Update 37a.md

Author: paatai

constants/37a.md

@@ -58,21 +58,21 @@ $$
 
 - The best known **explicit** exponent separating sensitivity from degree is currently $\log_3 6$ (the “Kushilevitz barrier”). Improving this exponent is an open problem.  “Kushilevitz function” was introduced (unpublished by Kushilevitz) in **Footnote 1 of Nisan and Wigderson’s paper** [NW95].
 
-- (Kushilevitz base.) One explicit polynomial representing the base function 
+- (Kushilevitz function.) One explicit polynomial representing the Kushilevitz function 
 $$
 h:\{0,1\}^6\to\{0,1\}
 $$
 is
 $h(z_1,\dots,z_6)=\sum_{i=1}^6 z_i - \sum_{1\le i<j\le 6} z_i z_j + (z_1z_3z_4 + z_1z_2z_5 + z_1z_4z_5 + z_2z_3z_4 + z_2z_3z_5 + z_1z_2z_6 + z_1z_3z_6 + z_2z_4z_6 + z_3z_5z_6 + z_4z_5z_6),$
 
-  which is Boolean on $\{0,1\}^6$, has degree $3$, and is fully sensitive at $(0,0,0,0,0,0)$.
+  which is Boolean on {0,1}^6, has degree $3$, and max sensitivity $s(f)=6$ achieving at $x=(0,0,0,0,0,0)$.
 
 
--  Before Kushilevitz’s 6-variable base (giving exponent $\log_3 6$), a simpler 3-variable base already yields exponent $\log_2 3$ via self-composition. One concrete choice is the "not-all-equal" function on 3 bits,
+-  Before Kushilevitz’s 6-variable function (giving exponent $\log_3 6$), a simpler 3-variable function already yields exponent $\log_2 3$. One concrete choice is the "not-all-equal" function on 3 bits,
 
 $g(x_1,x_2,x_3)=x_1+x_2+x_3-x_1x_2-x_1x_3-x_2x_3,$
 
-   which is Boolean on the cube, has $\deg(g)=2$, and has full sensitivity $s(g)=3$ at $(0,0,0)$. Composing $g$ with itself $k$ times multiplies degree and (pointwise) sensitivity at $0$, yielding $s=3^k$, $\deg=2^k$.
+   which is Boolean on the cube, has $\deg(g)=2$, and $s(g)=3$ at $x=(0,0,0)$.
 
 - For background on the general relationship between sensitivity, block sensitivity, and degree (including Huang’s proof of the Sensitivity Conjecture), see [H2019] and the surveys [BdW2002], [HKP2011].