diff f6bf760..6fbd3ac o3_model_massive_continuum_v2.txt
diff --git a/o3_model_massive_continuum_v2.txt b/o3_model_massive_continuum_v2.txt
index 62ce8e4..e1249be 100644
--- a/o3_model_massive_continuum_v2.txt
+++ b/o3_model_massive_continuum_v2.txt
@@ -374,7 +374,7 @@ bounded multiple of log H at the point of use.
Any lemma statement below says only "there exist constants such
that", and the reader can infer its dependence by matching the
statement's variables to the stages above. Where a specific
-constant is required in an inequality (for example "take
+constant is required in an ineuality (for example "take
H >= H_0(L, kappa, upsilon)"), the dependence is stated
explicitly.
@@ -591,7 +591,7 @@ derivative formula (1.12),
= sum_e w_e ( a^T E_e a ) ( sg(y) - sg(x) )^2
<= (1/2) b sum_e ( sg(y) - sg(x) )^2. (1.18)
-The first inequality uses Var nonnegative; the second uses
+The first ineuality uses Var nonnegative; the second uses
|a^T E_e a| <= 1 and w_e <= b (half weights and full weights are
both bounded by b). Integrating Phi'' over s in [0,1] and using
Phi'(0) = 0 (by O(3) invariance) and Phi(0) = 0 (no rotation),
@@ -1083,7 +1083,7 @@ lambda -> f_lambda in Lambda_0, uniformly in omega.
Step 6 (uniform over the compact family). Step 5 gives a Gaussian
tail with variance C b^{-D} at any fixed lambda. To lift this to a
-uniform statement over lambda, use Morrey's inequality with mesh
+uniform statement over lambda, use Morrey's ineuality with mesh
size b^{-6}: for any f in a compact family of C^2 functions with
bounded parameter derivatives, the sup over lambda in Lambda_0 is
controlled, up to a constant, by O(b^{6 d_0}) mesh points, with
@@ -1141,10 +1141,10 @@ Define the covering homomorphism rho : S^3 -> SO(3) (the standard
2-to-1 cover, rho(g) q = g q g^{-1} in the quaternion representation
of R^3). On a coarse edge X -> Y let
- Phi_{X,Y}( g; t ) = g_X exp( vartheta(t) ell_0( g_X^{-1} g_Y ) ), (1.53)
+ Phi_{X,Y}( g; t ) = g_X exp( theta(t) ell_0( g_X^{-1} g_Y ) ), (1.53)
-with vartheta : [0,1] -> R fixed, smooth, vartheta = 0 near t=0 and
-vartheta = 1 near t=1, and ell_0 : S^3 -> R^3 a measurable logarithm
+with theta : [0,1] -> R fixed, smooth, theta = 0 near t=0 and
+theta = 1 near t=1, and ell_0 : S^3 -> R^3 a measurable logarithm
with ||ell_0(g)|| <= pi and exp( ell_0(g) ) = g_X^{-1} g_Y. Then
rho( Phi( g; 0 ) ) = rho(g_X) and rho( Phi( g; 1 ) ) = rho(g_Y),
so the interpolated action along the coarse edge equals
@@ -1164,8 +1164,8 @@ model on widetilde(q). The g's simply parametrize different
HAAR INVARIANCE UNDER LEFT MULTIPLICATION. If k in S^3 is fixed and
g -> kg elementwise, then
- Phi_{X,Y}( kg; t ) = (kg_X) exp( vartheta(t) ell_0( g_X^{-1} k^{-1} k g_Y ) )
- = k g_X exp( vartheta(t) ell_0( g_X^{-1} g_Y ) )
+ Phi_{X,Y}( kg; t ) = (kg_X) exp( theta(t) ell_0( g_X^{-1} k^{-1} k g_Y ) )
+ = k g_X exp( theta(t) ell_0( g_X^{-1} g_Y ) )
= k Phi_{X,Y}( g; t ).
Hence the unnormalised density of the coarse configuration is
@@ -2241,7 +2241,7 @@ The union of edit label discrepancies contributes
The union of gas labels contributes
prod_{unedited} p_mu.
-(e) Sum over edit trees via the tree-graph inequality of Penrose type
+(e) Sum over edit trees via the tree-graph ineuality of Penrose type
[FernandezProcacci]. The one-child sum is bounded by the covering
cap:
@@ -2425,7 +2425,7 @@ Step 2 (High and low sets). Define
Both are open subsets of [.6 H_N, 1.4 H_N] because each b_j(beta)
is continuous in beta and admission is defined by strict
-inequalities.
+ineualities.
Nonemptiness. Take beta = 1.4 H_N. By (5.8) with j = N, k = 0:
@@ -3593,7 +3593,7 @@ window with |s' - s| small,
The two-point function C_beta(x) is Lipschitz in beta on
[H/2, 2H], with Lipschitz constant L_lip bounded uniformly in N
-and x by Griffiths-type inequalities. Therefore
+and x by Griffiths-type ineualities. Therefore
| C_N^{(s)}(x) - C_N^{(s')}(x) |
<= L_lip |s' - s| (1 + o_H(1)),