obeys
 
-  | m_Y - \hat m_Y | <= C_L T_j^2                       (2.10)
+  | m_Y - m_Y^hat | <= C_L T_j^2                       (2.10)
 
 uniformly in Y and in the layer j.
 
@@ -1769,7 +1769,7 @@ The exact block weight for the small-angle sector is the exponential
 of (3.7) plus a smooth remainder R(xi) = O(xi^4) and higher orders.
 
 Gaussian completion. Introduce a single ambient Gaussian Z ~
-N(0, C_s \otimes Id_{R^3}) with C_s = (1/2)(Pi_0 + Pi_0^*) the
+N(0, C_s tensor Id_{R^3}) with C_s = (1/2)(Pi_0 + Pi_0^*) the
 free covariance matrix of Lemma 2.4, and substitute xi = mu + g Z
 with g = b^{-1/2}, mu the conditional mean. Expanding the
 quadratic in Z and using C_s^{-1} - A = (AC_s - Id)C_s A + ...,
@@ -2990,7 +2990,7 @@ stated bound (8.1) with C := max(B_N, 1) absorbed.  []
 
 COROLLARY 8.1.5 (Uniform factorial tails). For every fixed m,
 
-  sup_{N} E | phi_N(f) |^m <= C (2m - 1)!! ||f||_{\infty}^m.   (8.2a)
+  sup_{N} E | phi_N(f) |^m <= C (2m - 1)!! ||f||_{infinity}^m.   (8.2a)
 
 This is what makes the moment sequences (as N -> infinity) Cauchy
 in each fixed finite-order moment.